id	sid	tid	token	lemma	pos
ejpam-4923	1	1	european	european	PROPN
ejpam-4923	1	2	journal	journal	PROPN
ejpam-4923	1	3	of	of	ADP
ejpam-4923	1	4	pure	pure	ADJ
ejpam-4923	1	5	and	and	CCONJ
ejpam-4923	1	6	applied	apply	VERB
ejpam-4923	1	7	mathematics	mathematic	NOUN
ejpam-4923	1	8	vol	vol	NOUN
ejpam-4923	1	9	.	.	PUNCT
ejpam-4923	2	1	16	16	NUM
ejpam-4923	2	2	,	,	PUNCT
ejpam-4923	2	3	no	no	INTJ
ejpam-4923	2	4	.	.	NOUN
ejpam-4923	2	5	4	4	NUM
ejpam-4923	2	6	,	,	PUNCT
ejpam-4923	2	7	2023	2023	NUM
ejpam-4923	2	8	,	,	PUNCT
ejpam-4923	2	9	2348	2348	NUM
ejpam-4923	2	10	-	-	SYM
ejpam-4923	2	11	2367	2367	NUM
ejpam-4923	2	12	issn	issn	PROPN
ejpam-4923	2	13	1307	1307	NUM
ejpam-4923	2	14	-	-	SYM
ejpam-4923	2	15	5543	5543	NUM
ejpam-4923	2	16	–	–	PUNCT
ejpam-4923	3	1	ejpam.com	ejpam.com	X
ejpam-4923	3	2	published	publish	VERB
ejpam-4923	3	3	by	by	ADP
ejpam-4923	3	4	new	new	PROPN
ejpam-4923	3	5	york	york	PROPN
ejpam-4923	3	6	business	business	PROPN
ejpam-4923	3	7	global	global	PROPN
ejpam-4923	3	8	the	the	DET
ejpam-4923	3	9	sl2(r	sl2(r	PROPN
ejpam-4923	3	10	)	)	PUNCT
ejpam-4923	3	11	group	group	NOUN
ejpam-4923	3	12	representations	representation	NOUN
ejpam-4923	3	13	on	on	ADP
ejpam-4923	3	14	spaces	space	NOUN
ejpam-4923	3	15	of	of	ADP
ejpam-4923	3	16	holomorphic	holomorphic	ADJ
ejpam-4923	3	17	functions	function	NOUN
ejpam-4923	3	18	on	on	ADP
ejpam-4923	3	19	the	the	DET
ejpam-4923	3	20	unit	unit	NOUN
ejpam-4923	3	21	disc	disc	PROPN
ejpam-4923	3	22	amjad	amjad	PROPN
ejpam-4923	3	23	saleh	saleh	PROPN
ejpam-4923	3	24	alghamdi	alghamdi	PROPN
ejpam-4923	3	25	department	department	PROPN
ejpam-4923	3	26	of	of	ADP
ejpam-4923	3	27	mathematics	mathematic	NOUN
ejpam-4923	3	28	,	,	PUNCT
ejpam-4923	3	29	jamoum	jamoum	PROPN
ejpam-4923	3	30	university	university	PROPN
ejpam-4923	3	31	collage	collage	NOUN
ejpam-4923	3	32	,	,	PUNCT
ejpam-4923	3	33	umm	umm	INTJ
ejpam-4923	3	34	al	al	PROPN
ejpam-4923	3	35	-	-	PUNCT
ejpam-4923	3	36	qura	qura	PROPN
ejpam-4923	3	37	university	university	NOUN
ejpam-4923	3	38	,	,	PUNCT
ejpam-4923	3	39	saudi	saudi	PROPN
ejpam-4923	3	40	arabia	arabia	PROPN
ejpam-4923	3	41	abstract	abstract	NOUN
ejpam-4923	3	42	.	.	PUNCT
ejpam-4923	4	1	we	we	PRON
ejpam-4923	4	2	can	can	AUX
ejpam-4923	4	3	realise	realise	VERB
ejpam-4923	4	4	the	the	DET
ejpam-4923	4	5	representations	representation	NOUN
ejpam-4923	4	6	of	of	ADP
ejpam-4923	4	7	the	the	DET
ejpam-4923	4	8	group	group	NOUN
ejpam-4923	4	9	sl2(r	sl2(r	PROPN
ejpam-4923	4	10	)	)	PUNCT
ejpam-4923	4	11	on	on	ADP
ejpam-4923	4	12	the	the	DET
ejpam-4923	4	13	unit	unit	NOUN
ejpam-4923	4	14	disc	disc	NOUN
ejpam-4923	4	15	.	.	PUNCT
ejpam-4923	5	1	this	this	PRON
ejpam-4923	5	2	is	be	AUX
ejpam-4923	5	3	due	due	ADJ
ejpam-4923	5	4	to	to	ADP
ejpam-4923	5	5	the	the	DET
ejpam-4923	5	6	isomorphism	isomorphism	NOUN
ejpam-4923	5	7	between	between	ADP
ejpam-4923	5	8	the	the	DET
ejpam-4923	5	9	group	group	NOUN
ejpam-4923	5	10	sl2(r	sl2(r	PROPN
ejpam-4923	5	11	)	)	PUNCT
ejpam-4923	5	12	and	and	CCONJ
ejpam-4923	5	13	the	the	DET
ejpam-4923	5	14	group	group	NOUN
ejpam-4923	5	15	su(1	su(1	NOUN
ejpam-4923	5	16	,	,	PUNCT
ejpam-4923	5	17	1	1	NUM
ejpam-4923	5	18	)	)	PUNCT
ejpam-4923	5	19	.	.	PUNCT
ejpam-4923	6	1	the	the	DET
ejpam-4923	6	2	discrete	discrete	ADJ
ejpam-4923	6	3	series	series	NOUN
ejpam-4923	6	4	representations	representation	NOUN
ejpam-4923	6	5	for	for	ADP
ejpam-4923	6	6	the	the	DET
ejpam-4923	6	7	group	group	NOUN
ejpam-4923	6	8	sl2(r	sl2(r	PROPN
ejpam-4923	6	9	)	)	PUNCT
ejpam-4923	6	10	given	give	VERB
ejpam-4923	6	11	by	by	ADP
ejpam-4923	6	12	πn(g)φ(z	πn(g)φ(z	PROPN
ejpam-4923	6	13	)	)	PUNCT
ejpam-4923	7	1	=	=	SYM
ejpam-4923	7	2	φ	φ	PROPN
ejpam-4923	7	3	(	(	PUNCT
ejpam-4923	7	4	dz	dz	PROPN
ejpam-4923	7	5	−	−	PROPN
ejpam-4923	7	6	b	b	PROPN
ejpam-4923	7	7	a−	a−	PROPN
ejpam-4923	7	8	cz	cz	NOUN
ejpam-4923	7	9	)	)	PUNCT
ejpam-4923	7	10	(	(	PUNCT
ejpam-4923	7	11	a−	a−	PROPN
ejpam-4923	7	12	cz)−n	cz)−n	PROPN
ejpam-4923	7	13	,	,	PUNCT
ejpam-4923	7	14	n	n	PROPN
ejpam-4923	7	15	∈	∈	PROPN
ejpam-4923	7	16	z.	z.	PROPN
ejpam-4923	7	17	(	(	PUNCT
ejpam-4923	7	18	1	1	X
ejpam-4923	7	19	)	)	PUNCT
ejpam-4923	7	20	are	be	AUX
ejpam-4923	7	21	on	on	ADP
ejpam-4923	7	22	the	the	DET
ejpam-4923	7	23	bergman	bergman	PROPN
ejpam-4923	7	24	space	space	NOUN
ejpam-4923	7	25	where	where	SCONJ
ejpam-4923	7	26	n	n	NUM
ejpam-4923	7	27	≥	≥	X
ejpam-4923	7	28	2	2	NUM
ejpam-4923	7	29	[	[	X
ejpam-4923	7	30	5	5	NUM
ejpam-4923	7	31	,	,	PUNCT
ejpam-4923	7	32	6	6	NUM
ejpam-4923	7	33	,	,	PUNCT
ejpam-4923	7	34	10	10	NUM
ejpam-4923	7	35	]	]	PUNCT
ejpam-4923	7	36	.	.	PUNCT
ejpam-4923	8	1	lang	lang	PROPN
ejpam-4923	9	1	[	[	X
ejpam-4923	9	2	13	13	NUM
ejpam-4923	9	3	,	,	PUNCT
ejpam-4923	9	4	ix	ix	PROPN
ejpam-4923	9	5	]	]	PUNCT
ejpam-4923	9	6	studied	study	VERB
ejpam-4923	9	7	the	the	DET
ejpam-4923	9	8	discrete	discrete	ADJ
ejpam-4923	9	9	series	series	NOUN
ejpam-4923	9	10	on	on	ADP
ejpam-4923	9	11	the	the	DET
ejpam-4923	9	12	group	group	NOUN
ejpam-4923	9	13	sl(r	sl(r	CCONJ
ejpam-4923	9	14	)	)	PUNCT
ejpam-4923	9	15	in	in	ADP
ejpam-4923	9	16	the	the	DET
ejpam-4923	9	17	upper	upper	ADJ
ejpam-4923	9	18	half	half	ADJ
ejpam-4923	9	19	-	-	PUNCT
ejpam-4923	9	20	plane	plane	NOUN
ejpam-4923	9	21	and	and	CCONJ
ejpam-4923	9	22	on	on	ADP
ejpam-4923	9	23	the	the	DET
ejpam-4923	9	24	unit	unit	NOUN
ejpam-4923	9	25	disc	disc	NOUN
ejpam-4923	9	26	.	.	PUNCT
ejpam-4923	10	1	for	for	ADP
ejpam-4923	10	2	n	n	NOUN
ejpam-4923	10	3	=	=	SYM
ejpam-4923	10	4	1	1	NUM
ejpam-4923	10	5	,	,	PUNCT
ejpam-4923	10	6	the	the	DET
ejpam-4923	10	7	sl2(r	sl2(r	PROPN
ejpam-4923	10	8	)	)	PUNCT
ejpam-4923	10	9	representation	representation	NOUN
ejpam-4923	10	10	is	be	AUX
ejpam-4923	10	11	called	call	VERB
ejpam-4923	10	12	the	the	DET
ejpam-4923	10	13	mock	mock	ADJ
ejpam-4923	10	14	discrete	discrete	ADJ
ejpam-4923	10	15	series	series	NOUN
ejpam-4923	10	16	.	.	PUNCT
ejpam-4923	11	1	the	the	DET
ejpam-4923	11	2	representation	representation	NOUN
ejpam-4923	11	3	space	space	NOUN
ejpam-4923	11	4	of	of	ADP
ejpam-4923	11	5	the	the	DET
ejpam-4923	11	6	mock	mock	ADJ
ejpam-4923	11	7	discrete	discrete	ADJ
ejpam-4923	11	8	series	series	NOUN
ejpam-4923	11	9	is	be	AUX
ejpam-4923	11	10	the	the	DET
ejpam-4923	11	11	hardy	hardy	ADJ
ejpam-4923	11	12	space	space	NOUN
ejpam-4923	11	13	[	[	X
ejpam-4923	11	14	5	5	NUM
ejpam-4923	11	15	,	,	PUNCT
ejpam-4923	11	16	6	6	NUM
ejpam-4923	11	17	,	,	PUNCT
ejpam-4923	11	18	10	10	NUM
ejpam-4923	11	19	]	]	PUNCT
ejpam-4923	11	20	.	.	PUNCT
ejpam-4923	12	1	in	in	ADP
ejpam-4923	12	2	this	this	DET
ejpam-4923	12	3	paper	paper	NOUN
ejpam-4923	12	4	we	we	PRON
ejpam-4923	12	5	describe	describe	VERB
ejpam-4923	12	6	the	the	DET
ejpam-4923	12	7	sl2(r	sl2(r	PROPN
ejpam-4923	12	8	)	)	PUNCT
ejpam-4923	12	9	representation	representation	NOUN
ejpam-4923	12	10	on	on	ADP
ejpam-4923	12	11	the	the	DET
ejpam-4923	12	12	dirichlet	dirichlet	PROPN
ejpam-4923	12	13	space	space	NOUN
ejpam-4923	12	14	.	.	PUNCT
ejpam-4923	13	1	2020	2020	NUM
ejpam-4923	13	2	mathematics	mathematic	NOUN
ejpam-4923	13	3	subject	subject	NOUN
ejpam-4923	13	4	classifications	classification	NOUN
ejpam-4923	13	5	:	:	PUNCT
ejpam-4923	13	6	32a10	32a10	NUM
ejpam-4923	13	7	,	,	PUNCT
ejpam-4923	13	8	31c25	31c25	NUM
ejpam-4923	13	9	key	key	ADJ
ejpam-4923	13	10	words	word	NOUN
ejpam-4923	13	11	and	and	CCONJ
ejpam-4923	13	12	phrases	phrase	NOUN
ejpam-4923	13	13	:	:	PUNCT
ejpam-4923	13	14	sl2(r	sl2(r	ADJ
ejpam-4923	13	15	)	)	PUNCT
ejpam-4923	13	16	group	group	NOUN
ejpam-4923	13	17	,	,	PUNCT
ejpam-4923	13	18	representations	representation	NOUN
ejpam-4923	13	19	,	,	PUNCT
ejpam-4923	13	20	dirichlet	dirichlet	PROPN
ejpam-4923	13	21	space	space	NOUN
ejpam-4923	13	22	,	,	PUNCT
ejpam-4923	13	23	su(1	su(1	NOUN
ejpam-4923	13	24	,	,	PUNCT
ejpam-4923	13	25	1	1	NUM
ejpam-4923	13	26	)	)	PUNCT
ejpam-4923	13	27	group	group	NOUN
ejpam-4923	13	28	1	1	NUM
ejpam-4923	13	29	.	.	PUNCT
ejpam-4923	13	30	introduction	introduction	NOUN
ejpam-4923	13	31	the	the	DET
ejpam-4923	13	32	lie	lie	NOUN
ejpam-4923	13	33	group	group	NOUN
ejpam-4923	13	34	sl2(r	sl2(r	PROPN
ejpam-4923	13	35	)	)	PUNCT
ejpam-4923	13	36	consists	consist	VERB
ejpam-4923	13	37	of	of	ADP
ejpam-4923	13	38	2	2	NUM
ejpam-4923	13	39	×	×	NOUN
ejpam-4923	13	40	2	2	NUM
ejpam-4923	13	41	matrices	matrix	NOUN
ejpam-4923	13	42	with	with	ADP
ejpam-4923	13	43	real	real	ADJ
ejpam-4923	13	44	entries	entry	NOUN
ejpam-4923	13	45	and	and	CCONJ
ejpam-4923	13	46	a	a	DET
ejpam-4923	13	47	determinant	determinant	ADJ
ejpam-4923	13	48	equal	equal	ADJ
ejpam-4923	13	49	to	to	ADP
ejpam-4923	13	50	one	one	NUM
ejpam-4923	13	51	sl2(r	sl2(r	NOUN
ejpam-4923	13	52	)	)	PUNCT
ejpam-4923	13	53	=	=	PRON
ejpam-4923	13	54	{	{	PUNCT
ejpam-4923	13	55	(	(	PUNCT
ejpam-4923	13	56	a	a	DET
ejpam-4923	13	57	b	b	NOUN
ejpam-4923	13	58	c	c	NOUN
ejpam-4923	13	59	d	d	NOUN
ejpam-4923	13	60	)	)	PUNCT
ejpam-4923	13	61	:	:	PUNCT
ejpam-4923	13	62	ad−	ad−	PROPN
ejpam-4923	13	63	bc	bc	X
ejpam-4923	13	64	=	=	SYM
ejpam-4923	13	65	1	1	PROPN
ejpam-4923	13	66	,	,	PUNCT
ejpam-4923	13	67	a	a	DET
ejpam-4923	13	68	,	,	PUNCT
ejpam-4923	13	69	b	b	NOUN
ejpam-4923	13	70	,	,	PUNCT
ejpam-4923	13	71	c	c	NOUN
ejpam-4923	13	72	,	,	PUNCT
ejpam-4923	13	73	d	d	PROPN
ejpam-4923	13	74	∈	∈	PROPN
ejpam-4923	13	75	r	r	NOUN
ejpam-4923	13	76	}	}	PUNCT
ejpam-4923	13	77	.	.	PUNCT
ejpam-4923	14	1	it	it	PRON
ejpam-4923	14	2	acts	act	VERB
ejpam-4923	14	3	on	on	ADP
ejpam-4923	14	4	the	the	DET
ejpam-4923	14	5	upper	upper	ADJ
ejpam-4923	14	6	half	half	ADJ
ejpam-4923	14	7	-	-	PUNCT
ejpam-4923	14	8	plane	plane	NOUN
ejpam-4923	14	9	by	by	ADP
ejpam-4923	14	10	möbius	möbius	PROPN
ejpam-4923	14	11	transformation	transformation	NOUN
ejpam-4923	14	12	g	g	PROPN
ejpam-4923	14	13	·	·	PUNCT
ejpam-4923	14	14	z	z	X
ejpam-4923	14	15	=	=	PUNCT
ejpam-4923	14	16	az	az	PROPN
ejpam-4923	14	17	+	+	NOUN
ejpam-4923	14	18	b	b	X
ejpam-4923	14	19	cz	cz	NOUN
ejpam-4923	15	1	+	+	CCONJ
ejpam-4923	15	2	d	d	NOUN
ejpam-4923	15	3	,	,	PUNCT
ejpam-4923	15	4	where	where	SCONJ
ejpam-4923	15	5	g	g	PROPN
ejpam-4923	15	6	∈	∈	PROPN
ejpam-4923	15	7	sl2(r	sl2(r	PROPN
ejpam-4923	15	8	)	)	PUNCT
ejpam-4923	16	1	and	and	CCONJ
ejpam-4923	16	2	z	z	NOUN
ejpam-4923	16	3	∈	∈	PROPN
ejpam-4923	16	4	{	{	PUNCT
ejpam-4923	16	5	z	z	NOUN
ejpam-4923	16	6	∈	∈	PROPN
ejpam-4923	16	7	c	c	PROPN
ejpam-4923	16	8	:	:	PUNCT
ejpam-4923	16	9	imz	imz	PROPN
ejpam-4923	16	10	>	>	X
ejpam-4923	16	11	0	0	NUM
ejpam-4923	16	12	}	}	PUNCT
ejpam-4923	16	13	.	.	PUNCT
ejpam-4923	17	1	the	the	DET
ejpam-4923	17	2	group	group	NOUN
ejpam-4923	17	3	sl2(r	sl2(r	PROPN
ejpam-4923	17	4	)	)	PUNCT
ejpam-4923	17	5	contains	contain	VERB
ejpam-4923	17	6	the	the	DET
ejpam-4923	17	7	following	follow	VERB
ejpam-4923	17	8	three	three	NUM
ejpam-4923	17	9	subgroups	subgroup	NOUN
ejpam-4923	17	10	:	:	PUNCT
ejpam-4923	17	11	k	k	X
ejpam-4923	17	12	=	=	PUNCT
ejpam-4923	17	13	{	{	PUNCT
ejpam-4923	17	14	(	(	PUNCT
ejpam-4923	17	15	cos	cos	ADP
ejpam-4923	17	16	θ	θ	PROPN
ejpam-4923	17	17	sin	sin	VERB
ejpam-4923	17	18	θ	θ	PROPN
ejpam-4923	17	19	−	−	PROPN
ejpam-4923	17	20	sin	sin	NOUN
ejpam-4923	17	21	θ	θ	PROPN
ejpam-4923	17	22	cos	cos	PROPN
ejpam-4923	17	23	θ	θ	PROPN
ejpam-4923	17	24	)	)	PUNCT
ejpam-4923	17	25	:	:	PUNCT
ejpam-4923	18	1	θ	θ	X
ejpam-4923	18	2	∈	∈	PROPN
ejpam-4923	18	3	r	r	NOUN
ejpam-4923	18	4	}	}	PUNCT
ejpam-4923	18	5	,	,	PUNCT
ejpam-4923	18	6	doi	doi	NOUN
ejpam-4923	18	7	:	:	PUNCT
ejpam-4923	18	8	https://doi.org/10.29020/nybg.ejpam.v16i4.4923	https://doi.org/10.29020/nybg.ejpam.v16i4.4923	PROPN
ejpam-4923	18	9	email	email	NOUN
ejpam-4923	18	10	address	address	NOUN
ejpam-4923	18	11	:	:	PUNCT
ejpam-4923	18	12	asmghamdi@uqu.edu.sa	asmghamdi@uqu.edu.sa	PROPN
ejpam-4923	18	13	(	(	PUNCT
ejpam-4923	18	14	a.	a.	PROPN
ejpam-4923	18	15	s.	s.	PROPN
ejpam-4923	18	16	alghamdi	alghamdi	PROPN
ejpam-4923	18	17	)	)	PUNCT
ejpam-4923	18	18	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4923	19	1	2348	2348	NUM
ejpam-4923	20	1	©	©	PROPN
ejpam-4923	20	2	2023	2023	NUM
ejpam-4923	20	3	ejpam	ejpam	NOUN
ejpam-4923	20	4	all	all	DET
ejpam-4923	20	5	rights	right	NOUN
ejpam-4923	20	6	reserved	reserve	VERB
ejpam-4923	20	7	.	.	PUNCT
ejpam-4923	21	1	a.	a.	PROPN
ejpam-4923	21	2	s.	s.	PROPN
ejpam-4923	21	3	alghamdi	alghamdi	PROPN
ejpam-4923	21	4	/	/	SYM
ejpam-4923	21	5	eur	eur	PROPN
ejpam-4923	21	6	.	.	PUNCT
ejpam-4923	22	1	j.	j.	PROPN
ejpam-4923	22	2	pure	pure	PROPN
ejpam-4923	22	3	appl	appl	PROPN
ejpam-4923	22	4	.	.	PROPN
ejpam-4923	22	5	math	math	PROPN
ejpam-4923	22	6	,	,	PUNCT
ejpam-4923	22	7	16	16	NUM
ejpam-4923	22	8	(	(	PUNCT
ejpam-4923	22	9	4	4	NUM
ejpam-4923	22	10	)	)	PUNCT
ejpam-4923	22	11	(	(	PUNCT
ejpam-4923	22	12	2023	2023	NUM
ejpam-4923	22	13	)	)	PUNCT
ejpam-4923	22	14	,	,	PUNCT
ejpam-4923	22	15	2348	2348	NUM
ejpam-4923	22	16	-	-	SYM
ejpam-4923	22	17	2367	2367	NUM
ejpam-4923	22	18	2349	2349	NUM
ejpam-4923	22	19	a	a	DET
ejpam-4923	22	20	=	=	X
ejpam-4923	22	21	{	{	PUNCT
ejpam-4923	22	22	(	(	PUNCT
ejpam-4923	22	23	α	α	NOUN
ejpam-4923	22	24	0	0	NUM
ejpam-4923	22	25	0	0	NUM
ejpam-4923	22	26	α−1	α−1	PROPN
ejpam-4923	22	27	)	)	PUNCT
ejpam-4923	22	28	:	:	PUNCT
ejpam-4923	23	1	α	α	X
ejpam-4923	23	2	>	>	X
ejpam-4923	23	3	0	0	NUM
ejpam-4923	23	4	}	}	PUNCT
ejpam-4923	23	5	,	,	PUNCT
ejpam-4923	23	6	n	n	NOUN
ejpam-4923	23	7	=	=	PRON
ejpam-4923	23	8	{	{	PUNCT
ejpam-4923	23	9	(	(	PUNCT
ejpam-4923	23	10	1	1	NUM
ejpam-4923	23	11	x	x	SYM
ejpam-4923	23	12	0	0	NUM
ejpam-4923	23	13	1	1	NUM
ejpam-4923	23	14	)	)	PUNCT
ejpam-4923	23	15	:	:	PUNCT
ejpam-4923	24	1	x	x	X
ejpam-4923	24	2	∈	∈	NOUN
ejpam-4923	24	3	r	r	NOUN
ejpam-4923	24	4	}	}	PUNCT
ejpam-4923	24	5	.	.	PUNCT
ejpam-4923	25	1	the	the	DET
ejpam-4923	25	2	lie	lie	NOUN
ejpam-4923	25	3	algebra	algebra	PROPN
ejpam-4923	25	4	sl2(r	sl2(r	PROPN
ejpam-4923	25	5	)	)	PUNCT
ejpam-4923	25	6	is	be	AUX
ejpam-4923	25	7	the	the	DET
ejpam-4923	25	8	set	set	NOUN
ejpam-4923	25	9	of	of	ADP
ejpam-4923	25	10	all	all	DET
ejpam-4923	25	11	2×	2×	NUM
ejpam-4923	25	12	2	2	NUM
ejpam-4923	25	13	real	real	ADJ
ejpam-4923	25	14	matrices	matrix	NOUN
ejpam-4923	25	15	of	of	ADP
ejpam-4923	25	16	trace	trace	NOUN
ejpam-4923	25	17	zero	zero	NUM
ejpam-4923	25	18	.	.	PUNCT
ejpam-4923	26	1	it	it	PRON
ejpam-4923	26	2	is	be	AUX
ejpam-4923	26	3	a	a	DET
ejpam-4923	26	4	threedimensional	threedimensional	ADJ
ejpam-4923	26	5	lie	lie	NOUN
ejpam-4923	26	6	algebra	algebra	NOUN
ejpam-4923	26	7	so	so	SCONJ
ejpam-4923	26	8	we	we	PRON
ejpam-4923	26	9	can	can	AUX
ejpam-4923	26	10	choose	choose	VERB
ejpam-4923	26	11	a	a	DET
ejpam-4923	26	12	basis{z	basis{z	NOUN
ejpam-4923	26	13	,	,	PUNCT
ejpam-4923	26	14	a	a	DET
ejpam-4923	26	15	,	,	PUNCT
ejpam-4923	26	16	b	b	NOUN
ejpam-4923	26	17	}	}	PUNCT
ejpam-4923	26	18	of	of	ADP
ejpam-4923	26	19	sl2(r	sl2(r	PROPN
ejpam-4923	26	20	)	)	PUNCT
ejpam-4923	26	21	by	by	ADP
ejpam-4923	26	22	setting	set	VERB
ejpam-4923	26	23	z	z	NOUN
ejpam-4923	26	24	=	=	SYM
ejpam-4923	26	25	(	(	PUNCT
ejpam-4923	26	26	0	0	NUM
ejpam-4923	26	27	1	1	NUM
ejpam-4923	26	28	−1	−1	NOUN
ejpam-4923	26	29	0	0	NUM
ejpam-4923	26	30	)	)	PUNCT
ejpam-4923	26	31	,	,	PUNCT
ejpam-4923	26	32	a	a	DET
ejpam-4923	26	33	=	=	NOUN
ejpam-4923	26	34	1	1	NUM
ejpam-4923	26	35	2	2	NUM
ejpam-4923	26	36	(	(	PUNCT
ejpam-4923	26	37	−1	−1	NOUN
ejpam-4923	26	38	0	0	SYM
ejpam-4923	26	39	0	0	NUM
ejpam-4923	26	40	1	1	NUM
ejpam-4923	26	41	)	)	PUNCT
ejpam-4923	26	42	and	and	CCONJ
ejpam-4923	26	43	b	b	X
ejpam-4923	26	44	=	=	SYM
ejpam-4923	26	45	1	1	NUM
ejpam-4923	26	46	2	2	NUM
ejpam-4923	26	47	(	(	PUNCT
ejpam-4923	26	48	0	0	NUM
ejpam-4923	26	49	1	1	NUM
ejpam-4923	26	50	1	1	NUM
ejpam-4923	26	51	0	0	NUM
ejpam-4923	26	52	)	)	PUNCT
ejpam-4923	26	53	.	.	PUNCT
ejpam-4923	27	1	(	(	PUNCT
ejpam-4923	27	2	2	2	X
ejpam-4923	27	3	)	)	PUNCT
ejpam-4923	27	4	note	note	NOUN
ejpam-4923	27	5	that	that	SCONJ
ejpam-4923	28	1	[	[	X
ejpam-4923	28	2	z	z	X
ejpam-4923	28	3	,	,	PUNCT
ejpam-4923	28	4	a	a	X
ejpam-4923	28	5	]	]	X
ejpam-4923	28	6	=	=	SYM
ejpam-4923	28	7	2b	2b	NOUN
ejpam-4923	28	8	,	,	PUNCT
ejpam-4923	28	9	[	[	X
ejpam-4923	28	10	z	z	X
ejpam-4923	28	11	,	,	PUNCT
ejpam-4923	28	12	b	b	NOUN
ejpam-4923	28	13	]	]	X
ejpam-4923	28	14	=	=	SYM
ejpam-4923	28	15	−2a	−2a	PROPN
ejpam-4923	28	16	,	,	PUNCT
ejpam-4923	28	17	[	[	X
ejpam-4923	28	18	a	a	DET
ejpam-4923	28	19	,	,	PUNCT
ejpam-4923	28	20	b	b	NOUN
ejpam-4923	28	21	]	]	X
ejpam-4923	28	22	=	=	SYM
ejpam-4923	28	23	−1	−1	NOUN
ejpam-4923	28	24	2	2	NUM
ejpam-4923	28	25	z.	z.	X
ejpam-4923	28	26	(	(	PUNCT
ejpam-4923	28	27	3	3	NUM
ejpam-4923	28	28	)	)	PUNCT
ejpam-4923	28	29	2	2	NUM
ejpam-4923	28	30	.	.	PUNCT
ejpam-4923	28	31	the	the	DET
ejpam-4923	28	32	group	group	NOUN
ejpam-4923	28	33	su(1	su(1	NOUN
ejpam-4923	28	34	,	,	PUNCT
ejpam-4923	28	35	1	1	NUM
ejpam-4923	28	36	)	)	PUNCT
ejpam-4923	28	37	the	the	DET
ejpam-4923	28	38	cayley	cayley	ADJ
ejpam-4923	28	39	transform	transform	NOUN
ejpam-4923	28	40	of	of	ADP
ejpam-4923	28	41	the	the	DET
ejpam-4923	28	42	upper	upper	ADJ
ejpam-4923	28	43	-	-	PUNCT
ejpam-4923	28	44	half	half	NOUN
ejpam-4923	28	45	plane	plane	NOUN
ejpam-4923	28	46	to	to	ADP
ejpam-4923	28	47	the	the	DET
ejpam-4923	28	48	unit	unit	NOUN
ejpam-4923	28	49	disc	disc	NOUN
ejpam-4923	28	50	d	d	NOUN
ejpam-4923	28	51	is	be	AUX
ejpam-4923	28	52	defined	define	VERB
ejpam-4923	28	53	by	by	ADP
ejpam-4923	28	54	w	w	PROPN
ejpam-4923	28	55	=	=	PROPN
ejpam-4923	28	56	z	z	NOUN
ejpam-4923	28	57	−	−	NOUN
ejpam-4923	29	1	i	i	PRON
ejpam-4923	29	2	z	z	PROPN
ejpam-4923	30	1	+	+	CCONJ
ejpam-4923	30	2	i	i	PRON
ejpam-4923	30	3	,	,	PUNCT
ejpam-4923	30	4	(	(	PUNCT
ejpam-4923	30	5	4	4	X
ejpam-4923	30	6	)	)	PUNCT
ejpam-4923	30	7	where	where	SCONJ
ejpam-4923	30	8	x	x	SYM
ejpam-4923	30	9	∈	∈	PROPN
ejpam-4923	30	10	d	d	NOUN
ejpam-4923	30	11	and	and	CCONJ
ejpam-4923	30	12	z	z	PROPN
ejpam-4923	30	13	∈	∈	PROPN
ejpam-4923	30	14	{	{	PUNCT
ejpam-4923	30	15	z	z	NOUN
ejpam-4923	30	16	∈	∈	PROPN
ejpam-4923	30	17	c	c	X
ejpam-4923	30	18	,	,	PUNCT
ejpam-4923	30	19	imz	imz	PROPN
ejpam-4923	30	20	>	>	X
ejpam-4923	30	21	0	0	NUM
ejpam-4923	30	22	}	}	PUNCT
ejpam-4923	30	23	.	.	PUNCT
ejpam-4923	31	1	by	by	ADP
ejpam-4923	31	2	the	the	DET
ejpam-4923	31	3	transformation	transformation	NOUN
ejpam-4923	31	4	(	(	PUNCT
ejpam-4923	31	5	4	4	X
ejpam-4923	31	6	)	)	PUNCT
ejpam-4923	31	7	we	we	PRON
ejpam-4923	31	8	can	can	AUX
ejpam-4923	31	9	transfer	transfer	VERB
ejpam-4923	31	10	the	the	DET
ejpam-4923	31	11	action	action	NOUN
ejpam-4923	31	12	of	of	ADP
ejpam-4923	31	13	the	the	DET
ejpam-4923	31	14	group	group	NOUN
ejpam-4923	31	15	sl2(r	sl2(r	PROPN
ejpam-4923	31	16	)	)	PUNCT
ejpam-4923	31	17	from	from	ADP
ejpam-4923	31	18	the	the	DET
ejpam-4923	31	19	upper	upper	ADJ
ejpam-4923	31	20	half	half	ADJ
ejpam-4923	31	21	-	-	PUNCT
ejpam-4923	31	22	plane	plane	NOUN
ejpam-4923	31	23	to	to	ADP
ejpam-4923	31	24	the	the	DET
ejpam-4923	31	25	action	action	NOUN
ejpam-4923	31	26	of	of	ADP
ejpam-4923	31	27	the	the	DET
ejpam-4923	31	28	group	group	NOUN
ejpam-4923	31	29	su(1	su(1	NOUN
ejpam-4923	31	30	,	,	PUNCT
ejpam-4923	31	31	1	1	NUM
ejpam-4923	31	32	)	)	PUNCT
ejpam-4923	31	33	on	on	ADP
ejpam-4923	31	34	the	the	DET
ejpam-4923	31	35	unit	unit	NOUN
ejpam-4923	31	36	disc	disc	NOUN
ejpam-4923	31	37	,	,	PUNCT
ejpam-4923	31	38	where	where	SCONJ
ejpam-4923	31	39	su(1	su(1	NOUN
ejpam-4923	31	40	,	,	PUNCT
ejpam-4923	31	41	1	1	NUM
ejpam-4923	31	42	)	)	PUNCT
ejpam-4923	31	43	=	=	PRON
ejpam-4923	31	44	{	{	PUNCT
ejpam-4923	31	45	(	(	PUNCT
ejpam-4923	31	46	α	α	X
ejpam-4923	31	47	β	β	X
ejpam-4923	31	48	β	β	X
ejpam-4923	31	49	α	α	NOUN
ejpam-4923	31	50	)	)	PUNCT
ejpam-4923	31	51	:	:	PUNCT
ejpam-4923	31	52	α	α	X
ejpam-4923	31	53	,	,	PUNCT
ejpam-4923	31	54	β	β	X
ejpam-4923	31	55	∈	∈	PROPN
ejpam-4923	31	56	c	c	X
ejpam-4923	31	57	,	,	PUNCT
ejpam-4923	31	58	|α|2	|α|2	NOUN
ejpam-4923	31	59	−	−	NOUN
ejpam-4923	31	60	|β|2	|β|2	VERB
ejpam-4923	31	61	=	=	SYM
ejpam-4923	31	62	1	1	NUM
ejpam-4923	31	63	}	}	PUNCT
ejpam-4923	31	64	.	.	PUNCT
ejpam-4923	32	1	furthermore	furthermore	ADV
ejpam-4923	32	2	,	,	PUNCT
ejpam-4923	32	3	the	the	DET
ejpam-4923	32	4	matrix	matrix	NOUN
ejpam-4923	32	5	(	(	PUNCT
ejpam-4923	32	6	a	a	DET
ejpam-4923	32	7	b	b	NOUN
ejpam-4923	32	8	c	c	PROPN
ejpam-4923	32	9	d	d	NOUN
ejpam-4923	32	10	)	)	PUNCT
ejpam-4923	32	11	∈	∈	PROPN
ejpam-4923	32	12	sl2(r	sl2(r	PROPN
ejpam-4923	32	13	)	)	PUNCT
ejpam-4923	32	14	can	can	AUX
ejpam-4923	32	15	be	be	AUX
ejpam-4923	32	16	an	an	DET
ejpam-4923	32	17	element	element	NOUN
ejpam-4923	32	18	of	of	ADP
ejpam-4923	32	19	the	the	DET
ejpam-4923	32	20	group	group	NOUN
ejpam-4923	32	21	su(1	su(1	NOUN
ejpam-4923	32	22	,	,	PUNCT
ejpam-4923	32	23	1	1	NUM
ejpam-4923	32	24	)	)	PUNCT
ejpam-4923	32	25	by	by	ADP
ejpam-4923	32	26	the	the	DET
ejpam-4923	32	27	following	follow	VERB
ejpam-4923	32	28	identity	identity	NOUN
ejpam-4923	32	29	:	:	PUNCT
ejpam-4923	32	30	1√	1√	PROPN
ejpam-4923	32	31	2	2	NUM
ejpam-4923	32	32	(	(	PUNCT
ejpam-4923	32	33	1	1	NUM
ejpam-4923	32	34	−i	−i	ADJ
ejpam-4923	32	35	−i	−i	ADJ
ejpam-4923	32	36	1	1	NUM
ejpam-4923	32	37	)	)	PUNCT
ejpam-4923	32	38	(	(	PUNCT
ejpam-4923	32	39	a	a	DET
ejpam-4923	32	40	b	b	X
ejpam-4923	32	41	c	c	PROPN
ejpam-4923	32	42	d	d	NOUN
ejpam-4923	32	43	)	)	PUNCT
ejpam-4923	32	44	1√	1√	PROPN
ejpam-4923	32	45	2	2	NUM
ejpam-4923	32	46	(	(	PUNCT
ejpam-4923	32	47	1	1	NUM
ejpam-4923	32	48	i	i	NOUN
ejpam-4923	32	49	i	i	VERB
ejpam-4923	32	50	1	1	X
ejpam-4923	32	51	)	)	PUNCT
ejpam-4923	32	52	=	=	SYM
ejpam-4923	32	53	(	(	PUNCT
ejpam-4923	32	54	α	α	X
ejpam-4923	32	55	β	β	X
ejpam-4923	32	56	β	β	X
ejpam-4923	32	57	α	α	NOUN
ejpam-4923	32	58	)	)	PUNCT
ejpam-4923	32	59	.	.	PUNCT
ejpam-4923	33	1	(	(	PUNCT
ejpam-4923	33	2	5	5	X
ejpam-4923	33	3	)	)	PUNCT
ejpam-4923	33	4	next	next	ADV
ejpam-4923	33	5	,	,	PUNCT
ejpam-4923	33	6	any	any	DET
ejpam-4923	33	7	g	g	PROPN
ejpam-4923	33	8	∈	∈	PROPN
ejpam-4923	33	9	su(1	su(1	NOUN
ejpam-4923	33	10	,	,	PUNCT
ejpam-4923	33	11	1	1	NUM
ejpam-4923	33	12	)	)	PUNCT
ejpam-4923	33	13	has	have	VERB
ejpam-4923	33	14	a	a	DET
ejpam-4923	33	15	unique	unique	ADJ
ejpam-4923	33	16	decomposition	decomposition	NOUN
ejpam-4923	33	17	of	of	ADP
ejpam-4923	33	18	the	the	DET
ejpam-4923	33	19	form	form	NOUN
ejpam-4923	33	20	(	(	PUNCT
ejpam-4923	33	21	α	α	X
ejpam-4923	33	22	β	β	X
ejpam-4923	33	23	β	β	X
ejpam-4923	33	24	α	α	NOUN
ejpam-4923	33	25	)	)	PUNCT
ejpam-4923	34	1	=	=	SYM
ejpam-4923	34	2	|α|	|α|	NOUN
ejpam-4923	34	3	(	(	PUNCT
ejpam-4923	34	4	1	1	NUM
ejpam-4923	34	5	βα−1	βα−1	PROPN
ejpam-4923	34	6	βα−1	βα−1	PROPN
ejpam-4923	34	7	1	1	NUM
ejpam-4923	34	8	)	)	PUNCT
ejpam-4923	34	9	(	(	PUNCT
ejpam-4923	34	10	α	α	PROPN
ejpam-4923	34	11	|α|	|α|	PROPN
ejpam-4923	34	12	0	0	NUM
ejpam-4923	34	13	0	0	NUM
ejpam-4923	34	14	α	α	PRON
ejpam-4923	34	15	|α|	|α|	PROPN
ejpam-4923	34	16	)	)	PUNCT
ejpam-4923	34	17	=	=	SYM
ejpam-4923	34	18	1√	1√	NUM
ejpam-4923	34	19	1−	1−	NUM
ejpam-4923	34	20	|u|2	|u|2	PROPN
ejpam-4923	34	21	(	(	PUNCT
ejpam-4923	34	22	1	1	NUM
ejpam-4923	34	23	u	u	NOUN
ejpam-4923	34	24	u	u	NOUN
ejpam-4923	34	25	1	1	NUM
ejpam-4923	34	26	)	)	PUNCT
ejpam-4923	34	27	(	(	PUNCT
ejpam-4923	34	28	eiθ	eiθ	NOUN
ejpam-4923	34	29	0	0	NUM
ejpam-4923	34	30	0	0	NUM
ejpam-4923	34	31	e−iθ	e−iθ	NOUN
ejpam-4923	34	32	)	)	PUNCT
ejpam-4923	34	33	,	,	PUNCT
ejpam-4923	34	34	(	(	PUNCT
ejpam-4923	34	35	6	6	NUM
ejpam-4923	34	36	)	)	PUNCT
ejpam-4923	34	37	where	where	SCONJ
ejpam-4923	34	38	θ	θ	PROPN
ejpam-4923	34	39	=	=	PUNCT
ejpam-4923	34	40	argα	argα	NOUN
ejpam-4923	34	41	,	,	PUNCT
ejpam-4923	34	42	u	u	NOUN
ejpam-4923	34	43	=	=	PROPN
ejpam-4923	34	44	βα−1	βα−1	PROPN
ejpam-4923	34	45	and	and	CCONJ
ejpam-4923	34	46	|u|	|u|	X
ejpam-4923	34	47	<	<	X
ejpam-4923	34	48	1	1	NUM
ejpam-4923	34	49	(	(	PUNCT
ejpam-4923	34	50	since	since	SCONJ
ejpam-4923	34	51	|α|2	|α|2	NOUN
ejpam-4923	34	52	−	−	NOUN
ejpam-4923	34	53	|β|2	|β|2	PROPN
ejpam-4923	34	54	=	=	SYM
ejpam-4923	34	55	1	1	NUM
ejpam-4923	34	56	)	)	PUNCT
ejpam-4923	34	57	.	.	PUNCT
ejpam-4923	35	1	let	let	VERB
ejpam-4923	35	2	u	u	NOUN
ejpam-4923	35	3	=	=	NOUN
ejpam-4923	35	4	reiϕ	reiϕ	NOUN
ejpam-4923	35	5	,	,	PUNCT
ejpam-4923	35	6	then	then	ADV
ejpam-4923	35	7	the	the	DET
ejpam-4923	35	8	identity	identity	NOUN
ejpam-4923	35	9	(	(	PUNCT
ejpam-4923	35	10	6	6	NUM
ejpam-4923	35	11	)	)	PUNCT
ejpam-4923	35	12	describes	describe	VERB
ejpam-4923	35	13	an	an	DET
ejpam-4923	35	14	element	element	NOUN
ejpam-4923	35	15	g	g	PROPN
ejpam-4923	35	16	∈	∈	PROPN
ejpam-4923	35	17	su(1	su(1	NOUN
ejpam-4923	35	18	,	,	PUNCT
ejpam-4923	35	19	1	1	NUM
ejpam-4923	35	20	)	)	PUNCT
ejpam-4923	35	21	by	by	ADP
ejpam-4923	35	22	a	a	DET
ejpam-4923	35	23	triplet	triplet	NOUN
ejpam-4923	35	24	of	of	ADP
ejpam-4923	35	25	numbers	number	NOUN
ejpam-4923	35	26	(	(	PUNCT
ejpam-4923	35	27	r	r	NOUN
ejpam-4923	35	28	,	,	PUNCT
ejpam-4923	35	29	ϕ	ϕ	NOUN
ejpam-4923	35	30	,	,	PUNCT
ejpam-4923	35	31	θ	θ	NOUN
ejpam-4923	35	32	)	)	PUNCT
ejpam-4923	36	1	where	where	SCONJ
ejpam-4923	36	2	0	0	NUM
ejpam-4923	36	3	≤	≤	NUM
ejpam-4923	36	4	r	r	NOUN
ejpam-4923	36	5	<	<	X
ejpam-4923	36	6	1	1	NUM
ejpam-4923	36	7	and	and	CCONJ
ejpam-4923	36	8	−π	−π	PRON
ejpam-4923	36	9	<	<	X
ejpam-4923	36	10	ϕ	ϕ	X
ejpam-4923	36	11	,	,	PUNCT
ejpam-4923	36	12	θ	θ	PROPN
ejpam-4923	36	13	≤	≤	NUM
ejpam-4923	36	14	π	π	X
ejpam-4923	36	15	.	.	PUNCT
ejpam-4923	37	1	the	the	DET
ejpam-4923	37	2	connection	connection	NOUN
ejpam-4923	37	3	with	with	ADP
ejpam-4923	37	4	the	the	DET
ejpam-4923	37	5	(	(	PUNCT
ejpam-4923	37	6	α	α	NOUN
ejpam-4923	37	7	,	,	PUNCT
ejpam-4923	37	8	β	β	NOUN
ejpam-4923	37	9	)	)	PUNCT
ejpam-4923	37	10	coordinates	coordinate	NOUN
ejpam-4923	37	11	is	be	AUX
ejpam-4923	37	12	as	as	SCONJ
ejpam-4923	37	13	follows	follow	VERB
ejpam-4923	37	14	:	:	PUNCT
ejpam-4923	37	15	α	α	X
ejpam-4923	37	16	=	=	PUNCT
ejpam-4923	37	17	eiθ√	eiθ√	VERB
ejpam-4923	37	18	1−	1−	NUM
ejpam-4923	37	19	|r|2	|r|2	NOUN
ejpam-4923	37	20	,	,	PUNCT
ejpam-4923	37	21	β	β	NOUN
ejpam-4923	37	22	=	=	SYM
ejpam-4923	37	23	rei(θ−ϕ)√	rei(θ−ϕ)√	ADJ
ejpam-4923	37	24	1−	1−	NUM
ejpam-4923	37	25	|r|2	|r|2	PROPN
ejpam-4923	37	26	,	,	PUNCT
ejpam-4923	37	27	a.	a.	PROPN
ejpam-4923	37	28	s.	s.	PROPN
ejpam-4923	37	29	alghamdi	alghamdi	PROPN
ejpam-4923	37	30	/	/	SYM
ejpam-4923	37	31	eur	eur	PROPN
ejpam-4923	37	32	.	.	PUNCT
ejpam-4923	38	1	j.	j.	PROPN
ejpam-4923	38	2	pure	pure	PROPN
ejpam-4923	38	3	appl	appl	PROPN
ejpam-4923	38	4	.	.	PROPN
ejpam-4923	38	5	math	math	PROPN
ejpam-4923	38	6	,	,	PUNCT
ejpam-4923	38	7	16	16	NUM
ejpam-4923	38	8	(	(	PUNCT
ejpam-4923	38	9	4	4	NUM
ejpam-4923	38	10	)	)	PUNCT
ejpam-4923	38	11	(	(	PUNCT
ejpam-4923	38	12	2023	2023	NUM
ejpam-4923	38	13	)	)	PUNCT
ejpam-4923	38	14	,	,	PUNCT
ejpam-4923	38	15	2348	2348	NUM
ejpam-4923	38	16	-	-	SYM
ejpam-4923	38	17	2367	2367	NUM
ejpam-4923	38	18	2350	2350	NUM
ejpam-4923	38	19	r	r	NOUN
ejpam-4923	38	20	=	=	NOUN
ejpam-4923	38	21	∣∣∣∣βα	∣∣∣∣βα	PROPN
ejpam-4923	38	22	∣∣∣∣	∣∣∣∣	NOUN
ejpam-4923	38	23	,	,	PUNCT
ejpam-4923	38	24	ϕ	ϕ	NOUN
ejpam-4923	38	25	=	=	SYM
ejpam-4923	38	26	−	−	PROPN
ejpam-4923	38	27	arg	arg	NOUN
ejpam-4923	38	28	β	β	X
ejpam-4923	38	29	α	α	NOUN
ejpam-4923	38	30	,	,	PUNCT
ejpam-4923	38	31	θ	θ	PROPN
ejpam-4923	38	32	=	=	PUNCT
ejpam-4923	38	33	argα	argα	NOUN
ejpam-4923	38	34	.	.	PUNCT
ejpam-4923	39	1	moreover	moreover	ADV
ejpam-4923	39	2	,	,	PUNCT
ejpam-4923	39	3	the	the	DET
ejpam-4923	39	4	decomposition	decomposition	NOUN
ejpam-4923	39	5	(	(	PUNCT
ejpam-4923	39	6	6	6	NUM
ejpam-4923	39	7	)	)	PUNCT
ejpam-4923	39	8	can	can	AUX
ejpam-4923	39	9	be	be	AUX
ejpam-4923	39	10	rewritten	rewrite	VERB
ejpam-4923	39	11	with	with	ADP
ejpam-4923	39	12	the	the	DET
ejpam-4923	39	13	same	same	ADJ
ejpam-4923	39	14	variables	variable	NOUN
ejpam-4923	39	15	as	as	ADP
ejpam-4923	39	16	(	(	PUNCT
ejpam-4923	39	17	α	α	X
ejpam-4923	39	18	β	β	X
ejpam-4923	39	19	β	β	X
ejpam-4923	39	20	α	α	NOUN
ejpam-4923	39	21	)	)	PUNCT
ejpam-4923	40	1	=	=	PUNCT
ejpam-4923	40	2	(	(	PUNCT
ejpam-4923	40	3	ei	ei	X
ejpam-4923	40	4	ϕ	ϕ	X
ejpam-4923	40	5	2	2	NUM
ejpam-4923	40	6	0	0	NUM
ejpam-4923	40	7	0	0	NUM
ejpam-4923	40	8	e−iϕ	e−iϕ	NOUN
ejpam-4923	40	9	2	2	NUM
ejpam-4923	40	10	)	)	PUNCT
ejpam-4923	40	11			PROPN
ejpam-4923	40	12	1√	1√	PROPN
ejpam-4923	40	13	1−|r|2	1−|r|2	NUM
ejpam-4923	40	14	r√	r√	NOUN
ejpam-4923	40	15	1−|r|2	1−|r|2	NUM
ejpam-4923	40	16	r√	r√	NOUN
ejpam-4923	40	17	1−|r|2	1−|r|2	PROPN
ejpam-4923	40	18	1√	1√	PROPN
ejpam-4923	40	19	1−|r|2	1−|r|2	NUM
ejpam-4923	40	20	(ei(θ−ϕ	(ei(θ−ϕ	NOUN
ejpam-4923	40	21	2	2	NUM
ejpam-4923	40	22	)	)	PUNCT
ejpam-4923	40	23	0	0	NUM
ejpam-4923	40	24	0	0	PUNCT
ejpam-4923	41	1	e−i(θ−ϕ	e−i(θ−ϕ	NUM
ejpam-4923	41	2	2	2	NUM
ejpam-4923	41	3	)	)	PUNCT
ejpam-4923	41	4	)	)	PUNCT
ejpam-4923	42	1	(	(	PUNCT
ejpam-4923	42	2	7	7	X
ejpam-4923	42	3	)	)	PUNCT
ejpam-4923	42	4	the	the	DET
ejpam-4923	42	5	last	last	ADJ
ejpam-4923	42	6	presentation	presentation	NOUN
ejpam-4923	42	7	is	be	AUX
ejpam-4923	42	8	a	a	DET
ejpam-4923	42	9	decomposition	decomposition	NOUN
ejpam-4923	42	10	of	of	ADP
ejpam-4923	42	11	the	the	DET
ejpam-4923	42	12	group	group	NOUN
ejpam-4923	42	13	su(1	su(1	NOUN
ejpam-4923	42	14	,	,	PUNCT
ejpam-4923	42	15	1	1	NUM
ejpam-4923	42	16	)	)	PUNCT
ejpam-4923	42	17	as	as	ADP
ejpam-4923	42	18	the	the	DET
ejpam-4923	42	19	product	product	NOUN
ejpam-4923	42	20	kak	kak	NOUN
ejpam-4923	42	21	of	of	ADP
ejpam-4923	42	22	its	its	PRON
ejpam-4923	42	23	subgroups	subgroup	NOUN
ejpam-4923	42	24	,	,	PUNCT
ejpam-4923	42	25	which	which	PRON
ejpam-4923	42	26	is	be	AUX
ejpam-4923	42	27	called	call	VERB
ejpam-4923	42	28	the	the	DET
ejpam-4923	42	29	cartan	cartan	ADJ
ejpam-4923	42	30	decomposition	decomposition	NOUN
ejpam-4923	42	31	.	.	PUNCT
ejpam-4923	43	1	the	the	DET
ejpam-4923	43	2	base	base	NOUN
ejpam-4923	43	3	of	of	ADP
ejpam-4923	43	4	the	the	DET
ejpam-4923	43	5	lie	lie	NOUN
ejpam-4923	43	6	algebra	algebra	PROPN
ejpam-4923	43	7	sl2(r	sl2(r	PROPN
ejpam-4923	43	8	)	)	PUNCT
ejpam-4923	43	9	consists	consist	VERB
ejpam-4923	43	10	of	of	ADP
ejpam-4923	43	11	the	the	DET
ejpam-4923	43	12	following	follow	VERB
ejpam-4923	43	13	three	three	NUM
ejpam-4923	43	14	matrices	matrix	NOUN
ejpam-4923	43	15	:	:	PUNCT
ejpam-4923	43	16	z̃	z̃	PROPN
ejpam-4923	43	17	=	=	SYM
ejpam-4923	43	18	(	(	PUNCT
ejpam-4923	43	19	i	i	NOUN
ejpam-4923	43	20	0	0	NUM
ejpam-4923	43	21	0	0	NUM
ejpam-4923	43	22	−i	−i	NOUN
ejpam-4923	43	23	)	)	PUNCT
ejpam-4923	43	24	,	,	PUNCT
ejpam-4923	44	1	ã	ã	PROPN
ejpam-4923	44	2	=	=	PRON
ejpam-4923	44	3	(	(	PUNCT
ejpam-4923	44	4	0	0	NUM
ejpam-4923	44	5	−	−	NOUN
ejpam-4923	45	1	i	i	PRON
ejpam-4923	45	2	2	2	NUM
ejpam-4923	45	3	i	i	NOUN
ejpam-4923	45	4	2	2	NUM
ejpam-4923	45	5	0	0	NUM
ejpam-4923	45	6	)	)	PUNCT
ejpam-4923	45	7	and	and	CCONJ
ejpam-4923	45	8	b̃	b̃	PROPN
ejpam-4923	45	9	=	=	PUNCT
ejpam-4923	46	1	(	(	PUNCT
ejpam-4923	46	2	0	0	NUM
ejpam-4923	46	3	1	1	NUM
ejpam-4923	46	4	2	2	NUM
ejpam-4923	46	5	1	1	NUM
ejpam-4923	46	6	2	2	NUM
ejpam-4923	46	7	0	0	NUM
ejpam-4923	46	8	)	)	PUNCT
ejpam-4923	46	9	.	.	PUNCT
ejpam-4923	47	1	(	(	PUNCT
ejpam-4923	47	2	8)	8)	NUM
ejpam-4923	47	3	the	the	DET
ejpam-4923	47	4	matrices	matrix	NOUN
ejpam-4923	47	5	z̃	z̃	PROPN
ejpam-4923	47	6	,	,	PUNCT
ejpam-4923	47	7	ã	ã	PROPN
ejpam-4923	47	8	and	and	CCONJ
ejpam-4923	47	9	b̃	b̃	PROPN
ejpam-4923	47	10	satisfy	satisfy	VERB
ejpam-4923	47	11	the	the	DET
ejpam-4923	47	12	commutation	commutation	NOUN
ejpam-4923	47	13	relation	relation	NOUN
ejpam-4923	47	14	(	(	PUNCT
ejpam-4923	47	15	3	3	NUM
ejpam-4923	47	16	)	)	PUNCT
ejpam-4923	47	17	.	.	PUNCT
ejpam-4923	48	1	also	also	ADV
ejpam-4923	48	2	,	,	PUNCT
ejpam-4923	48	3	the	the	DET
ejpam-4923	48	4	exponential	exponential	ADJ
ejpam-4923	48	5	map	map	NOUN
ejpam-4923	48	6	of	of	ADP
ejpam-4923	48	7	each	each	DET
ejpam-4923	48	8	matrix	matrix	NOUN
ejpam-4923	48	9	generates	generate	VERB
ejpam-4923	48	10	a	a	DET
ejpam-4923	48	11	one	one	NUM
ejpam-4923	48	12	-	-	PUNCT
ejpam-4923	48	13	dimensional	dimensional	ADJ
ejpam-4923	48	14	subgroup	subgroup	NOUN
ejpam-4923	48	15	of	of	ADP
ejpam-4923	48	16	the	the	DET
ejpam-4923	48	17	su(1	su(1	NOUN
ejpam-4923	48	18	,	,	PUNCT
ejpam-4923	48	19	1	1	NUM
ejpam-4923	48	20	)	)	PUNCT
ejpam-4923	48	21	group	group	NOUN
ejpam-4923	48	22	,	,	PUNCT
ejpam-4923	48	23	that	that	PRON
ejpam-4923	48	24	is	be	AUX
ejpam-4923	48	25	eθz̃	eθz̃	ADJ
ejpam-4923	48	26	=	=	X
ejpam-4923	48	27	(	(	PUNCT
ejpam-4923	48	28	eiθ	eiθ	NOUN
ejpam-4923	48	29	0	0	NUM
ejpam-4923	48	30	0	0	NUM
ejpam-4923	48	31	e−iθ	e−iθ	NOUN
ejpam-4923	48	32	)	)	PUNCT
ejpam-4923	48	33	,	,	PUNCT
ejpam-4923	48	34	(	(	PUNCT
ejpam-4923	48	35	9	9	NUM
ejpam-4923	48	36	)	)	PUNCT
ejpam-4923	48	37	eθã	eθã	NOUN
ejpam-4923	48	38	=	=	SYM
ejpam-4923	48	39	(	(	PUNCT
ejpam-4923	48	40	cosh	cosh	NOUN
ejpam-4923	48	41	θ	θ	PROPN
ejpam-4923	48	42	2	2	NUM
ejpam-4923	49	1	−i	−i	NOUN
ejpam-4923	49	2	sinh	sinh	NOUN
ejpam-4923	49	3	θ	θ	PROPN
ejpam-4923	49	4	2	2	NUM
ejpam-4923	49	5	i	i	PRON
ejpam-4923	49	6	sinh	sinh	VERB
ejpam-4923	49	7	θ	θ	PROPN
ejpam-4923	49	8	2	2	NUM
ejpam-4923	49	9	cosh	cosh	NOUN
ejpam-4923	49	10	θ	θ	NOUN
ejpam-4923	49	11	2	2	NUM
ejpam-4923	49	12	)	)	PUNCT
ejpam-4923	49	13	,	,	PUNCT
ejpam-4923	49	14	(	(	PUNCT
ejpam-4923	49	15	10	10	NUM
ejpam-4923	49	16	)	)	PUNCT
ejpam-4923	49	17	eθb̃	eθb̃	NOUN
ejpam-4923	49	18	=	=	SYM
ejpam-4923	49	19	(	(	PUNCT
ejpam-4923	49	20	cosh	cosh	NOUN
ejpam-4923	49	21	θ	θ	PROPN
ejpam-4923	49	22	2	2	NUM
ejpam-4923	49	23	sinh	sinh	NOUN
ejpam-4923	49	24	θ	θ	PROPN
ejpam-4923	49	25	2	2	NUM
ejpam-4923	49	26	sinh	sinh	NOUN
ejpam-4923	49	27	θ	θ	PROPN
ejpam-4923	49	28	2	2	NUM
ejpam-4923	49	29	cosh	cosh	NOUN
ejpam-4923	49	30	θ	θ	NOUN
ejpam-4923	49	31	2	2	NUM
ejpam-4923	49	32	)	)	PUNCT
ejpam-4923	49	33	.	.	PUNCT
ejpam-4923	50	1	(	(	PUNCT
ejpam-4923	50	2	11	11	NUM
ejpam-4923	50	3	)	)	SYM
ejpam-4923	50	4	3	3	NUM
ejpam-4923	50	5	.	.	PUNCT
ejpam-4923	50	6	induced	induce	VERB
ejpam-4923	50	7	representation	representation	NOUN
ejpam-4923	50	8	on	on	ADP
ejpam-4923	50	9	the	the	DET
ejpam-4923	50	10	unit	unit	NOUN
ejpam-4923	50	11	disc	disc	NOUN
ejpam-4923	50	12	in	in	ADP
ejpam-4923	50	13	this	this	DET
ejpam-4923	50	14	section	section	NOUN
ejpam-4923	50	15	,	,	PUNCT
ejpam-4923	50	16	we	we	PRON
ejpam-4923	50	17	induce	induce	VERB
ejpam-4923	50	18	a	a	DET
ejpam-4923	50	19	representation	representation	NOUN
ejpam-4923	50	20	of	of	ADP
ejpam-4923	50	21	the	the	DET
ejpam-4923	50	22	group	group	NOUN
ejpam-4923	50	23	su(1	su(1	NOUN
ejpam-4923	50	24	,	,	PUNCT
ejpam-4923	50	25	1	1	NUM
ejpam-4923	50	26	)	)	PUNCT
ejpam-4923	50	27	from	from	ADP
ejpam-4923	50	28	the	the	DET
ejpam-4923	50	29	subgroup	subgroup	PROPN
ejpam-4923	50	30	k.	k.	PROPN
ejpam-4923	51	1	mainly	mainly	ADV
ejpam-4923	51	2	,	,	PUNCT
ejpam-4923	51	3	we	we	PRON
ejpam-4923	51	4	use	use	VERB
ejpam-4923	51	5	the	the	DET
ejpam-4923	51	6	references	reference	NOUN
ejpam-4923	51	7	[	[	X
ejpam-4923	51	8	8	8	NUM
ejpam-4923	51	9	,	,	PUNCT
ejpam-4923	51	10	11	11	NUM
ejpam-4923	51	11	]	]	PUNCT
ejpam-4923	51	12	.	.	PUNCT
ejpam-4923	52	1	the	the	DET
ejpam-4923	52	2	one	one	NUM
ejpam-4923	52	3	-	-	PUNCT
ejpam-4923	52	4	dimensional	dimensional	ADJ
ejpam-4923	52	5	compact	compact	ADJ
ejpam-4923	52	6	subgroup	subgroup	NOUN
ejpam-4923	52	7	k	k	PROPN
ejpam-4923	52	8	is	be	AUX
ejpam-4923	52	9	defined	define	VERB
ejpam-4923	52	10	as	as	SCONJ
ejpam-4923	52	11	follows	follow	VERB
ejpam-4923	52	12	:	:	PUNCT
ejpam-4923	53	1	k	k	X
ejpam-4923	53	2	=	=	PUNCT
ejpam-4923	53	3	{	{	PUNCT
ejpam-4923	53	4	(	(	PUNCT
ejpam-4923	53	5	eiθ	eiθ	NOUN
ejpam-4923	53	6	0	0	NUM
ejpam-4923	53	7	0	0	NUM
ejpam-4923	53	8	e−iθ	e−iθ	NOUN
ejpam-4923	53	9	)	)	PUNCT
ejpam-4923	53	10	,	,	PUNCT
ejpam-4923	53	11	−π	−π	ADV
ejpam-4923	53	12	<	<	X
ejpam-4923	53	13	θ	θ	PROPN
ejpam-4923	53	14	≤	≤	NUM
ejpam-4923	53	15	π	π	PROPN
ejpam-4923	53	16	.	.	PUNCT
ejpam-4923	53	17	}	}	PUNCT
ejpam-4923	53	18	(	(	PUNCT
ejpam-4923	53	19	12	12	NUM
ejpam-4923	53	20	)	)	PUNCT
ejpam-4923	53	21	using	use	VERB
ejpam-4923	53	22	the	the	DET
ejpam-4923	53	23	decomposition	decomposition	NOUN
ejpam-4923	53	24	(	(	PUNCT
ejpam-4923	53	25	6	6	NUM
ejpam-4923	53	26	)	)	PUNCT
ejpam-4923	53	27	of	of	ADP
ejpam-4923	53	28	any	any	DET
ejpam-4923	53	29	element	element	NOUN
ejpam-4923	53	30	g	g	PROPN
ejpam-4923	53	31	∈	∈	PROPN
ejpam-4923	53	32	su(1	su(1	NOUN
ejpam-4923	53	33	,	,	PUNCT
ejpam-4923	53	34	1	1	NUM
ejpam-4923	53	35	)	)	PUNCT
ejpam-4923	53	36	,	,	PUNCT
ejpam-4923	53	37	we	we	PRON
ejpam-4923	53	38	can	can	AUX
ejpam-4923	53	39	identify	identify	VERB
ejpam-4923	53	40	the	the	DET
ejpam-4923	53	41	homogeneous	homogeneous	ADJ
ejpam-4923	53	42	space	space	NOUN
ejpam-4923	53	43	x	x	PUNCT
ejpam-4923	53	44	=	=	SYM
ejpam-4923	53	45	su(1	su(1	NOUN
ejpam-4923	53	46	,	,	PUNCT
ejpam-4923	53	47	1)/k	1)/k	NUM
ejpam-4923	53	48	with	with	ADP
ejpam-4923	53	49	the	the	DET
ejpam-4923	53	50	open	open	ADJ
ejpam-4923	53	51	unit	unit	NOUN
ejpam-4923	53	52	disc	disc	NOUN
ejpam-4923	53	53	d.	d.	PROPN
ejpam-4923	53	54	let	let	VERB
ejpam-4923	53	55	the	the	DET
ejpam-4923	53	56	section	section	NOUN
ejpam-4923	53	57	s	s	PART
ejpam-4923	53	58	:	:	PUNCT
ejpam-4923	53	59	d	d	X
ejpam-4923	53	60	→	→	SYM
ejpam-4923	53	61	su(1	su(1	NOUN
ejpam-4923	53	62	,	,	PUNCT
ejpam-4923	53	63	1	1	NUM
ejpam-4923	53	64	)	)	PUNCT
ejpam-4923	53	65	be	be	AUX
ejpam-4923	53	66	defined	define	VERB
ejpam-4923	53	67	as	as	SCONJ
ejpam-4923	53	68	follows	follow	VERB
ejpam-4923	53	69	:	:	PUNCT
ejpam-4923	53	70	s	s	X
ejpam-4923	53	71	:	:	PUNCT
ejpam-4923	53	72	u	u	PROPN
ejpam-4923	53	73	7→	7→	PROPN
ejpam-4923	53	74	1√	1√	NOUN
ejpam-4923	53	75	1−	1−	NUM
ejpam-4923	54	1	|u|2	|u|2	PROPN
ejpam-4923	54	2	(	(	PUNCT
ejpam-4923	54	3	1	1	NUM
ejpam-4923	54	4	u	u	NOUN
ejpam-4923	54	5	ū	ū	NOUN
ejpam-4923	54	6	1	1	NUM
ejpam-4923	54	7	)	)	PUNCT
ejpam-4923	54	8	.	.	PUNCT
ejpam-4923	55	1	(	(	PUNCT
ejpam-4923	55	2	13	13	NUM
ejpam-4923	55	3	)	)	PUNCT
ejpam-4923	55	4	there	there	PRON
ejpam-4923	55	5	is	be	VERB
ejpam-4923	55	6	a	a	DET
ejpam-4923	55	7	natural	natural	ADJ
ejpam-4923	55	8	projection	projection	NOUN
ejpam-4923	55	9	map	map	NOUN
ejpam-4923	55	10	p	p	X
ejpam-4923	55	11	:	:	PUNCT
ejpam-4923	55	12	su(1	su(1	NOUN
ejpam-4923	55	13	,	,	PUNCT
ejpam-4923	55	14	1	1	NUM
ejpam-4923	55	15	)	)	PUNCT
ejpam-4923	55	16	→	→	SYM
ejpam-4923	55	17	d	d	X
ejpam-4923	55	18	,	,	PUNCT
ejpam-4923	55	19	which	which	PRON
ejpam-4923	55	20	assigns	assign	VERB
ejpam-4923	55	21	to	to	ADP
ejpam-4923	55	22	an	an	DET
ejpam-4923	55	23	element	element	NOUN
ejpam-4923	55	24	of	of	ADP
ejpam-4923	55	25	su(1	su(1	NOUN
ejpam-4923	55	26	,	,	PUNCT
ejpam-4923	55	27	1	1	NUM
ejpam-4923	55	28	)	)	PUNCT
ejpam-4923	55	29	its	its	PRON
ejpam-4923	55	30	equivalence	equivalence	NOUN
ejpam-4923	55	31	class	class	NOUN
ejpam-4923	55	32	in	in	ADP
ejpam-4923	55	33	su(1	su(1	NOUN
ejpam-4923	55	34	,	,	PUNCT
ejpam-4923	55	35	1)/k	1)/k	NUM
ejpam-4923	55	36	:	:	PUNCT
ejpam-4923	55	37	p	p	X
ejpam-4923	55	38	:	:	PUNCT
ejpam-4923	55	39	(	(	PUNCT
ejpam-4923	55	40	α	α	X
ejpam-4923	55	41	β	β	X
ejpam-4923	55	42	β	β	X
ejpam-4923	55	43	α	α	NOUN
ejpam-4923	55	44	)	)	PUNCT
ejpam-4923	55	45	7→	7→	NUM
ejpam-4923	55	46	β	β	SYM
ejpam-4923	55	47	α	α	NOUN
ejpam-4923	55	48	.	.	PUNCT
ejpam-4923	56	1	(	(	PUNCT
ejpam-4923	56	2	14	14	NUM
ejpam-4923	56	3	)	)	PUNCT
ejpam-4923	56	4	a.	a.	NOUN
ejpam-4923	56	5	s.	s.	PROPN
ejpam-4923	56	6	alghamdi	alghamdi	PROPN
ejpam-4923	56	7	/	/	SYM
ejpam-4923	56	8	eur	eur	PROPN
ejpam-4923	56	9	.	.	PUNCT
ejpam-4923	57	1	j.	j.	PROPN
ejpam-4923	57	2	pure	pure	PROPN
ejpam-4923	57	3	appl	appl	PROPN
ejpam-4923	57	4	.	.	PROPN
ejpam-4923	57	5	math	math	PROPN
ejpam-4923	57	6	,	,	PUNCT
ejpam-4923	57	7	16	16	NUM
ejpam-4923	57	8	(	(	PUNCT
ejpam-4923	57	9	4	4	NUM
ejpam-4923	57	10	)	)	PUNCT
ejpam-4923	57	11	(	(	PUNCT
ejpam-4923	57	12	2023	2023	NUM
ejpam-4923	57	13	)	)	PUNCT
ejpam-4923	57	14	,	,	PUNCT
ejpam-4923	57	15	2348	2348	NUM
ejpam-4923	57	16	-	-	SYM
ejpam-4923	57	17	2367	2367	NUM
ejpam-4923	57	18	2351	2351	NUM
ejpam-4923	57	19	mapping	mapping	NOUN
ejpam-4923	57	20	r	r	NOUN
ejpam-4923	57	21	:	:	PUNCT
ejpam-4923	57	22	su(1	su(1	NOUN
ejpam-4923	57	23	,	,	PUNCT
ejpam-4923	57	24	1	1	NUM
ejpam-4923	57	25	)	)	PUNCT
ejpam-4923	57	26	→	→	SYM
ejpam-4923	57	27	k	k	PROPN
ejpam-4923	57	28	associates	associates	PROPN
ejpam-4923	57	29	f	f	PROPN
ejpam-4923	57	30	to	to	ADP
ejpam-4923	57	31	the	the	DET
ejpam-4923	57	32	natural	natural	ADJ
ejpam-4923	57	33	projection	projection	NOUN
ejpam-4923	57	34	p	p	NOUN
ejpam-4923	57	35	,	,	PUNCT
ejpam-4923	57	36	and	and	CCONJ
ejpam-4923	57	37	the	the	DET
ejpam-4923	57	38	section	section	NOUN
ejpam-4923	57	39	s	s	VERB
ejpam-4923	57	40	is	be	AUX
ejpam-4923	57	41	defined	define	VERB
ejpam-4923	57	42	as	as	SCONJ
ejpam-4923	57	43	follows	follow	VERB
ejpam-4923	57	44	:	:	PUNCT
ejpam-4923	57	45	r	r	NOUN
ejpam-4923	57	46	:	:	PUNCT
ejpam-4923	57	47	(	(	PUNCT
ejpam-4923	57	48	α	α	X
ejpam-4923	57	49	β	β	X
ejpam-4923	57	50	β	β	X
ejpam-4923	57	51	α	α	NOUN
ejpam-4923	57	52	)	)	PUNCT
ejpam-4923	57	53	7→	7→	PROPN
ejpam-4923	57	54	(	(	PUNCT
ejpam-4923	57	55	α	α	PROPN
ejpam-4923	57	56	|α|	|α|	PROPN
ejpam-4923	57	57	0	0	NUM
ejpam-4923	57	58	0	0	NUM
ejpam-4923	57	59	α	α	PRON
ejpam-4923	57	60	|α|	|α|	PROPN
ejpam-4923	57	61	)	)	PUNCT
ejpam-4923	57	62	(	(	PUNCT
ejpam-4923	57	63	15	15	NUM
ejpam-4923	57	64	)	)	PUNCT
ejpam-4923	57	65	for	for	ADP
ejpam-4923	57	66	the	the	DET
ejpam-4923	57	67	homogeneous	homogeneous	ADJ
ejpam-4923	57	68	space	space	NOUN
ejpam-4923	57	69	su(1	su(1	NOUN
ejpam-4923	57	70	,	,	PUNCT
ejpam-4923	57	71	1)/k	1)/k	NUM
ejpam-4923	57	72	defines	define	VERB
ejpam-4923	57	73	a	a	DET
ejpam-4923	57	74	left	left	ADJ
ejpam-4923	57	75	action	action	NOUN
ejpam-4923	57	76	denoted	denote	VERB
ejpam-4923	57	77	by	by	ADP
ejpam-4923	57	78	”	"	PUNCT
ejpam-4923	57	79	·	·	PUNCT
ejpam-4923	57	80	”	"	PUNCT
ejpam-4923	57	81	as	as	SCONJ
ejpam-4923	57	82	follows	follow	VERB
ejpam-4923	57	83	:	:	PUNCT
ejpam-4923	57	84	g	g	NOUN
ejpam-4923	57	85	:	:	PUNCT
ejpam-4923	57	86	u	u	NOUN
ejpam-4923	57	87	7→	7→	NUM
ejpam-4923	57	88	g	g	NOUN
ejpam-4923	57	89	·	·	PUNCT
ejpam-4923	57	90	u	u	NOUN
ejpam-4923	57	91	=	=	PROPN
ejpam-4923	57	92	p(g	p(g	PROPN
ejpam-4923	57	93	∗	∗	NOUN
ejpam-4923	57	94	s(u	s(u	PROPN
ejpam-4923	57	95	)	)	PUNCT
ejpam-4923	57	96	)	)	PUNCT
ejpam-4923	57	97	,	,	PUNCT
ejpam-4923	57	98	(	(	PUNCT
ejpam-4923	57	99	16	16	NUM
ejpam-4923	57	100	)	)	PUNCT
ejpam-4923	57	101	where	where	SCONJ
ejpam-4923	57	102	∗	∗	NOUN
ejpam-4923	57	103	is	be	AUX
ejpam-4923	57	104	the	the	DET
ejpam-4923	57	105	multiplication	multiplication	NOUN
ejpam-4923	57	106	of	of	ADP
ejpam-4923	57	107	the	the	DET
ejpam-4923	57	108	group	group	NOUN
ejpam-4923	57	109	su(1	su(1	NOUN
ejpam-4923	57	110	,	,	PUNCT
ejpam-4923	57	111	1	1	NUM
ejpam-4923	57	112	)	)	PUNCT
ejpam-4923	57	113	.	.	PUNCT
ejpam-4923	58	1	the	the	DET
ejpam-4923	58	2	invariant	invariant	ADJ
ejpam-4923	58	3	measure	measure	NOUN
ejpam-4923	58	4	dµ(u	dµ(u	NOUN
ejpam-4923	58	5	)	)	PUNCT
ejpam-4923	58	6	on	on	ADP
ejpam-4923	58	7	d	d	PROPN
ejpam-4923	58	8	comes	come	VERB
ejpam-4923	58	9	from	from	ADP
ejpam-4923	58	10	the	the	DET
ejpam-4923	58	11	decomposition	decomposition	NOUN
ejpam-4923	58	12	dg	dg	VERB
ejpam-4923	58	13	=	=	SYM
ejpam-4923	58	14	dµ(u)dk	dµ(u)dk	NOUN
ejpam-4923	58	15	,	,	PUNCT
ejpam-4923	58	16	where	where	SCONJ
ejpam-4923	58	17	dg	dg	NOUN
ejpam-4923	58	18	and	and	CCONJ
ejpam-4923	58	19	dk	dk	PROPN
ejpam-4923	58	20	are	be	AUX
ejpam-4923	58	21	the	the	DET
ejpam-4923	58	22	haar	haar	NOUN
ejpam-4923	58	23	measures	measure	NOUN
ejpam-4923	58	24	on	on	ADP
ejpam-4923	58	25	g	g	PROPN
ejpam-4923	58	26	=	=	SYM
ejpam-4923	58	27	su(1	su(1	NOUN
ejpam-4923	58	28	,	,	PUNCT
ejpam-4923	58	29	1	1	NUM
ejpam-4923	58	30	)	)	PUNCT
ejpam-4923	58	31	and	and	CCONJ
ejpam-4923	58	32	k	k	PROPN
ejpam-4923	58	33	respectively	respectively	ADV
ejpam-4923	58	34	.	.	PUNCT
ejpam-4923	59	1	the	the	DET
ejpam-4923	59	2	measure	measure	NOUN
ejpam-4923	59	3	dµ(u	dµ(u	VERB
ejpam-4923	59	4	)	)	PUNCT
ejpam-4923	59	5	is	be	AUX
ejpam-4923	59	6	given	give	VERB
ejpam-4923	59	7	by	by	ADP
ejpam-4923	59	8	dµ(u	dµ(u	NOUN
ejpam-4923	59	9	)	)	PUNCT
ejpam-4923	60	1	=	=	SYM
ejpam-4923	60	2	du	du	PROPN
ejpam-4923	60	3	∧	∧	PROPN
ejpam-4923	60	4	dū	dū	NOUN
ejpam-4923	60	5	(	(	PUNCT
ejpam-4923	60	6	1−	1−	NUM
ejpam-4923	60	7	|u|2)2	|u|2)2	NOUN
ejpam-4923	60	8	.	.	PUNCT
ejpam-4923	61	1	(	(	PUNCT
ejpam-4923	61	2	17	17	NUM
ejpam-4923	61	3	)	)	PUNCT
ejpam-4923	61	4	let	let	VERB
ejpam-4923	61	5	χn	χn	X
ejpam-4923	61	6	:	:	PUNCT
ejpam-4923	61	7	t	t	PROPN
ejpam-4923	61	8	→	→	SYM
ejpam-4923	61	9	c	c	X
ejpam-4923	61	10	be	be	AUX
ejpam-4923	61	11	a	a	DET
ejpam-4923	61	12	character	character	NOUN
ejpam-4923	61	13	of	of	ADP
ejpam-4923	61	14	the	the	DET
ejpam-4923	61	15	subgroup	subgroup	NOUN
ejpam-4923	61	16	k	k	PROPN
ejpam-4923	61	17	≃	≃	PROPN
ejpam-4923	61	18	t	t	PROPN
ejpam-4923	61	19	defined	define	VERB
ejpam-4923	61	20	as	as	ADP
ejpam-4923	61	21	follows	follow	VERB
ejpam-4923	61	22	:	:	PUNCT
ejpam-4923	61	23	χn(w	χn(w	PUNCT
ejpam-4923	61	24	)	)	PUNCT
ejpam-4923	62	1	=	=	SYM
ejpam-4923	62	2	wn	wn	PROPN
ejpam-4923	62	3	,	,	PUNCT
ejpam-4923	62	4	n	n	PROPN
ejpam-4923	62	5	∈	∈	PROPN
ejpam-4923	62	6	z.	z.	PROPN
ejpam-4923	62	7	(	(	PUNCT
ejpam-4923	62	8	18	18	NUM
ejpam-4923	62	9	)	)	PUNCT
ejpam-4923	62	10	this	this	DET
ejpam-4923	62	11	character	character	NOUN
ejpam-4923	62	12	induces	induce	VERB
ejpam-4923	62	13	a	a	DET
ejpam-4923	62	14	representation	representation	NOUN
ejpam-4923	62	15	of	of	ADP
ejpam-4923	62	16	su(1	su(1	NOUN
ejpam-4923	62	17	,	,	PUNCT
ejpam-4923	62	18	1	1	NUM
ejpam-4923	62	19	)	)	PUNCT
ejpam-4923	62	20	constructed	construct	VERB
ejpam-4923	62	21	in	in	ADP
ejpam-4923	62	22	the	the	DET
ejpam-4923	62	23	hilbert	hilbert	NOUN
ejpam-4923	62	24	space	space	NOUN
ejpam-4923	62	25	lχn	lχn	ADV
ejpam-4923	62	26	2	2	NUM
ejpam-4923	62	27	(	(	PUNCT
ejpam-4923	62	28	su(1	su(1	NOUN
ejpam-4923	62	29	,	,	PUNCT
ejpam-4923	62	30	1	1	NUM
ejpam-4923	62	31	)	)	PUNCT
ejpam-4923	62	32	)	)	PUNCT
ejpam-4923	62	33	,	,	PUNCT
ejpam-4923	62	34	consisting	consist	VERB
ejpam-4923	62	35	of	of	ADP
ejpam-4923	62	36	the	the	DET
ejpam-4923	62	37	functions	function	NOUN
ejpam-4923	62	38	fn	fn	NOUN
ejpam-4923	62	39	:	:	PUNCT
ejpam-4923	62	40	su(1	su(1	NOUN
ejpam-4923	62	41	,	,	PUNCT
ejpam-4923	62	42	1	1	NUM
ejpam-4923	62	43	)	)	PUNCT
ejpam-4923	62	44	→	→	PUNCT
ejpam-4923	62	45	c	c	NOUN
ejpam-4923	62	46	with	with	ADP
ejpam-4923	62	47	the	the	DET
ejpam-4923	62	48	property	property	NOUN
ejpam-4923	62	49	fn	fn	NOUN
ejpam-4923	63	1	[	[	X
ejpam-4923	63	2	(	(	PUNCT
ejpam-4923	63	3	α	α	X
ejpam-4923	63	4	β	β	X
ejpam-4923	63	5	β	β	X
ejpam-4923	63	6	α	α	NOUN
ejpam-4923	63	7	)	)	PUNCT
ejpam-4923	63	8	]	]	PUNCT
ejpam-4923	64	1	=	=	PUNCT
ejpam-4923	64	2	χn	χn	X
ejpam-4923	64	3	(	(	PUNCT
ejpam-4923	64	4	α	α	PROPN
ejpam-4923	64	5	|α|	|α|	PROPN
ejpam-4923	64	6	)	)	PUNCT
ejpam-4923	64	7	f	f	PROPN
ejpam-4923	64	8	(	(	PUNCT
ejpam-4923	64	9	β	β	X
ejpam-4923	64	10	α	α	NOUN
ejpam-4923	64	11	)	)	PUNCT
ejpam-4923	64	12	,	,	PUNCT
ejpam-4923	64	13	(	(	PUNCT
ejpam-4923	64	14	19	19	NUM
ejpam-4923	64	15	)	)	PUNCT
ejpam-4923	64	16	where	where	SCONJ
ejpam-4923	64	17	f	f	PROPN
ejpam-4923	64	18	∈	∈	PROPN
ejpam-4923	64	19	l2(d	l2(d	PROPN
ejpam-4923	64	20	)	)	PUNCT
ejpam-4923	64	21	.	.	PUNCT
ejpam-4923	65	1	then	then	ADV
ejpam-4923	65	2	,	,	PUNCT
ejpam-4923	65	3	the	the	DET
ejpam-4923	65	4	norm	norm	NOUN
ejpam-4923	65	5	of	of	ADP
ejpam-4923	65	6	the	the	DET
ejpam-4923	65	7	function	function	NOUN
ejpam-4923	65	8	fn	fn	NOUN
ejpam-4923	65	9	is	be	AUX
ejpam-4923	65	10	defined	define	VERB
ejpam-4923	65	11	as	as	SCONJ
ejpam-4923	65	12	follows	follow	VERB
ejpam-4923	65	13	:	:	PUNCT
ejpam-4923	65	14	∥fn∥2	∥fn∥2	NUM
ejpam-4923	66	1	=	=	SYM
ejpam-4923	66	2	∫	∫	PROPN
ejpam-4923	67	1	d	d	X
ejpam-4923	67	2	|f	|f	PROPN
ejpam-4923	67	3	(	(	PUNCT
ejpam-4923	67	4	u)|2	u)|2	NOUN
ejpam-4923	67	5	du	du	PROPN
ejpam-4923	67	6	∧	∧	PROPN
ejpam-4923	67	7	dū	dū	NOUN
ejpam-4923	67	8	(	(	PUNCT
ejpam-4923	67	9	1−	1−	NUM
ejpam-4923	67	10	|u|2)2	|u|2)2	NOUN
ejpam-4923	67	11	.	.	PUNCT
ejpam-4923	68	1	(	(	PUNCT
ejpam-4923	68	2	20	20	NUM
ejpam-4923	68	3	)	)	PUNCT
ejpam-4923	68	4	the	the	DET
ejpam-4923	68	5	space	space	NOUN
ejpam-4923	68	6	lχn	lχn	ADV
ejpam-4923	68	7	2	2	NUM
ejpam-4923	68	8	(	(	PUNCT
ejpam-4923	68	9	su(1	su(1	NOUN
ejpam-4923	68	10	,	,	PUNCT
ejpam-4923	68	11	1	1	NUM
ejpam-4923	68	12	)	)	PUNCT
ejpam-4923	68	13	)	)	PUNCT
ejpam-4923	68	14	is	be	AUX
ejpam-4923	68	15	invariant	invariant	ADJ
ejpam-4923	68	16	under	under	ADP
ejpam-4923	68	17	the	the	DET
ejpam-4923	68	18	left	left	ADJ
ejpam-4923	68	19	shift	shift	NOUN
ejpam-4923	68	20	of	of	ADP
ejpam-4923	68	21	the	the	DET
ejpam-4923	68	22	su(1	su(1	NOUN
ejpam-4923	68	23	,	,	PUNCT
ejpam-4923	68	24	1	1	NUM
ejpam-4923	68	25	)	)	PUNCT
ejpam-4923	68	26	group	group	NOUN
ejpam-4923	68	27	.	.	PUNCT
ejpam-4923	69	1	the	the	DET
ejpam-4923	69	2	restriction	restriction	NOUN
ejpam-4923	69	3	of	of	ADP
ejpam-4923	69	4	the	the	DET
ejpam-4923	69	5	left	left	ADJ
ejpam-4923	69	6	shift	shift	NOUN
ejpam-4923	69	7	on	on	ADP
ejpam-4923	69	8	lχn	lχn	ADV
ejpam-4923	69	9	2	2	NUM
ejpam-4923	69	10	(	(	PUNCT
ejpam-4923	69	11	su(1	su(1	NOUN
ejpam-4923	69	12	,	,	PUNCT
ejpam-4923	69	13	1	1	NUM
ejpam-4923	69	14	)	)	PUNCT
ejpam-4923	69	15	)	)	PUNCT
ejpam-4923	69	16	is	be	AUX
ejpam-4923	69	17	the	the	DET
ejpam-4923	69	18	left	left	ADJ
ejpam-4923	69	19	regular	regular	ADJ
ejpam-4923	69	20	representation	representation	NOUN
ejpam-4923	69	21	of	of	ADP
ejpam-4923	69	22	su(1	su(1	NOUN
ejpam-4923	69	23	,	,	PUNCT
ejpam-4923	69	24	1	1	NUM
ejpam-4923	69	25	)	)	PUNCT
ejpam-4923	69	26	,	,	PUNCT
ejpam-4923	69	27	which	which	PRON
ejpam-4923	69	28	can	can	AUX
ejpam-4923	69	29	be	be	AUX
ejpam-4923	69	30	written	write	VERB
ejpam-4923	69	31	as	as	SCONJ
ejpam-4923	69	32	follows	follow	VERB
ejpam-4923	69	33	:	:	PUNCT
ejpam-4923	70	1	[	[	X
ejpam-4923	70	2	λ(g)fn](g	λ(g)fn](g	NOUN
ejpam-4923	70	3	′	′	NUM
ejpam-4923	70	4	)	)	PUNCT
ejpam-4923	70	5	=	=	PRON
ejpam-4923	70	6	fn(g	fn(g	PUNCT
ejpam-4923	70	7	−1	−1	NOUN
ejpam-4923	70	8	∗	∗	NOUN
ejpam-4923	70	9	g′	g′	NOUN
ejpam-4923	70	10	)	)	PUNCT
ejpam-4923	70	11	,	,	PUNCT
ejpam-4923	70	12	(	(	PUNCT
ejpam-4923	70	13	21	21	NUM
ejpam-4923	70	14	)	)	PUNCT
ejpam-4923	70	15	where	where	SCONJ
ejpam-4923	70	16	∗	∗	NOUN
ejpam-4923	70	17	is	be	AUX
ejpam-4923	70	18	a	a	DET
ejpam-4923	70	19	matrix	matrix	NOUN
ejpam-4923	70	20	multiplication	multiplication	NOUN
ejpam-4923	70	21	.	.	PUNCT
ejpam-4923	71	1	the	the	DET
ejpam-4923	71	2	lifting	lifting	NOUN
ejpam-4923	71	3	map	map	NOUN
ejpam-4923	71	4	lχn	lχn	ADV
ejpam-4923	71	5	:	:	PUNCT
ejpam-4923	71	6	l2(d	l2(d	PROPN
ejpam-4923	71	7	)	)	PUNCT
ejpam-4923	71	8	→	→	SYM
ejpam-4923	71	9	lχn	lχn	ADV
ejpam-4923	71	10	2	2	NUM
ejpam-4923	71	11	(	(	PUNCT
ejpam-4923	71	12	su(1	su(1	NOUN
ejpam-4923	71	13	,	,	PUNCT
ejpam-4923	71	14	1	1	NUM
ejpam-4923	71	15	)	)	PUNCT
ejpam-4923	71	16	)	)	PUNCT
ejpam-4923	71	17	for	for	ADP
ejpam-4923	71	18	the	the	DET
ejpam-4923	71	19	subgroup	subgroup	PROPN
ejpam-4923	71	20	k	k	PROPN
ejpam-4923	71	21	and	and	CCONJ
ejpam-4923	71	22	its	its	PRON
ejpam-4923	71	23	character	character	NOUN
ejpam-4923	71	24	χn	χn	ADV
ejpam-4923	71	25	is	be	AUX
ejpam-4923	71	26	defined	define	VERB
ejpam-4923	71	27	as	as	SCONJ
ejpam-4923	71	28	follows	follow	VERB
ejpam-4923	71	29	:	:	PUNCT
ejpam-4923	71	30	[	[	X
ejpam-4923	71	31	lχnf	lχnf	ADV
ejpam-4923	71	32	]	]	PUNCT
ejpam-4923	71	33	(	(	PUNCT
ejpam-4923	71	34	α	α	X
ejpam-4923	71	35	β	β	X
ejpam-4923	71	36	β	β	X
ejpam-4923	71	37	α	α	NOUN
ejpam-4923	71	38	)	)	PUNCT
ejpam-4923	72	1	=	=	PUNCT
ejpam-4923	72	2	χn	χn	X
ejpam-4923	72	3	(	(	PUNCT
ejpam-4923	72	4	r	r	NOUN
ejpam-4923	72	5	(	(	PUNCT
ejpam-4923	72	6	α	α	X
ejpam-4923	72	7	β	β	X
ejpam-4923	72	8	β	β	X
ejpam-4923	72	9	α	α	NOUN
ejpam-4923	72	10	)	)	PUNCT
ejpam-4923	72	11	)	)	PUNCT
ejpam-4923	73	1	f	f	PROPN
ejpam-4923	73	2	(	(	PUNCT
ejpam-4923	73	3	p	p	X
ejpam-4923	73	4	(	(	PUNCT
ejpam-4923	73	5	α	α	X
ejpam-4923	73	6	β	β	X
ejpam-4923	73	7	β	β	X
ejpam-4923	73	8	α	α	NOUN
ejpam-4923	73	9	)	)	PUNCT
ejpam-4923	73	10	)	)	PUNCT
ejpam-4923	74	1	=	=	PRON
ejpam-4923	74	2	(	(	PUNCT
ejpam-4923	74	3	ᾱ	ᾱ	NOUN
ejpam-4923	74	4	|α|	|α|	PROPN
ejpam-4923	74	5	)	)	PUNCT
ejpam-4923	74	6	n	n	PROPN
ejpam-4923	74	7	f	f	NOUN
ejpam-4923	74	8	(	(	PUNCT
ejpam-4923	74	9	β	β	X
ejpam-4923	74	10	α	α	NOUN
ejpam-4923	74	11	)	)	PUNCT
ejpam-4923	74	12	.	.	PUNCT
ejpam-4923	75	1	(	(	PUNCT
ejpam-4923	75	2	22	22	X
ejpam-4923	75	3	)	)	PUNCT
ejpam-4923	75	4	the	the	DET
ejpam-4923	75	5	pulling	pull	VERB
ejpam-4923	75	6	map	map	NOUN
ejpam-4923	75	7	is	be	AUX
ejpam-4923	75	8	given	give	VERB
ejpam-4923	75	9	by	by	ADP
ejpam-4923	75	10	the	the	DET
ejpam-4923	75	11	following	following	NOUN
ejpam-4923	75	12	:	:	PUNCT
ejpam-4923	75	13	p	p	X
ejpam-4923	75	14	:	:	PUNCT
ejpam-4923	75	15	lχn	lχn	ADV
ejpam-4923	75	16	2	2	NUM
ejpam-4923	75	17	(	(	PUNCT
ejpam-4923	75	18	su(1	su(1	NOUN
ejpam-4923	75	19	,	,	PUNCT
ejpam-4923	75	20	1	1	NUM
ejpam-4923	75	21	)	)	PUNCT
ejpam-4923	75	22	)	)	PUNCT
ejpam-4923	76	1	→	→	PUNCT
ejpam-4923	76	2	l2(d	l2(d	PROPN
ejpam-4923	76	3	)	)	PUNCT
ejpam-4923	76	4	,	,	PUNCT
ejpam-4923	76	5	a.	a.	PROPN
ejpam-4923	76	6	s.	s.	PROPN
ejpam-4923	76	7	alghamdi	alghamdi	PROPN
ejpam-4923	76	8	/	/	SYM
ejpam-4923	76	9	eur	eur	PROPN
ejpam-4923	76	10	.	.	PUNCT
ejpam-4923	77	1	j.	j.	PROPN
ejpam-4923	77	2	pure	pure	PROPN
ejpam-4923	77	3	appl	appl	PROPN
ejpam-4923	77	4	.	.	PROPN
ejpam-4923	77	5	math	math	PROPN
ejpam-4923	77	6	,	,	PUNCT
ejpam-4923	77	7	16	16	NUM
ejpam-4923	77	8	(	(	PUNCT
ejpam-4923	77	9	4	4	NUM
ejpam-4923	77	10	)	)	PUNCT
ejpam-4923	77	11	(	(	PUNCT
ejpam-4923	77	12	2023	2023	NUM
ejpam-4923	77	13	)	)	PUNCT
ejpam-4923	77	14	,	,	PUNCT
ejpam-4923	77	15	2348	2348	NUM
ejpam-4923	77	16	-	-	SYM
ejpam-4923	77	17	2367	2367	NUM
ejpam-4923	77	18	2352	2352	NUM
ejpam-4923	77	19	p(f	p(f	PROPN
ejpam-4923	77	20	(	(	PUNCT
ejpam-4923	77	21	w	w	PROPN
ejpam-4923	77	22	,	,	PUNCT
ejpam-4923	77	23	w̄	w̄	NOUN
ejpam-4923	77	24	)	)	PUNCT
ejpam-4923	77	25	)	)	PUNCT
ejpam-4923	78	1	=	=	SYM
ejpam-4923	78	2	f	f	PROPN
ejpam-4923	78	3	(	(	PUNCT
ejpam-4923	78	4	s(w	s(w	PROPN
ejpam-4923	78	5	)	)	PUNCT
ejpam-4923	78	6	)	)	PUNCT
ejpam-4923	78	7	,	,	PUNCT
ejpam-4923	78	8	such	such	ADJ
ejpam-4923	78	9	that	that	SCONJ
ejpam-4923	78	10	p	p	PROPN
ejpam-4923	78	11	◦	◦	NOUN
ejpam-4923	78	12	lχn	lχn	ADV
ejpam-4923	78	13	=	=	VERB
ejpam-4923	79	1	i	i	PROPN
ejpam-4923	79	2	and	and	CCONJ
ejpam-4923	79	3	lχn	lχn	ADV
ejpam-4923	79	4	◦	◦	NOUN
ejpam-4923	79	5	p	p	NOUN
ejpam-4923	79	6	=	=	PUNCT
ejpam-4923	79	7	i.	i.	NOUN
ejpam-4923	79	8	therefore	therefore	ADV
ejpam-4923	79	9	,	,	PUNCT
ejpam-4923	79	10	the	the	DET
ejpam-4923	79	11	representation	representation	NOUN
ejpam-4923	79	12	πn	πn	INTJ
ejpam-4923	79	13	:	:	PUNCT
ejpam-4923	79	14	l2(d	l2(d	PROPN
ejpam-4923	79	15	)	)	PUNCT
ejpam-4923	79	16	→	→	SYM
ejpam-4923	79	17	l2(d	l2(d	PROPN
ejpam-4923	79	18	)	)	PUNCT
ejpam-4923	79	19	,	,	PUNCT
ejpam-4923	79	20	which	which	PRON
ejpam-4923	79	21	is	be	AUX
ejpam-4923	79	22	induced	induce	VERB
ejpam-4923	79	23	by	by	ADP
ejpam-4923	79	24	the	the	DET
ejpam-4923	79	25	character	character	NOUN
ejpam-4923	79	26	χn	χn	X
ejpam-4923	79	27	is	be	AUX
ejpam-4923	79	28	given	give	VERB
ejpam-4923	79	29	by	by	ADP
ejpam-4923	79	30	the	the	DET
ejpam-4923	79	31	following	following	NOUN
ejpam-4923	79	32	:	:	PUNCT
ejpam-4923	79	33	[	[	PUNCT
ejpam-4923	79	34	πn	πn	INTJ
ejpam-4923	79	35	(	(	PUNCT
ejpam-4923	79	36	α	α	X
ejpam-4923	79	37	β	β	X
ejpam-4923	79	38	β	β	X
ejpam-4923	79	39	α	α	NOUN
ejpam-4923	79	40	)	)	PUNCT
ejpam-4923	79	41	]	]	PUNCT
ejpam-4923	80	1	=	=	PUNCT
ejpam-4923	80	2	p	p	X
ejpam-4923	80	3	◦	◦	NOUN
ejpam-4923	80	4	λ	λ	X
ejpam-4923	80	5	(	(	PUNCT
ejpam-4923	80	6	α	α	X
ejpam-4923	80	7	β	β	X
ejpam-4923	80	8	β	β	X
ejpam-4923	80	9	α	α	NOUN
ejpam-4923	80	10	)	)	PUNCT
ejpam-4923	80	11	◦	◦	NOUN
ejpam-4923	80	12	lχn	lχn	ADV
ejpam-4923	80	13	.	.	PUNCT
ejpam-4923	81	1	by	by	ADP
ejpam-4923	81	2	simple	simple	ADJ
ejpam-4923	81	3	calculation	calculation	NOUN
ejpam-4923	81	4	,	,	PUNCT
ejpam-4923	81	5	we	we	PRON
ejpam-4923	81	6	get	get	VERB
ejpam-4923	81	7	:	:	PUNCT
ejpam-4923	81	8	[	[	X
ejpam-4923	81	9	πn(g)f	πn(g)f	X
ejpam-4923	81	10	]	]	X
ejpam-4923	81	11	(	(	PUNCT
ejpam-4923	81	12	w	w	NOUN
ejpam-4923	81	13	,	,	PUNCT
ejpam-4923	81	14	w̄	w̄	NOUN
ejpam-4923	81	15	)	)	PUNCT
ejpam-4923	81	16	=	=	SYM
ejpam-4923	82	1	(	(	PUNCT
ejpam-4923	82	2	α−	α−	ADP
ejpam-4923	82	3	βw)n	βw)n	SYM
ejpam-4923	82	4	|α−	|α−	ADJ
ejpam-4923	82	5	βw|n	βw|n	X
ejpam-4923	83	1	f	f	X
ejpam-4923	83	2	(	(	PUNCT
ejpam-4923	83	3	αw	αw	ADP
ejpam-4923	83	4	−	−	PROPN
ejpam-4923	83	5	β	β	X
ejpam-4923	83	6	α−	α−	ADP
ejpam-4923	83	7	βw	βw	ADV
ejpam-4923	83	8	,	,	PUNCT
ejpam-4923	83	9	αw	αw	ADP
ejpam-4923	83	10	−	−	PROPN
ejpam-4923	83	11	β	β	X
ejpam-4923	83	12	α−	α−	ADP
ejpam-4923	83	13	βw	βw	ADP
ejpam-4923	83	14	)	)	PUNCT
ejpam-4923	83	15	=	=	SYM
ejpam-4923	84	1	(	(	PUNCT
ejpam-4923	84	2	α−	α−	ADP
ejpam-4923	84	3	βw	βw	ADP
ejpam-4923	84	4	α−	α−	ADP
ejpam-4923	84	5	βw̄	βw̄	NOUN
ejpam-4923	84	6	)	)	PUNCT
ejpam-4923	84	7	n	n	X
ejpam-4923	84	8	2	2	NUM
ejpam-4923	84	9	f	f	X
ejpam-4923	84	10	(	(	PUNCT
ejpam-4923	84	11	αw	αw	ADP
ejpam-4923	84	12	−	−	PROPN
ejpam-4923	84	13	β	β	X
ejpam-4923	84	14	α−	α−	ADP
ejpam-4923	84	15	βw	βw	ADV
ejpam-4923	84	16	,	,	PUNCT
ejpam-4923	84	17	αw	αw	ADP
ejpam-4923	84	18	−	−	PROPN
ejpam-4923	84	19	β	β	X
ejpam-4923	84	20	α−	α−	ADP
ejpam-4923	84	21	βw	βw	ADP
ejpam-4923	84	22	)	)	PUNCT
ejpam-4923	84	23	.	.	PUNCT
ejpam-4923	85	1	(	(	PUNCT
ejpam-4923	85	2	23	23	NUM
ejpam-4923	85	3	)	)	PUNCT
ejpam-4923	86	1	[	[	X
ejpam-4923	86	2	9	9	NUM
ejpam-4923	86	3	]	]	PUNCT
ejpam-4923	86	4	for	for	ADP
ejpam-4923	86	5	n	n	PRON
ejpam-4923	86	6	∈	∈	PROPN
ejpam-4923	86	7	z	z	PROPN
ejpam-4923	86	8	,	,	PUNCT
ejpam-4923	86	9	an	an	DET
ejpam-4923	86	10	n	n	ADV
ejpam-4923	86	11	-	-	PUNCT
ejpam-4923	86	12	peeling	peel	VERB
ejpam-4923	86	13	is	be	AUX
ejpam-4923	86	14	an	an	DET
ejpam-4923	86	15	isometry	isometry	ADJ
ejpam-4923	86	16	pn	pn	NOUN
ejpam-4923	86	17	:	:	PUNCT
ejpam-4923	86	18	l2(d	l2(d	PROPN
ejpam-4923	86	19	,	,	PUNCT
ejpam-4923	86	20	dw	dw	NOUN
ejpam-4923	86	21	)	)	PUNCT
ejpam-4923	86	22	→	→	SYM
ejpam-4923	86	23	l2(d	l2(d	PROPN
ejpam-4923	86	24	,	,	PUNCT
ejpam-4923	86	25	(	(	PUNCT
ejpam-4923	86	26	1−|w|2)n−2dw∧dw̄	1−|w|2)n−2dw∧dw̄	NUM
ejpam-4923	86	27	)	)	PUNCT
ejpam-4923	86	28	defined	define	VERB
ejpam-4923	86	29	as	as	SCONJ
ejpam-4923	86	30	follows	follow	VERB
ejpam-4923	86	31	:	:	PUNCT
ejpam-4923	86	32	pn	pn	NOUN
ejpam-4923	86	33	:	:	PUNCT
ejpam-4923	86	34	f(w	f(w	PROPN
ejpam-4923	86	35	)	)	PUNCT
ejpam-4923	86	36	7→	7→	NOUN
ejpam-4923	87	1	[	[	X
ejpam-4923	87	2	pnf	pnf	X
ejpam-4923	87	3	]	]	X
ejpam-4923	87	4	(	(	PUNCT
ejpam-4923	87	5	w	w	NOUN
ejpam-4923	87	6	)	)	PUNCT
ejpam-4923	87	7	=	=	SYM
ejpam-4923	87	8	f(w	f(w	PROPN
ejpam-4923	87	9	)	)	PUNCT
ejpam-4923	87	10	(	(	PUNCT
ejpam-4923	87	11	1−	1−	NUM
ejpam-4923	87	12	|w|2	|w|2	NOUN
ejpam-4923	87	13	)	)	PUNCT
ejpam-4923	87	14	n	n	PRON
ejpam-4923	87	15	2	2	NUM
ejpam-4923	87	16	,	,	PUNCT
ejpam-4923	87	17	w	w	NOUN
ejpam-4923	87	18	=	=	SYM
ejpam-4923	87	19	u+	u+	NUM
ejpam-4923	87	20	iv	iv	NUM
ejpam-4923	87	21	.	.	PUNCT
ejpam-4923	88	1	(	(	PUNCT
ejpam-4923	88	2	24	24	NUM
ejpam-4923	88	3	)	)	PUNCT
ejpam-4923	88	4	the	the	DET
ejpam-4923	88	5	representation	representation	NOUN
ejpam-4923	88	6	(	(	PUNCT
ejpam-4923	88	7	23	23	NUM
ejpam-4923	88	8	)	)	PUNCT
ejpam-4923	88	9	is	be	AUX
ejpam-4923	88	10	intertwined	intertwine	VERB
ejpam-4923	88	11	π̆n	π̆n	NUM
ejpam-4923	88	12	◦	◦	NOUN
ejpam-4923	88	13	pn	pn	NOUN
ejpam-4923	88	14	=	=	SYM
ejpam-4923	88	15	pn	pn	PROPN
ejpam-4923	88	16	◦	◦	NOUN
ejpam-4923	88	17	πn	πn	INTJ
ejpam-4923	88	18	by	by	ADP
ejpam-4923	88	19	the	the	DET
ejpam-4923	88	20	n	n	ADV
ejpam-4923	88	21	-	-	PUNCT
ejpam-4923	88	22	peeling	peel	VERB
ejpam-4923	88	23	with	with	ADP
ejpam-4923	88	24	the	the	DET
ejpam-4923	88	25	following	follow	VERB
ejpam-4923	88	26	representation	representation	NOUN
ejpam-4923	88	27	:	:	PUNCT
ejpam-4923	89	1	[	[	X
ejpam-4923	89	2	π̆n(g)f	π̆n(g)f	X
ejpam-4923	89	3	]	]	X
ejpam-4923	89	4	(	(	PUNCT
ejpam-4923	89	5	w	w	NOUN
ejpam-4923	89	6	)	)	PUNCT
ejpam-4923	89	7	=	=	SYM
ejpam-4923	89	8	(	(	PUNCT
ejpam-4923	89	9	α−	α−	ADP
ejpam-4923	89	10	βw)−nf	βw)−nf	PROPN
ejpam-4923	89	11	(	(	PUNCT
ejpam-4923	89	12	αw	αw	ADP
ejpam-4923	89	13	−	−	PROPN
ejpam-4923	89	14	β	β	X
ejpam-4923	89	15	α−	α−	ADP
ejpam-4923	89	16	βw	βw	ADP
ejpam-4923	89	17	)	)	PUNCT
ejpam-4923	89	18	,	,	PUNCT
ejpam-4923	89	19	(	(	PUNCT
ejpam-4923	89	20	25	25	NUM
ejpam-4923	89	21	)	)	PUNCT
ejpam-4923	89	22	which	which	PRON
ejpam-4923	89	23	is	be	AUX
ejpam-4923	89	24	unitary	unitary	ADJ
ejpam-4923	89	25	in	in	ADP
ejpam-4923	89	26	l2(d	l2(d	PROPN
ejpam-4923	89	27	,	,	PUNCT
ejpam-4923	89	28	(	(	PUNCT
ejpam-4923	89	29	1	1	NUM
ejpam-4923	89	30	−	−	NOUN
ejpam-4923	89	31	|w|2)n−2dw	|w|2)n−2dw	ADJ
ejpam-4923	89	32	∧	∧	NOUN
ejpam-4923	89	33	dw̄	dw̄	NOUN
ejpam-4923	89	34	)	)	PUNCT
ejpam-4923	89	35	.	.	PUNCT
ejpam-4923	90	1	the	the	DET
ejpam-4923	90	2	demonstration	demonstration	NOUN
ejpam-4923	90	3	of	of	ADP
ejpam-4923	90	4	the	the	DET
ejpam-4923	90	5	intertwining	intertwine	VERB
ejpam-4923	90	6	properties	property	NOUN
ejpam-4923	90	7	is	be	AUX
ejpam-4923	90	8	based	base	VERB
ejpam-4923	90	9	on	on	ADP
ejpam-4923	90	10	the	the	DET
ejpam-4923	90	11	following	follow	VERB
ejpam-4923	90	12	analogue	analogue	NOUN
ejpam-4923	90	13	of	of	ADP
ejpam-4923	90	14	identity	identity	NOUN
ejpam-4923	90	15	for	for	ADP
ejpam-4923	90	16	the	the	DET
ejpam-4923	90	17	unit	unit	NOUN
ejpam-4923	90	18	disc	disc	NOUN
ejpam-4923	90	19	:	:	PUNCT
ejpam-4923	90	20	1−	1−	NUM
ejpam-4923	90	21	∣∣∣∣αw	∣∣∣∣αw	NOUN
ejpam-4923	90	22	−	−	PROPN
ejpam-4923	90	23	β	β	X
ejpam-4923	90	24	α−	α−	ADP
ejpam-4923	90	25	βw	βw	ADV
ejpam-4923	90	26	∣∣∣∣	∣∣∣∣	NOUN
ejpam-4923	90	27	=	=	SYM
ejpam-4923	90	28	1−	1−	NUM
ejpam-4923	90	29	|w|2	|w|2	PROPN
ejpam-4923	90	30	|α−	|α−	ADJ
ejpam-4923	90	31	βw|2	βw|2	NOUN
ejpam-4923	90	32	.	.	PUNCT
ejpam-4923	91	1	the	the	DET
ejpam-4923	91	2	matrix	matrix	NOUN
ejpam-4923	91	3	(	(	PUNCT
ejpam-4923	91	4	α	α	X
ejpam-4923	91	5	β	β	X
ejpam-4923	91	6	β	β	X
ejpam-4923	91	7	α	α	NOUN
ejpam-4923	91	8	)	)	PUNCT
ejpam-4923	91	9	∈	∈	PROPN
ejpam-4923	91	10	su(1	su(1	NOUN
ejpam-4923	91	11	,	,	PUNCT
ejpam-4923	91	12	1	1	NUM
ejpam-4923	91	13	)	)	PUNCT
ejpam-4923	91	14	is	be	AUX
ejpam-4923	91	15	transformed	transform	VERB
ejpam-4923	91	16	to	to	ADP
ejpam-4923	91	17	(	(	PUNCT
ejpam-4923	91	18	a	a	DET
ejpam-4923	91	19	b	b	NOUN
ejpam-4923	91	20	c	c	PROPN
ejpam-4923	91	21	d	d	NOUN
ejpam-4923	91	22	)	)	PUNCT
ejpam-4923	91	23	∈	∈	PROPN
ejpam-4923	91	24	sl2(r	sl2(r	PROPN
ejpam-4923	91	25	)	)	PUNCT
ejpam-4923	91	26	by	by	ADP
ejpam-4923	91	27	the	the	DET
ejpam-4923	91	28	identity	identity	NOUN
ejpam-4923	91	29	(	(	PUNCT
ejpam-4923	91	30	5	5	NUM
ejpam-4923	91	31	)	)	PUNCT
ejpam-4923	91	32	.	.	PUNCT
ejpam-4923	92	1	therefore	therefore	ADV
ejpam-4923	92	2	,	,	PUNCT
ejpam-4923	92	3	the	the	DET
ejpam-4923	92	4	representation	representation	NOUN
ejpam-4923	92	5	ρ̆kn	ρ̆kn	NOUN
ejpam-4923	92	6	can	can	AUX
ejpam-4923	92	7	be	be	AUX
ejpam-4923	92	8	transformed	transform	VERB
ejpam-4923	92	9	to	to	ADP
ejpam-4923	92	10	a	a	DET
ejpam-4923	92	11	holomorphic	holomorphic	ADJ
ejpam-4923	92	12	representation	representation	NOUN
ejpam-4923	92	13	of	of	ADP
ejpam-4923	92	14	the	the	DET
ejpam-4923	92	15	group	group	NOUN
ejpam-4923	92	16	sl2(r	sl2(r	NOUN
ejpam-4923	92	17	):	):	PUNCT
ejpam-4923	92	18	[	[	X
ejpam-4923	92	19	π̆n(g)f	π̆n(g)f	X
ejpam-4923	92	20	]	]	X
ejpam-4923	92	21	(	(	PUNCT
ejpam-4923	92	22	z	z	NOUN
ejpam-4923	92	23	)	)	PUNCT
ejpam-4923	92	24	=	=	PUNCT
ejpam-4923	92	25	(	(	PUNCT
ejpam-4923	92	26	d−	d−	PROPN
ejpam-4923	92	27	bz)−nf	bz)−nf	PROPN
ejpam-4923	92	28	(	(	PUNCT
ejpam-4923	92	29	az	az	NOUN
ejpam-4923	92	30	−	−	PROPN
ejpam-4923	92	31	c	c	PROPN
ejpam-4923	92	32	d−	d−	PROPN
ejpam-4923	92	33	bz	bz	PROPN
ejpam-4923	92	34	)	)	PUNCT
ejpam-4923	92	35	,	,	PUNCT
ejpam-4923	92	36	(	(	PUNCT
ejpam-4923	92	37	26	26	NUM
ejpam-4923	92	38	)	)	PUNCT
ejpam-4923	92	39	which	which	PRON
ejpam-4923	92	40	is	be	AUX
ejpam-4923	92	41	unitary	unitary	ADJ
ejpam-4923	92	42	on	on	ADP
ejpam-4923	92	43	the	the	DET
ejpam-4923	92	44	upper	upper	ADJ
ejpam-4923	92	45	half	half	ADJ
ejpam-4923	92	46	-	-	PUNCT
ejpam-4923	92	47	plane	plane	NOUN
ejpam-4923	92	48	where	where	SCONJ
ejpam-4923	92	49	z	z	NOUN
ejpam-4923	92	50	=	=	PUNCT
ejpam-4923	92	51	x	x	PUNCT
ejpam-4923	92	52	+	+	NUM
ejpam-4923	92	53	iy	iy	PROPN
ejpam-4923	92	54	∈	∈	PROPN
ejpam-4923	92	55	r2	r2	PROPN
ejpam-4923	92	56	+	+	CCONJ
ejpam-4923	92	57	with	with	ADP
ejpam-4923	92	58	the	the	DET
ejpam-4923	92	59	measure	measure	NOUN
ejpam-4923	92	60	dµ(g	dµ(g	PUNCT
ejpam-4923	92	61	)	)	PUNCT
ejpam-4923	92	62	=	=	SYM
ejpam-4923	92	63	dxdy	dxdy	PROPN
ejpam-4923	92	64	y2	y2	PROPN
ejpam-4923	92	65	.	.	PUNCT
ejpam-4923	93	1	a.	a.	PROPN
ejpam-4923	93	2	s.	s.	PROPN
ejpam-4923	93	3	alghamdi	alghamdi	PROPN
ejpam-4923	93	4	/	/	SYM
ejpam-4923	93	5	eur	eur	PROPN
ejpam-4923	93	6	.	.	PUNCT
ejpam-4923	94	1	j.	j.	PROPN
ejpam-4923	94	2	pure	pure	PROPN
ejpam-4923	94	3	appl	appl	PROPN
ejpam-4923	94	4	.	.	PROPN
ejpam-4923	94	5	math	math	PROPN
ejpam-4923	94	6	,	,	PUNCT
ejpam-4923	94	7	16	16	NUM
ejpam-4923	94	8	(	(	PUNCT
ejpam-4923	94	9	4	4	NUM
ejpam-4923	94	10	)	)	PUNCT
ejpam-4923	94	11	(	(	PUNCT
ejpam-4923	94	12	2023	2023	NUM
ejpam-4923	94	13	)	)	PUNCT
ejpam-4923	94	14	,	,	PUNCT
ejpam-4923	94	15	2348	2348	NUM
ejpam-4923	94	16	-	-	SYM
ejpam-4923	94	17	2367	2367	NUM
ejpam-4923	94	18	2353	2353	NUM
ejpam-4923	94	19	4	4	NUM
ejpam-4923	94	20	.	.	PUNCT
ejpam-4923	95	1	actions	action	NOUN
ejpam-4923	95	2	of	of	ADP
ejpam-4923	95	3	ladder	ladder	NOUN
ejpam-4923	95	4	operators	operator	NOUN
ejpam-4923	95	5	in	in	ADP
ejpam-4923	95	6	this	this	DET
ejpam-4923	95	7	section	section	NOUN
ejpam-4923	95	8	,	,	PUNCT
ejpam-4923	95	9	we	we	PRON
ejpam-4923	95	10	study	study	VERB
ejpam-4923	95	11	the	the	DET
ejpam-4923	95	12	left	left	ADJ
ejpam-4923	95	13	and	and	CCONJ
ejpam-4923	95	14	right	right	ADJ
ejpam-4923	95	15	actions	action	NOUN
ejpam-4923	95	16	of	of	ADP
ejpam-4923	95	17	the	the	DET
ejpam-4923	95	18	ladder	ladder	NOUN
ejpam-4923	95	19	operators	operator	NOUN
ejpam-4923	95	20	for	for	ADP
ejpam-4923	95	21	the	the	DET
ejpam-4923	95	22	representation	representation	NOUN
ejpam-4923	95	23	πn	πn	INTJ
ejpam-4923	95	24	given	give	VERB
ejpam-4923	95	25	by	by	ADP
ejpam-4923	95	26	(	(	PUNCT
ejpam-4923	95	27	23	23	NUM
ejpam-4923	95	28	)	)	PUNCT
ejpam-4923	95	29	.	.	PUNCT
ejpam-4923	96	1	first	first	ADV
ejpam-4923	96	2	,	,	PUNCT
ejpam-4923	96	3	the	the	DET
ejpam-4923	96	4	derived	derive	VERB
ejpam-4923	96	5	representations	representation	NOUN
ejpam-4923	96	6	are	be	AUX
ejpam-4923	96	7	given	give	VERB
ejpam-4923	96	8	as	as	SCONJ
ejpam-4923	96	9	follows	follow	VERB
ejpam-4923	96	10	:	:	PUNCT
ejpam-4923	97	1	[	[	X
ejpam-4923	97	2	ef	ef	X
ejpam-4923	97	3	]	]	PUNCT
ejpam-4923	97	4	(	(	PUNCT
ejpam-4923	97	5	w	w	PROPN
ejpam-4923	97	6	,	,	PUNCT
ejpam-4923	97	7	w	w	NOUN
ejpam-4923	97	8	)	)	PUNCT
ejpam-4923	97	9	=	=	SYM
ejpam-4923	97	10	d	d	NOUN
ejpam-4923	97	11	dt	dt	NOUN
ejpam-4923	97	12	πn(e	πn(e	PUNCT
ejpam-4923	97	13	tz̃)f(w	tz̃)f(w	NOUN
ejpam-4923	97	14	,	,	PUNCT
ejpam-4923	97	15	w)|t=0	w)|t=0	PROPN
ejpam-4923	97	16	=	=	PROPN
ejpam-4923	98	1	[	[	X
ejpam-4923	98	2	−ini	−ini	X
ejpam-4923	98	3	−	−	PROPN
ejpam-4923	98	4	2iw∂w	2iw∂w	NUM
ejpam-4923	99	1	+	+	CCONJ
ejpam-4923	99	2	2iw∂w̄]f(w	2iw∂w̄]f(w	NUM
ejpam-4923	99	3	,	,	PUNCT
ejpam-4923	99	4	w	w	NOUN
ejpam-4923	99	5	)	)	PUNCT
ejpam-4923	99	6	,	,	PUNCT
ejpam-4923	99	7	(	(	PUNCT
ejpam-4923	99	8	27	27	NUM
ejpam-4923	99	9	)	)	PUNCT
ejpam-4923	100	1	[	[	X
ejpam-4923	100	2	a1f	a1f	X
ejpam-4923	100	3	]	]	X
ejpam-4923	100	4	(	(	PUNCT
ejpam-4923	100	5	w	w	PROPN
ejpam-4923	100	6	,	,	PUNCT
ejpam-4923	100	7	w	w	NOUN
ejpam-4923	100	8	)	)	PUNCT
ejpam-4923	100	9	=	=	SYM
ejpam-4923	100	10	d	d	NOUN
ejpam-4923	100	11	dt	dt	NOUN
ejpam-4923	100	12	πn(e	πn(e	PUNCT
ejpam-4923	100	13	tã)f(w	tã)f(w	PROPN
ejpam-4923	100	14	,	,	PUNCT
ejpam-4923	100	15	w)|t=0	w)|t=0	NOUN
ejpam-4923	100	16	=	=	SYM
ejpam-4923	100	17	[	[	PUNCT
ejpam-4923	100	18	ni	ni	NOUN
ejpam-4923	100	19	4	4	NUM
ejpam-4923	100	20	(	(	PUNCT
ejpam-4923	100	21	w	w	NOUN
ejpam-4923	100	22	+	+	NUM
ejpam-4923	100	23	w)i	w)i	NOUN
ejpam-4923	100	24	+	+	CCONJ
ejpam-4923	100	25	i	i	NOUN
ejpam-4923	100	26	2	2	NUM
ejpam-4923	100	27	(	(	PUNCT
ejpam-4923	100	28	1	1	NUM
ejpam-4923	100	29	+	+	NUM
ejpam-4923	100	30	w2)∂w	w2)∂w	NOUN
ejpam-4923	100	31	−	−	NOUN
ejpam-4923	100	32	i	i	PRON
ejpam-4923	100	33	2	2	NUM
ejpam-4923	100	34	(	(	PUNCT
ejpam-4923	100	35	1	1	NUM
ejpam-4923	100	36	+	+	CCONJ
ejpam-4923	100	37	w2)∂w̄	w2)∂w̄	PUNCT
ejpam-4923	100	38	]	]	X
ejpam-4923	101	1	f(w	f(w	PROPN
ejpam-4923	101	2	,	,	PUNCT
ejpam-4923	101	3	w	w	NOUN
ejpam-4923	101	4	)	)	PUNCT
ejpam-4923	101	5	,	,	PUNCT
ejpam-4923	101	6	(	(	PUNCT
ejpam-4923	101	7	28	28	NUM
ejpam-4923	101	8	)	)	PUNCT
ejpam-4923	102	1	[	[	X
ejpam-4923	102	2	b1f	b1f	X
ejpam-4923	102	3	]	]	X
ejpam-4923	102	4	(	(	PUNCT
ejpam-4923	102	5	w	w	PROPN
ejpam-4923	102	6	,	,	PUNCT
ejpam-4923	102	7	w	w	NOUN
ejpam-4923	102	8	)	)	PUNCT
ejpam-4923	102	9	=	=	SYM
ejpam-4923	102	10	d	d	NOUN
ejpam-4923	102	11	dt	dt	NOUN
ejpam-4923	102	12	πn(e	πn(e	PUNCT
ejpam-4923	102	13	tb̃)f(w	tb̃)f(w	PROPN
ejpam-4923	102	14	,	,	PUNCT
ejpam-4923	102	15	w)|t=0	w)|t=0	NOUN
ejpam-4923	102	16	=	=	SYM
ejpam-4923	102	17	[	[	PUNCT
ejpam-4923	102	18	n	n	NUM
ejpam-4923	102	19	4	4	NUM
ejpam-4923	102	20	(	(	PUNCT
ejpam-4923	102	21	w	w	NOUN
ejpam-4923	102	22	−	−	PROPN
ejpam-4923	102	23	w̄)i	w̄)i	NOUN
ejpam-4923	102	24	+	+	CCONJ
ejpam-4923	102	25	1	1	NUM
ejpam-4923	102	26	2	2	NUM
ejpam-4923	102	27	(	(	PUNCT
ejpam-4923	102	28	w2	w2	NOUN
ejpam-4923	102	29	−	−	PROPN
ejpam-4923	102	30	1)∂w	1)∂w	NOUN
ejpam-4923	102	31	+	+	CCONJ
ejpam-4923	102	32	1	1	NUM
ejpam-4923	102	33	2	2	NUM
ejpam-4923	102	34	(	(	PUNCT
ejpam-4923	102	35	w2	w2	NOUN
ejpam-4923	102	36	−	−	PROPN
ejpam-4923	102	37	1)∂w̄	1)∂w̄	PROPN
ejpam-4923	102	38	]	]	PUNCT
ejpam-4923	102	39	f(w	f(w	PROPN
ejpam-4923	102	40	,	,	PUNCT
ejpam-4923	102	41	w	w	NOUN
ejpam-4923	102	42	)	)	PUNCT
ejpam-4923	102	43	.	.	PUNCT
ejpam-4923	103	1	(	(	PUNCT
ejpam-4923	103	2	29	29	NUM
ejpam-4923	103	3	)	)	PUNCT
ejpam-4923	103	4	the	the	DET
ejpam-4923	103	5	ladder	ladder	NOUN
ejpam-4923	103	6	operators	operator	NOUN
ejpam-4923	103	7	are	be	AUX
ejpam-4923	103	8	defined	define	VERB
ejpam-4923	103	9	as	as	ADP
ejpam-4923	103	10	l+	l+	NOUN
ejpam-4923	103	11	=	=	SYM
ejpam-4923	103	12	b1	b1	NOUN
ejpam-4923	103	13	−	−	NOUN
ejpam-4923	103	14	ia1	ia1	NOUN
ejpam-4923	103	15	=	=	SYM
ejpam-4923	103	16	n	n	PRON
ejpam-4923	103	17	2	2	NUM
ejpam-4923	103	18	wi	wi	PROPN
ejpam-4923	103	19	+	+	CCONJ
ejpam-4923	103	20	w2∂w	w2∂w	PROPN
ejpam-4923	103	21	−	−	PROPN
ejpam-4923	103	22	∂w	∂w	PROPN
ejpam-4923	103	23	,	,	PUNCT
ejpam-4923	103	24	l−	l−	NOUN
ejpam-4923	103	25	=	=	NOUN
ejpam-4923	103	26	b1	b1	NOUN
ejpam-4923	103	27	+	+	CCONJ
ejpam-4923	103	28	ia1	ia1	NOUN
ejpam-4923	103	29	=	=	SYM
ejpam-4923	104	1	−n	−n	NOUN
ejpam-4923	104	2	2	2	NUM
ejpam-4923	104	3	wi	wi	PROPN
ejpam-4923	104	4	+	+	CCONJ
ejpam-4923	104	5	w̄2∂w	w̄2∂w	X
ejpam-4923	104	6	−	−	PROPN
ejpam-4923	104	7	∂w	∂w	PROPN
ejpam-4923	104	8	,	,	PUNCT
ejpam-4923	104	9	and	and	CCONJ
ejpam-4923	104	10	satisfy	satisfy	VERB
ejpam-4923	104	11	the	the	DET
ejpam-4923	104	12	following	follow	VERB
ejpam-4923	104	13	relations	relation	NOUN
ejpam-4923	104	14	:	:	PUNCT
ejpam-4923	105	1	[	[	X
ejpam-4923	105	2	e	e	NOUN
ejpam-4923	105	3	,	,	PUNCT
ejpam-4923	105	4	l±	l±	X
ejpam-4923	105	5	]	]	X
ejpam-4923	105	6	=	=	PUNCT
ejpam-4923	105	7	±2il±	±2il±	ADJ
ejpam-4923	105	8	,	,	PUNCT
ejpam-4923	105	9	[	[	X
ejpam-4923	105	10	l+	l+	NOUN
ejpam-4923	105	11	,	,	PUNCT
ejpam-4923	105	12	l−	l−	PROPN
ejpam-4923	105	13	]	]	X
ejpam-4923	105	14	=	=	PUNCT
ejpam-4923	105	15	−ie	−ie	NOUN
ejpam-4923	105	16	.	.	PUNCT
ejpam-4923	106	1	(	(	PUNCT
ejpam-4923	106	2	30	30	NUM
ejpam-4923	106	3	)	)	PUNCT
ejpam-4923	106	4	the	the	DET
ejpam-4923	106	5	casimir	casimir	NOUN
ejpam-4923	106	6	operator	operator	NOUN
ejpam-4923	106	7	is	be	AUX
ejpam-4923	106	8	given	give	VERB
ejpam-4923	106	9	by	by	ADP
ejpam-4923	106	10	dπn(c	dπn(c	PROPN
ejpam-4923	106	11	)	)	PUNCT
ejpam-4923	106	12	=	=	SYM
ejpam-4923	106	13	e2	e2	PROPN
ejpam-4923	106	14	−	−	PROPN
ejpam-4923	106	15	2[l+l−	2[l+l−	NUM
ejpam-4923	106	16	+	+	SYM
ejpam-4923	106	17	l−l+	l−l+	PROPN
ejpam-4923	106	18	]	]	X
ejpam-4923	106	19	=	=	SYM
ejpam-4923	106	20	(	(	PUNCT
ejpam-4923	106	21	ww	ww	PROPN
ejpam-4923	106	22	−	−	PROPN
ejpam-4923	106	23	1)[n2i	1)[n2i	PROPN
ejpam-4923	106	24	+	+	NUM
ejpam-4923	106	25	2nw∂w	2nw∂w	NUM
ejpam-4923	106	26	−	−	NOUN
ejpam-4923	106	27	2nw̄∂w	2nw̄∂w	NUM
ejpam-4923	106	28	+	+	CCONJ
ejpam-4923	106	29	4(ww	4(ww	NOUN
ejpam-4923	106	30	−	−	PROPN
ejpam-4923	106	31	1)∂w∂w	1)∂w∂w	PROPN
ejpam-4923	106	32	]	]	PUNCT
ejpam-4923	106	33	.	.	PUNCT
ejpam-4923	107	1	(	(	PUNCT
ejpam-4923	107	2	31	31	NUM
ejpam-4923	107	3	)	)	PUNCT
ejpam-4923	107	4	the	the	DET
ejpam-4923	107	5	casimir	casimir	NOUN
ejpam-4923	107	6	operator	operator	NOUN
ejpam-4923	107	7	in	in	ADP
ejpam-4923	107	8	the	the	DET
ejpam-4923	107	9	polar	polar	ADJ
ejpam-4923	107	10	coordinate	coordinate	NOUN
ejpam-4923	107	11	w	w	PROPN
ejpam-4923	107	12	=	=	X
ejpam-4923	107	13	reiθ	reiθ	PROPN
ejpam-4923	107	14	is	be	AUX
ejpam-4923	107	15	as	as	SCONJ
ejpam-4923	107	16	follows	follow	VERB
ejpam-4923	107	17	:	:	PUNCT
ejpam-4923	107	18	dπn(c	dπn(c	NOUN
ejpam-4923	107	19	)	)	PUNCT
ejpam-4923	107	20	=	=	SYM
ejpam-4923	108	1	(	(	PUNCT
ejpam-4923	108	2	r2	r2	PROPN
ejpam-4923	108	3	−	−	PROPN
ejpam-4923	108	4	1)(n2i	1)(n2i	NUM
ejpam-4923	108	5	−	−	NOUN
ejpam-4923	108	6	2in∂θ)−	2in∂θ)−	NUM
ejpam-4923	108	7	(	(	PUNCT
ejpam-4923	108	8	r2	r2	PROPN
ejpam-4923	108	9	−	−	PROPN
ejpam-4923	108	10	1)2(∂2r	1)2(∂2r	NUM
ejpam-4923	109	1	+	+	CCONJ
ejpam-4923	109	2	r−1∂r	r−1∂r	X
ejpam-4923	109	3	+	+	CCONJ
ejpam-4923	109	4	r−2∂2θ	r−2∂2θ	ADJ
ejpam-4923	109	5	)	)	PUNCT
ejpam-4923	109	6	.	.	PUNCT
ejpam-4923	110	1	(	(	PUNCT
ejpam-4923	110	2	32	32	NUM
ejpam-4923	110	3	)	)	PUNCT
ejpam-4923	110	4	lemma	lemma	PROPN
ejpam-4923	110	5	1	1	NUM
ejpam-4923	110	6	.	.	PUNCT
ejpam-4923	111	1	the	the	DET
ejpam-4923	111	2	operator	operator	NOUN
ejpam-4923	111	3	(	(	PUNCT
ejpam-4923	111	4	27	27	NUM
ejpam-4923	111	5	)	)	PUNCT
ejpam-4923	111	6	has	have	VERB
ejpam-4923	111	7	two	two	NUM
ejpam-4923	111	8	eigenfunctions	eigenfunction	NOUN
ejpam-4923	111	9	:	:	PUNCT
ejpam-4923	111	10	(	(	PUNCT
ejpam-4923	111	11	i	i	NOUN
ejpam-4923	111	12	)	)	PUNCT
ejpam-4923	111	13	for	for	ADP
ejpam-4923	111	14	m	m	PROPN
ejpam-4923	111	15	̸=	̸=	PROPN
ejpam-4923	111	16	2	2	NUM
ejpam-4923	111	17	,	,	PUNCT
ejpam-4923	111	18	4	4	NUM
ejpam-4923	111	19	,	,	PUNCT
ejpam-4923	111	20	6	6	NUM
ejpam-4923	111	21	,	,	PUNCT
ejpam-4923	111	22	8	8	NUM
ejpam-4923	111	23	......	......	PUNCT
ejpam-4923	111	24	,	,	PUNCT
ejpam-4923	111	25	f−m	f−m	NOUN
ejpam-4923	111	26	2	2	NUM
ejpam-4923	111	27	,	,	PUNCT
ejpam-4923	111	28	n(w	n(w	NOUN
ejpam-4923	111	29	,	,	PUNCT
ejpam-4923	111	30	w	w	NOUN
ejpam-4923	111	31	)	)	PUNCT
ejpam-4923	111	32	=	=	PRON
ejpam-4923	111	33	w−m	w−m	ADJ
ejpam-4923	111	34	2	2	NUM
ejpam-4923	111	35	(	(	PUNCT
ejpam-4923	111	36	1−	1−	NUM
ejpam-4923	111	37	ww̄	ww̄	NOUN
ejpam-4923	111	38	)	)	PUNCT
ejpam-4923	111	39	1±	1±	NUM
ejpam-4923	111	40	√	√	NUM
ejpam-4923	111	41	1−µ	1−µ	NUM
ejpam-4923	111	42	2	2	NUM
ejpam-4923	111	43	f	f	NOUN
ejpam-4923	111	44	(	(	PUNCT
ejpam-4923	111	45	1	1	NUM
ejpam-4923	111	46	2	2	NUM
ejpam-4923	111	47	[	[	SYM
ejpam-4923	111	48	1	1	NUM
ejpam-4923	111	49	+	+	CCONJ
ejpam-4923	111	50	n−m±	n−m±	NUM
ejpam-4923	111	51	√	√	PROPN
ejpam-4923	111	52	1−	1−	NUM
ejpam-4923	111	53	µ	µ	X
ejpam-4923	111	54	]	]	X
ejpam-4923	111	55	,	,	PUNCT
ejpam-4923	111	56	1	1	NUM
ejpam-4923	111	57	2	2	NUM
ejpam-4923	111	58	[	[	X
ejpam-4923	111	59	1−	1−	NUM
ejpam-4923	111	60	n±	n±	ADV
ejpam-4923	111	61	√	√	PROPN
ejpam-4923	111	62	1−	1−	NUM
ejpam-4923	111	63	µ	µ	X
ejpam-4923	111	64	]	]	X
ejpam-4923	111	65	,	,	PUNCT
ejpam-4923	111	66	1−	1−	NUM
ejpam-4923	111	67	m	m	NOUN
ejpam-4923	111	68	2	2	NUM
ejpam-4923	111	69	,	,	PUNCT
ejpam-4923	111	70	ww	ww	PROPN
ejpam-4923	111	71	)	)	PUNCT
ejpam-4923	111	72	,	,	PUNCT
ejpam-4923	111	73	(	(	PUNCT
ejpam-4923	111	74	33	33	NUM
ejpam-4923	111	75	)	)	PUNCT
ejpam-4923	111	76	a.	a.	NOUN
ejpam-4923	111	77	s.	s.	PROPN
ejpam-4923	111	78	alghamdi	alghamdi	PROPN
ejpam-4923	111	79	/	/	SYM
ejpam-4923	111	80	eur	eur	PROPN
ejpam-4923	111	81	.	.	PUNCT
ejpam-4923	112	1	j.	j.	PROPN
ejpam-4923	112	2	pure	pure	PROPN
ejpam-4923	112	3	appl	appl	PROPN
ejpam-4923	112	4	.	.	PROPN
ejpam-4923	112	5	math	math	PROPN
ejpam-4923	112	6	,	,	PUNCT
ejpam-4923	112	7	16	16	NUM
ejpam-4923	112	8	(	(	PUNCT
ejpam-4923	112	9	4	4	NUM
ejpam-4923	112	10	)	)	PUNCT
ejpam-4923	112	11	(	(	PUNCT
ejpam-4923	112	12	2023	2023	NUM
ejpam-4923	112	13	)	)	PUNCT
ejpam-4923	112	14	,	,	PUNCT
ejpam-4923	112	15	2348	2348	NUM
ejpam-4923	112	16	-	-	SYM
ejpam-4923	112	17	2367	2367	NUM
ejpam-4923	112	18	2354	2354	NUM
ejpam-4923	112	19	(	(	PUNCT
ejpam-4923	112	20	ii	ii	NOUN
ejpam-4923	112	21	)	)	PUNCT
ejpam-4923	112	22	for	for	ADP
ejpam-4923	112	23	m	m	PROPN
ejpam-4923	112	24	̸=	̸=	PROPN
ejpam-4923	112	25	−2,−4,−6,−8	−2,−4,−6,−8	NUM
ejpam-4923	112	26	......	......	PROPN
ejpam-4923	112	27	,	,	PUNCT
ejpam-4923	112	28	f̃−m	f̃−m	PROPN
ejpam-4923	112	29	2	2	NUM
ejpam-4923	112	30	,	,	PUNCT
ejpam-4923	112	31	n(w	n(w	NOUN
ejpam-4923	112	32	,	,	PUNCT
ejpam-4923	112	33	w	w	NOUN
ejpam-4923	112	34	)	)	PUNCT
ejpam-4923	112	35	=	=	PUNCT
ejpam-4923	113	1	w	w	PROPN
ejpam-4923	113	2	m	m	VERB
ejpam-4923	113	3	2	2	NUM
ejpam-4923	113	4	(	(	PUNCT
ejpam-4923	113	5	1−	1−	NUM
ejpam-4923	113	6	ww	ww	PROPN
ejpam-4923	113	7	)	)	PUNCT
ejpam-4923	113	8	1±	1±	NUM
ejpam-4923	113	9	√	√	NUM
ejpam-4923	113	10	1−µ	1−µ	NUM
ejpam-4923	113	11	2	2	NUM
ejpam-4923	113	12	f	f	NOUN
ejpam-4923	113	13	(	(	PUNCT
ejpam-4923	113	14	1	1	NUM
ejpam-4923	113	15	2	2	NUM
ejpam-4923	113	16	[	[	PUNCT
ejpam-4923	113	17	1−	1−	NUM
ejpam-4923	113	18	n+m±	n+m±	NUM
ejpam-4923	113	19	√	√	PROPN
ejpam-4923	113	20	1−	1−	NUM
ejpam-4923	113	21	µ	µ	X
ejpam-4923	113	22	]	]	X
ejpam-4923	113	23	,	,	PUNCT
ejpam-4923	113	24	1	1	NUM
ejpam-4923	113	25	2	2	NUM
ejpam-4923	113	26	[	[	SYM
ejpam-4923	113	27	1	1	NUM
ejpam-4923	113	28	+	+	CCONJ
ejpam-4923	113	29	n±	n±	ADV
ejpam-4923	113	30	√	√	PROPN
ejpam-4923	113	31	1−	1−	NUM
ejpam-4923	113	32	µ	µ	X
ejpam-4923	113	33	]	]	X
ejpam-4923	113	34	,	,	PUNCT
ejpam-4923	113	35	1	1	NUM
ejpam-4923	113	36	+	+	CCONJ
ejpam-4923	113	37	m	m	PROPN
ejpam-4923	113	38	2	2	NUM
ejpam-4923	113	39	,	,	PUNCT
ejpam-4923	113	40	ww	ww	PROPN
ejpam-4923	113	41	)	)	PUNCT
ejpam-4923	113	42	,	,	PUNCT
ejpam-4923	113	43	(	(	PUNCT
ejpam-4923	113	44	34	34	NUM
ejpam-4923	113	45	)	)	PUNCT
ejpam-4923	113	46	where	where	SCONJ
ejpam-4923	113	47	f	f	PROPN
ejpam-4923	113	48	is	be	AUX
ejpam-4923	113	49	a	a	DET
ejpam-4923	113	50	hypergeometric	hypergeometric	ADJ
ejpam-4923	113	51	function	function	NOUN
ejpam-4923	113	52	.	.	PUNCT
ejpam-4923	114	1	proof	proof	NOUN
ejpam-4923	114	2	.	.	PUNCT
ejpam-4923	115	1	to	to	PART
ejpam-4923	115	2	find	find	VERB
ejpam-4923	115	3	the	the	DET
ejpam-4923	115	4	eigenfunction	eigenfunction	NOUN
ejpam-4923	115	5	of	of	ADP
ejpam-4923	115	6	the	the	DET
ejpam-4923	115	7	subgroup	subgroup	NOUN
ejpam-4923	115	8	k	k	PROPN
ejpam-4923	115	9	,	,	PUNCT
ejpam-4923	115	10	we	we	PRON
ejpam-4923	115	11	will	will	AUX
ejpam-4923	115	12	solve	solve	VERB
ejpam-4923	115	13	the	the	DET
ejpam-4923	115	14	following	follow	VERB
ejpam-4923	115	15	partial	partial	ADJ
ejpam-4923	115	16	differential	differential	NOUN
ejpam-4923	115	17	equation	equation	NOUN
ejpam-4923	115	18	by	by	ADP
ejpam-4923	115	19	using	use	VERB
ejpam-4923	115	20	the	the	DET
ejpam-4923	115	21	method	method	NOUN
ejpam-4923	115	22	of	of	ADP
ejpam-4923	115	23	characteristics	characteristic	NOUN
ejpam-4923	115	24	:	:	PUNCT
ejpam-4923	116	1	[	[	X
ejpam-4923	116	2	ef	ef	X
ejpam-4923	116	3	]	]	PUNCT
ejpam-4923	116	4	(	(	PUNCT
ejpam-4923	116	5	w	w	PROPN
ejpam-4923	116	6	,	,	PUNCT
ejpam-4923	116	7	w	w	NOUN
ejpam-4923	116	8	)	)	PUNCT
ejpam-4923	116	9	=	=	PUNCT
ejpam-4923	117	1	[	[	X
ejpam-4923	117	2	−ini	−ini	X
ejpam-4923	117	3	−	−	PROPN
ejpam-4923	117	4	2iw∂w	2iw∂w	NUM
ejpam-4923	117	5	+	+	CCONJ
ejpam-4923	117	6	2iw∂w̄]f(w	2iw∂w̄]f(w	NUM
ejpam-4923	117	7	,	,	PUNCT
ejpam-4923	117	8	w̄	w̄	NOUN
ejpam-4923	117	9	)	)	PUNCT
ejpam-4923	117	10	=	=	SYM
ejpam-4923	118	1	0	0	X
ejpam-4923	118	2	.	.	PUNCT
ejpam-4923	119	1	we	we	PRON
ejpam-4923	119	2	can	can	AUX
ejpam-4923	119	3	write	write	VERB
ejpam-4923	119	4	the	the	DET
ejpam-4923	119	5	characteristics	characteristic	NOUN
ejpam-4923	119	6	for	for	ADP
ejpam-4923	119	7	this	this	DET
ejpam-4923	119	8	equation	equation	NOUN
ejpam-4923	119	9	as	as	SCONJ
ejpam-4923	119	10	follows	follow	VERB
ejpam-4923	119	11	:	:	PUNCT
ejpam-4923	119	12	df	df	PROPN
ejpam-4923	119	13	inf	inf	PROPN
ejpam-4923	119	14	=	=	PROPN
ejpam-4923	119	15	dw	dw	PROPN
ejpam-4923	119	16	−2iw	−2iw	NOUN
ejpam-4923	119	17	=	=	PROPN
ejpam-4923	119	18	dw	dw	PROPN
ejpam-4923	119	19	2iw	2iw	NOUN
ejpam-4923	119	20	.	.	PUNCT
ejpam-4923	120	1	dw	dw	PROPN
ejpam-4923	120	2	−2iw	−2iw	NOUN
ejpam-4923	120	3	=	=	PUNCT
ejpam-4923	120	4	dw̄	dw̄	PROPN
ejpam-4923	120	5	2iw̄	2iw̄	PROPN
ejpam-4923	120	6	⇒	⇒	PROPN
ejpam-4923	120	7	c1	c1	PROPN
ejpam-4923	120	8	=	=	SYM
ejpam-4923	120	9	ww	ww	PROPN
ejpam-4923	120	10	.	.	PUNCT
ejpam-4923	121	1	we	we	PRON
ejpam-4923	121	2	need	need	VERB
ejpam-4923	121	3	to	to	PART
ejpam-4923	121	4	obtain	obtain	VERB
ejpam-4923	121	5	another	another	DET
ejpam-4923	121	6	integral	integral	ADJ
ejpam-4923	121	7	curve	curve	NOUN
ejpam-4923	121	8	that	that	PRON
ejpam-4923	121	9	involves	involve	VERB
ejpam-4923	121	10	f	f	PROPN
ejpam-4923	121	11	.	.	PUNCT
ejpam-4923	122	1	this	this	PRON
ejpam-4923	122	2	is	be	AUX
ejpam-4923	122	3	possible	possible	ADJ
ejpam-4923	122	4	from	from	ADP
ejpam-4923	122	5	the	the	DET
ejpam-4923	122	6	following	follow	VERB
ejpam-4923	122	7	equation	equation	NOUN
ejpam-4923	122	8	:	:	PUNCT
ejpam-4923	122	9	df	df	PROPN
ejpam-4923	122	10	inf	inf	NOUN
ejpam-4923	122	11	=	=	PROPN
ejpam-4923	122	12	dw	dw	PROPN
ejpam-4923	122	13	−2iw	−2iw	PROPN
ejpam-4923	122	14	,	,	PUNCT
ejpam-4923	122	15	we	we	PRON
ejpam-4923	122	16	get	get	VERB
ejpam-4923	122	17	c2	c2	PROPN
ejpam-4923	122	18	=	=	PUNCT
ejpam-4923	122	19	w	w	PROPN
ejpam-4923	122	20	n	n	NUM
ejpam-4923	122	21	2	2	NUM
ejpam-4923	122	22	f.	f.	NOUN
ejpam-4923	122	23	then	then	ADV
ejpam-4923	122	24	,	,	PUNCT
ejpam-4923	122	25	the	the	DET
ejpam-4923	122	26	general	general	ADJ
ejpam-4923	122	27	solution	solution	NOUN
ejpam-4923	122	28	of	of	ADP
ejpam-4923	122	29	(	(	PUNCT
ejpam-4923	122	30	4	4	NUM
ejpam-4923	122	31	)	)	PUNCT
ejpam-4923	122	32	is	be	AUX
ejpam-4923	122	33	of	of	ADP
ejpam-4923	122	34	the	the	DET
ejpam-4923	122	35	form	form	NOUN
ejpam-4923	122	36	c2	c2	PROPN
ejpam-4923	122	37	=	=	SYM
ejpam-4923	122	38	ϕ(c1	ϕ(c1	PROPN
ejpam-4923	122	39	)	)	PUNCT
ejpam-4923	122	40	,	,	PUNCT
ejpam-4923	122	41	that	that	PRON
ejpam-4923	122	42	is	be	AUX
ejpam-4923	122	43	f(w	f(w	PROPN
ejpam-4923	122	44	,	,	PUNCT
ejpam-4923	122	45	w	w	NOUN
ejpam-4923	122	46	)	)	PUNCT
ejpam-4923	122	47	=	=	SYM
ejpam-4923	122	48	w−n	w−n	PROPN
ejpam-4923	122	49	2	2	NUM
ejpam-4923	122	50	ϕ(ww̄	ϕ(ww̄	PROPN
ejpam-4923	122	51	)	)	PUNCT
ejpam-4923	122	52	.	.	PUNCT
ejpam-4923	123	1	now	now	ADV
ejpam-4923	123	2	,	,	PUNCT
ejpam-4923	123	3	for	for	ADP
ejpam-4923	123	4	m	m	PROPN
ejpam-4923	123	5	∈	∈	PROPN
ejpam-4923	123	6	z	z	NOUN
ejpam-4923	123	7	the	the	DET
ejpam-4923	123	8	eigenfunction	eigenfunction	NOUN
ejpam-4923	123	9	is	be	AUX
ejpam-4923	123	10	given	give	VERB
ejpam-4923	123	11	by	by	ADP
ejpam-4923	123	12	f−m	f−m	NOUN
ejpam-4923	123	13	2	2	NUM
ejpam-4923	123	14	(	(	PUNCT
ejpam-4923	123	15	w	w	PROPN
ejpam-4923	123	16	,	,	PUNCT
ejpam-4923	123	17	w	w	NOUN
ejpam-4923	123	18	)	)	PUNCT
ejpam-4923	123	19	=	=	PRON
ejpam-4923	123	20	w−m	w−m	VERB
ejpam-4923	123	21	2	2	NUM
ejpam-4923	123	22	ϕ(ww	ϕ(ww	NOUN
ejpam-4923	123	23	)	)	PUNCT
ejpam-4923	123	24	,	,	PUNCT
ejpam-4923	123	25	(	(	PUNCT
ejpam-4923	123	26	35	35	NUM
ejpam-4923	123	27	)	)	PUNCT
ejpam-4923	123	28	which	which	PRON
ejpam-4923	123	29	satisfies	satisfy	VERB
ejpam-4923	123	30	[	[	X
ejpam-4923	123	31	efm](w	efm](w	PROPN
ejpam-4923	123	32	,	,	PUNCT
ejpam-4923	123	33	w	w	NOUN
ejpam-4923	123	34	)	)	PUNCT
ejpam-4923	123	35	=	=	SYM
ejpam-4923	124	1	i(m−	i(m−	PROPN
ejpam-4923	124	2	n)fm(w	n)fm(w	NOUN
ejpam-4923	124	3	,	,	PUNCT
ejpam-4923	124	4	w	w	NOUN
ejpam-4923	124	5	)	)	PUNCT
ejpam-4923	124	6	.	.	PUNCT
ejpam-4923	125	1	(	(	PUNCT
ejpam-4923	125	2	36	36	NUM
ejpam-4923	125	3	)	)	PUNCT
ejpam-4923	125	4	therefore	therefore	ADV
ejpam-4923	125	5	,	,	PUNCT
ejpam-4923	125	6	the	the	DET
ejpam-4923	125	7	eigenvalue	eigenvalue	NOUN
ejpam-4923	125	8	of	of	ADP
ejpam-4923	125	9	the	the	DET
ejpam-4923	125	10	operator	operator	NOUN
ejpam-4923	125	11	e	e	NOUN
ejpam-4923	125	12	is	be	AUX
ejpam-4923	125	13	m−	m−	PROPN
ejpam-4923	125	14	n.	n.	PROPN
ejpam-4923	125	15	next	next	ADV
ejpam-4923	125	16	,	,	PUNCT
ejpam-4923	125	17	let	let	VERB
ejpam-4923	125	18	w	w	PROPN
ejpam-4923	125	19	=	=	PUNCT
ejpam-4923	125	20	reiθ	reiθ	PROPN
ejpam-4923	125	21	.	.	PUNCT
ejpam-4923	126	1	then	then	ADV
ejpam-4923	126	2	the	the	DET
ejpam-4923	126	3	eigenfunction	eigenfunction	NOUN
ejpam-4923	126	4	(	(	PUNCT
ejpam-4923	126	5	35	35	NUM
ejpam-4923	126	6	)	)	PUNCT
ejpam-4923	126	7	will	will	AUX
ejpam-4923	126	8	be	be	AUX
ejpam-4923	126	9	given	give	VERB
ejpam-4923	126	10	by	by	ADP
ejpam-4923	126	11	f−m	f−m	NOUN
ejpam-4923	126	12	2	2	NUM
ejpam-4923	126	13	(	(	PUNCT
ejpam-4923	126	14	r	r	NOUN
ejpam-4923	126	15	,	,	PUNCT
ejpam-4923	126	16	θ	θ	NOUN
ejpam-4923	126	17	)	)	PUNCT
ejpam-4923	126	18	=	=	SYM
ejpam-4923	126	19	(	(	PUNCT
ejpam-4923	126	20	reiθ)−	reiθ)−	NOUN
ejpam-4923	126	21	m	m	PROPN
ejpam-4923	126	22	2	2	NUM
ejpam-4923	126	23	ϕ(r2	ϕ(r2	NOUN
ejpam-4923	126	24	)	)	PUNCT
ejpam-4923	126	25	.	.	PUNCT
ejpam-4923	127	1	the	the	DET
ejpam-4923	127	2	casimir	casimir	NOUN
ejpam-4923	127	3	operator	operator	NOUN
ejpam-4923	127	4	(	(	PUNCT
ejpam-4923	127	5	32	32	NUM
ejpam-4923	127	6	)	)	PUNCT
ejpam-4923	127	7	is	be	AUX
ejpam-4923	127	8	applied	apply	VERB
ejpam-4923	127	9	to	to	ADP
ejpam-4923	127	10	f−m	f−m	NOUN
ejpam-4923	127	11	2	2	NUM
ejpam-4923	127	12	(	(	PUNCT
ejpam-4923	127	13	r	r	NOUN
ejpam-4923	127	14	,	,	PUNCT
ejpam-4923	127	15	θ	θ	NOUN
ejpam-4923	127	16	)	)	PUNCT
ejpam-4923	128	1	[	[	X
ejpam-4923	128	2	dπn(c)f−m	dπn(c)f−m	PROPN
ejpam-4923	128	3	2	2	NUM
ejpam-4923	128	4	,	,	PUNCT
ejpam-4923	128	5	n](r	n](r	NOUN
ejpam-4923	128	6	,	,	PUNCT
ejpam-4923	128	7	θ	θ	PROPN
ejpam-4923	128	8	)	)	PUNCT
ejpam-4923	128	9	=	=	SYM
ejpam-4923	129	1	(	(	PUNCT
ejpam-4923	129	2	reiθ)−	reiθ)−	NOUN
ejpam-4923	129	3	m	m	PROPN
ejpam-4923	129	4	2	2	NUM
ejpam-4923	129	5	[	[	PUNCT
ejpam-4923	129	6	(	(	PUNCT
ejpam-4923	129	7	r2	r2	PROPN
ejpam-4923	129	8	−	−	PROPN
ejpam-4923	129	9	1)(n2	1)(n2	NUM
ejpam-4923	129	10	−	−	PROPN
ejpam-4923	129	11	nm)ϕ(r2	nm)ϕ(r2	NUM
ejpam-4923	129	12	)	)	PUNCT
ejpam-4923	129	13	−	−	PROPN
ejpam-4923	130	1	2(r2	2(r2	NUM
ejpam-4923	130	2	−	−	NOUN
ejpam-4923	130	3	1)2((−m+	1)2((−m+	PROPN
ejpam-4923	130	4	2)ϕ′(r2	2)ϕ′(r2	NUM
ejpam-4923	130	5	)	)	PUNCT
ejpam-4923	131	1	+	+	NUM
ejpam-4923	132	1	2r2ϕ	2r2ϕ	NUM
ejpam-4923	132	2	′′	′′	PROPN
ejpam-4923	132	3	(	(	PUNCT
ejpam-4923	132	4	r2	r2	PROPN
ejpam-4923	132	5	)	)	PUNCT
ejpam-4923	132	6	)	)	PUNCT
ejpam-4923	132	7	]	]	PUNCT
ejpam-4923	132	8	.	.	PUNCT
ejpam-4923	133	1	(	(	PUNCT
ejpam-4923	133	2	37	37	NUM
ejpam-4923	133	3	)	)	PUNCT
ejpam-4923	133	4	a.	a.	NOUN
ejpam-4923	133	5	s.	s.	PROPN
ejpam-4923	133	6	alghamdi	alghamdi	PROPN
ejpam-4923	133	7	/	/	SYM
ejpam-4923	133	8	eur	eur	PROPN
ejpam-4923	133	9	.	.	PUNCT
ejpam-4923	134	1	j.	j.	PROPN
ejpam-4923	134	2	pure	pure	PROPN
ejpam-4923	134	3	appl	appl	PROPN
ejpam-4923	134	4	.	.	PROPN
ejpam-4923	134	5	math	math	PROPN
ejpam-4923	134	6	,	,	PUNCT
ejpam-4923	134	7	16	16	NUM
ejpam-4923	134	8	(	(	PUNCT
ejpam-4923	134	9	4	4	NUM
ejpam-4923	134	10	)	)	PUNCT
ejpam-4923	134	11	(	(	PUNCT
ejpam-4923	134	12	2023	2023	NUM
ejpam-4923	134	13	)	)	PUNCT
ejpam-4923	134	14	,	,	PUNCT
ejpam-4923	134	15	2348	2348	NUM
ejpam-4923	134	16	-	-	SYM
ejpam-4923	134	17	2367	2367	NUM
ejpam-4923	134	18	2355	2355	NUM
ejpam-4923	134	19	to	to	PART
ejpam-4923	134	20	find	find	VERB
ejpam-4923	134	21	the	the	DET
ejpam-4923	134	22	value	value	NOUN
ejpam-4923	134	23	of	of	ADP
ejpam-4923	134	24	ϕ	ϕ	NOUN
ejpam-4923	134	25	in	in	ADP
ejpam-4923	134	26	(	(	PUNCT
ejpam-4923	134	27	35	35	NUM
ejpam-4923	134	28	)	)	PUNCT
ejpam-4923	135	1	,	,	PUNCT
ejpam-4923	135	2	we	we	PRON
ejpam-4923	135	3	need	need	VERB
ejpam-4923	135	4	to	to	PART
ejpam-4923	135	5	solve	solve	VERB
ejpam-4923	135	6	the	the	DET
ejpam-4923	135	7	differential	differential	ADJ
ejpam-4923	135	8	equation	equation	NOUN
ejpam-4923	135	9	[	[	X
ejpam-4923	135	10	dπn(c)f	dπn(c)f	X
ejpam-4923	135	11	]	]	X
ejpam-4923	135	12	(	(	PUNCT
ejpam-4923	135	13	r	r	NOUN
ejpam-4923	135	14	,	,	PUNCT
ejpam-4923	135	15	θ	θ	NOUN
ejpam-4923	135	16	)	)	PUNCT
ejpam-4923	135	17	=	=	SYM
ejpam-4923	135	18	µf(r	µf(r	X
ejpam-4923	135	19	,	,	PUNCT
ejpam-4923	135	20	θ	θ	NOUN
ejpam-4923	135	21	)	)	PUNCT
ejpam-4923	135	22	.	.	PUNCT
ejpam-4923	136	1	that	that	PRON
ejpam-4923	136	2	is	be	AUX
ejpam-4923	136	3	,	,	PUNCT
ejpam-4923	136	4	[	[	X
ejpam-4923	136	5	(	(	PUNCT
ejpam-4923	136	6	r2	r2	PROPN
ejpam-4923	136	7	−	−	PROPN
ejpam-4923	136	8	1)(n2	1)(n2	NUM
ejpam-4923	137	1	−	−	PROPN
ejpam-4923	137	2	nm)−	nm)−	PROPN
ejpam-4923	137	3	µ]ϕ(r2)−	µ]ϕ(r2)−	VERB
ejpam-4923	137	4	2(r2	2(r2	NUM
ejpam-4923	137	5	−	−	NUM
ejpam-4923	137	6	1)2(−m+	1)2(−m+	NUM
ejpam-4923	137	7	2)ϕ′(r2	2)ϕ′(r2	NUM
ejpam-4923	137	8	)	)	PUNCT
ejpam-4923	138	1	−	−	ADP
ejpam-4923	138	2	4(r2	4(r2	NUM
ejpam-4923	138	3	−	−	PROPN
ejpam-4923	138	4	1)2r2ϕ	1)2r2ϕ	PROPN
ejpam-4923	138	5	′′	′′	PROPN
ejpam-4923	138	6	(	(	PUNCT
ejpam-4923	138	7	r2	r2	PROPN
ejpam-4923	138	8	)	)	PUNCT
ejpam-4923	138	9	=	=	SYM
ejpam-4923	138	10	0	0	X
ejpam-4923	138	11	.	.	PUNCT
ejpam-4923	138	12	(	(	PUNCT
ejpam-4923	138	13	38	38	NUM
ejpam-4923	138	14	)	)	PUNCT
ejpam-4923	138	15	let	let	VERB
ejpam-4923	138	16	x	x	NOUN
ejpam-4923	138	17	=	=	PUNCT
ejpam-4923	138	18	r2	r2	PROPN
ejpam-4923	138	19	.	.	PUNCT
ejpam-4923	139	1	then	then	ADV
ejpam-4923	139	2	we	we	PRON
ejpam-4923	139	3	get	get	VERB
ejpam-4923	139	4	[	[	X
ejpam-4923	139	5	(	(	PUNCT
ejpam-4923	139	6	x−	x−	PROPN
ejpam-4923	139	7	1)(n2	1)(n2	NUM
ejpam-4923	139	8	−	−	PROPN
ejpam-4923	140	1	nm)−	nm)−	PROPN
ejpam-4923	140	2	µ]ϕ(x)−	µ]ϕ(x)−	PROPN
ejpam-4923	140	3	2(x−	2(x−	NUM
ejpam-4923	140	4	1)2(−m+	1)2(−m+	NUM
ejpam-4923	140	5	2)ϕ′(x	2)ϕ′(x	NUM
ejpam-4923	140	6	)	)	PUNCT
ejpam-4923	141	1	−	−	PROPN
ejpam-4923	141	2	4(x−	4(x−	NUM
ejpam-4923	142	1	1)2x2ϕ	1)2x2ϕ	NUM
ejpam-4923	142	2	′′	′′	PROPN
ejpam-4923	142	3	(	(	PUNCT
ejpam-4923	142	4	x	x	X
ejpam-4923	142	5	)	)	PUNCT
ejpam-4923	142	6	=	=	SYM
ejpam-4923	142	7	0	0	X
ejpam-4923	142	8	.	.	PUNCT
ejpam-4923	142	9	(	(	PUNCT
ejpam-4923	142	10	39	39	NUM
ejpam-4923	142	11	)	)	PUNCT
ejpam-4923	142	12	now	now	ADV
ejpam-4923	142	13	,	,	PUNCT
ejpam-4923	142	14	let	let	VERB
ejpam-4923	142	15	ϕ(x	ϕ(x	PRON
ejpam-4923	142	16	)	)	PUNCT
ejpam-4923	142	17	=	=	PUNCT
ejpam-4923	143	1	xα(1−	xα(1−	PROPN
ejpam-4923	143	2	x)βψ(x	x)βψ(x	NUM
ejpam-4923	143	3	)	)	PUNCT
ejpam-4923	143	4	.	.	PUNCT
ejpam-4923	144	1	then	then	ADV
ejpam-4923	144	2	by	by	ADP
ejpam-4923	144	3	substitute	substitute	NOUN
ejpam-4923	144	4	ϕ(x	ϕ(x	PROPN
ejpam-4923	144	5	)	)	PUNCT
ejpam-4923	144	6	in	in	ADP
ejpam-4923	144	7	(	(	PUNCT
ejpam-4923	144	8	39	39	NUM
ejpam-4923	144	9	)	)	PUNCT
ejpam-4923	144	10	,	,	PUNCT
ejpam-4923	144	11	we	we	PRON
ejpam-4923	144	12	get	get	VERB
ejpam-4923	144	13	α	α	NOUN
ejpam-4923	144	14	=	=	PUNCT
ejpam-4923	144	15	m	m	VERB
ejpam-4923	144	16	2	2	NUM
ejpam-4923	144	17	or	or	CCONJ
ejpam-4923	144	18	0	0	NUM
ejpam-4923	144	19	,	,	PUNCT
ejpam-4923	144	20	β	β	X
ejpam-4923	144	21	=	=	SYM
ejpam-4923	144	22	1±	1±	NUM
ejpam-4923	144	23	√	√	NUM
ejpam-4923	144	24	1−	1−	NUM
ejpam-4923	144	25	µ	µ	PRON
ejpam-4923	144	26	2	2	NUM
ejpam-4923	144	27	.	.	PUNCT
ejpam-4923	145	1	hence	hence	ADV
ejpam-4923	145	2	,	,	PUNCT
ejpam-4923	145	3	we	we	PRON
ejpam-4923	145	4	have	have	VERB
ejpam-4923	145	5	two	two	NUM
ejpam-4923	145	6	solutions	solution	NOUN
ejpam-4923	145	7	:	:	PUNCT
ejpam-4923	145	8	(	(	PUNCT
ejpam-4923	145	9	i	i	NOUN
ejpam-4923	145	10	)	)	PUNCT
ejpam-4923	145	11	ϕ(x	ϕ(x	PROPN
ejpam-4923	145	12	)	)	PUNCT
ejpam-4923	145	13	=	=	PUNCT
ejpam-4923	145	14	(	(	PUNCT
ejpam-4923	145	15	1−	1−	NUM
ejpam-4923	145	16	x	x	SYM
ejpam-4923	145	17	)	)	PUNCT
ejpam-4923	145	18	1±	1±	NUM
ejpam-4923	145	19	√	√	NUM
ejpam-4923	145	20	1−µ	1−µ	NUM
ejpam-4923	145	21	2	2	NUM
ejpam-4923	145	22	ψ(x	ψ(x	NOUN
ejpam-4923	145	23	)	)	PUNCT
ejpam-4923	145	24	,	,	PUNCT
ejpam-4923	145	25	(	(	PUNCT
ejpam-4923	145	26	ii	ii	NOUN
ejpam-4923	145	27	)	)	PUNCT
ejpam-4923	145	28	ϕ(x	ϕ(x	X
ejpam-4923	145	29	)	)	PUNCT
ejpam-4923	146	1	=	=	PUNCT
ejpam-4923	147	1	x	x	PUNCT
ejpam-4923	147	2	m	m	VERB
ejpam-4923	147	3	2	2	NUM
ejpam-4923	147	4	(	(	PUNCT
ejpam-4923	147	5	1−	1−	NUM
ejpam-4923	147	6	x	x	SYM
ejpam-4923	147	7	)	)	PUNCT
ejpam-4923	147	8	1±	1±	NUM
ejpam-4923	147	9	√	√	NUM
ejpam-4923	147	10	1−µ	1−µ	NUM
ejpam-4923	147	11	2	2	NUM
ejpam-4923	147	12	ψ(x	ψ(x	NOUN
ejpam-4923	147	13	)	)	PUNCT
ejpam-4923	147	14	.	.	PUNCT
ejpam-4923	148	1	by	by	ADP
ejpam-4923	148	2	substituting	substitute	VERB
ejpam-4923	148	3	the	the	DET
ejpam-4923	148	4	first	first	ADJ
ejpam-4923	148	5	solution	solution	NOUN
ejpam-4923	148	6	in	in	ADP
ejpam-4923	148	7	the	the	DET
ejpam-4923	148	8	differential	differential	NOUN
ejpam-4923	148	9	equation(39	equation(39	NOUN
ejpam-4923	148	10	)	)	PUNCT
ejpam-4923	148	11	,	,	PUNCT
ejpam-4923	148	12	we	we	PRON
ejpam-4923	148	13	get	get	VERB
ejpam-4923	148	14	x(1−	x(1−	NOUN
ejpam-4923	148	15	x)ψ	x)ψ	PUNCT
ejpam-4923	149	1	′′	′′	PROPN
ejpam-4923	149	2	(	(	PUNCT
ejpam-4923	149	3	x	x	X
ejpam-4923	149	4	)	)	PUNCT
ejpam-4923	149	5	+	+	CCONJ
ejpam-4923	149	6	(	(	PUNCT
ejpam-4923	149	7	1−	1−	NUM
ejpam-4923	149	8	m	m	NOUN
ejpam-4923	149	9	2	2	NUM
ejpam-4923	149	10	−	−	PROPN
ejpam-4923	149	11	(	(	PUNCT
ejpam-4923	149	12	1±	1±	NUM
ejpam-4923	149	13	√	√	NUM
ejpam-4923	149	14	1−	1−	NUM
ejpam-4923	149	15	µ+	µ+	PUNCT
ejpam-4923	149	16	1−	1−	NUM
ejpam-4923	149	17	m	m	NOUN
ejpam-4923	149	18	2	2	NUM
ejpam-4923	149	19	)	)	PUNCT
ejpam-4923	149	20	x	x	SYM
ejpam-4923	149	21	)	)	PUNCT
ejpam-4923	149	22	ψ	ψ	X
ejpam-4923	149	23	′	′	NUM
ejpam-4923	149	24	(	(	PUNCT
ejpam-4923	149	25	x	x	X
ejpam-4923	149	26	)	)	PUNCT
ejpam-4923	149	27	+	+	CCONJ
ejpam-4923	149	28	[	[	PUNCT
ejpam-4923	149	29	µ	µ	X
ejpam-4923	149	30	2	2	NUM
ejpam-4923	149	31	+	+	CCONJ
ejpam-4923	149	32	(	(	PUNCT
ejpam-4923	149	33	−1∓	−1∓	NUM
ejpam-4923	149	34	√	√	PROPN
ejpam-4923	149	35	1−	1−	NUM
ejpam-4923	149	36	µ	µ	PRON
ejpam-4923	149	37	2	2	NUM
ejpam-4923	149	38	)	)	PUNCT
ejpam-4923	149	39	(	(	PUNCT
ejpam-4923	149	40	1−	1−	NUM
ejpam-4923	149	41	m	m	NOUN
ejpam-4923	149	42	2	2	NUM
ejpam-4923	149	43	)	)	PUNCT
ejpam-4923	149	44	+	+	CCONJ
ejpam-4923	149	45	1	1	NUM
ejpam-4923	149	46	4	4	NUM
ejpam-4923	149	47	(	(	PUNCT
ejpam-4923	149	48	n2	n2	ADJ
ejpam-4923	149	49	−	−	PROPN
ejpam-4923	149	50	nm	nm	NOUN
ejpam-4923	149	51	)	)	PUNCT
ejpam-4923	149	52	]	]	PUNCT
ejpam-4923	149	53	ψ(x	ψ(x	X
ejpam-4923	149	54	)	)	PUNCT
ejpam-4923	149	55	=	=	SYM
ejpam-4923	150	1	0	0	X
ejpam-4923	150	2	.	.	PUNCT
ejpam-4923	151	1	(	(	PUNCT
ejpam-4923	151	2	40	40	NUM
ejpam-4923	151	3	)	)	PUNCT
ejpam-4923	151	4	this	this	PRON
ejpam-4923	151	5	is	be	AUX
ejpam-4923	151	6	a	a	DET
ejpam-4923	151	7	hypergeometric	hypergeometric	ADJ
ejpam-4923	151	8	differential	differential	NOUN
ejpam-4923	151	9	equation	equation	NOUN
ejpam-4923	151	10	that	that	PRON
ejpam-4923	151	11	takes	take	VERB
ejpam-4923	151	12	the	the	DET
ejpam-4923	151	13	following	follow	VERB
ejpam-4923	151	14	form	form	NOUN
ejpam-4923	151	15	:	:	PUNCT
ejpam-4923	151	16	x(1−	x(1−	PROPN
ejpam-4923	151	17	x)ψ	x)ψ	PUNCT
ejpam-4923	152	1	′′	′′	PROPN
ejpam-4923	152	2	(	(	PUNCT
ejpam-4923	152	3	x	x	X
ejpam-4923	152	4	)	)	PUNCT
ejpam-4923	152	5	+	+	CCONJ
ejpam-4923	152	6	[	[	X
ejpam-4923	152	7	c−	c−	NOUN
ejpam-4923	152	8	(	(	PUNCT
ejpam-4923	152	9	a+	a+	X
ejpam-4923	152	10	b+	b+	NUM
ejpam-4923	152	11	1)x]ψ	1)x]ψ	NUM
ejpam-4923	152	12	′	′	NUM
ejpam-4923	152	13	(	(	PUNCT
ejpam-4923	152	14	x)−	x)−	PROPN
ejpam-4923	152	15	abψ(x	abψ(x	NOUN
ejpam-4923	152	16	)	)	PUNCT
ejpam-4923	152	17	=	=	SYM
ejpam-4923	152	18	0	0	X
ejpam-4923	152	19	.	.	PUNCT
ejpam-4923	153	1	by	by	ADP
ejpam-4923	153	2	simple	simple	ADJ
ejpam-4923	153	3	calculation	calculation	NOUN
ejpam-4923	153	4	,	,	PUNCT
ejpam-4923	153	5	we	we	PRON
ejpam-4923	153	6	get	get	VERB
ejpam-4923	153	7	a	a	DET
ejpam-4923	153	8	=	=	NOUN
ejpam-4923	153	9	1	1	NUM
ejpam-4923	153	10	2	2	NUM
ejpam-4923	153	11	[	[	SYM
ejpam-4923	153	12	1	1	NUM
ejpam-4923	153	13	+	+	CCONJ
ejpam-4923	153	14	n−m±	n−m±	NUM
ejpam-4923	153	15	√	√	PROPN
ejpam-4923	153	16	1−	1−	NUM
ejpam-4923	153	17	µ	µ	X
ejpam-4923	153	18	]	]	X
ejpam-4923	153	19	,	,	PUNCT
ejpam-4923	153	20	b	b	X
ejpam-4923	153	21	=	=	SYM
ejpam-4923	153	22	1	1	NUM
ejpam-4923	153	23	2	2	NUM
ejpam-4923	153	24	[	[	X
ejpam-4923	153	25	1−	1−	NUM
ejpam-4923	153	26	n±	n±	ADV
ejpam-4923	153	27	√	√	PROPN
ejpam-4923	153	28	1−	1−	NUM
ejpam-4923	153	29	µ	µ	X
ejpam-4923	153	30	]	]	PUNCT
ejpam-4923	153	31	,	,	PUNCT
ejpam-4923	153	32	c	c	X
ejpam-4923	153	33	=	=	SYM
ejpam-4923	153	34	1−	1−	NUM
ejpam-4923	153	35	m	m	NOUN
ejpam-4923	153	36	2	2	NUM
ejpam-4923	153	37	.	.	PUNCT
ejpam-4923	153	38	a.	a.	PROPN
ejpam-4923	153	39	s.	s.	PROPN
ejpam-4923	153	40	alghamdi	alghamdi	PROPN
ejpam-4923	153	41	/	/	SYM
ejpam-4923	153	42	eur	eur	PROPN
ejpam-4923	153	43	.	.	PUNCT
ejpam-4923	154	1	j.	j.	PROPN
ejpam-4923	154	2	pure	pure	PROPN
ejpam-4923	154	3	appl	appl	PROPN
ejpam-4923	154	4	.	.	PROPN
ejpam-4923	154	5	math	math	PROPN
ejpam-4923	154	6	,	,	PUNCT
ejpam-4923	154	7	16	16	NUM
ejpam-4923	154	8	(	(	PUNCT
ejpam-4923	154	9	4	4	NUM
ejpam-4923	154	10	)	)	PUNCT
ejpam-4923	154	11	(	(	PUNCT
ejpam-4923	154	12	2023	2023	NUM
ejpam-4923	154	13	)	)	PUNCT
ejpam-4923	154	14	,	,	PUNCT
ejpam-4923	154	15	2348	2348	NUM
ejpam-4923	154	16	-	-	SYM
ejpam-4923	154	17	2367	2367	NUM
ejpam-4923	154	18	2356	2356	NUM
ejpam-4923	154	19	then	then	ADV
ejpam-4923	154	20	,	,	PUNCT
ejpam-4923	154	21	ψ(x	ψ(x	PROPN
ejpam-4923	154	22	)	)	PUNCT
ejpam-4923	155	1	=	=	SYM
ejpam-4923	155	2	f	f	X
ejpam-4923	155	3	(	(	PUNCT
ejpam-4923	155	4	a	a	PRON
ejpam-4923	155	5	,	,	PUNCT
ejpam-4923	155	6	b	b	NOUN
ejpam-4923	155	7	,	,	PUNCT
ejpam-4923	155	8	c	c	NOUN
ejpam-4923	155	9	,	,	PUNCT
ejpam-4923	155	10	x	x	NOUN
ejpam-4923	155	11	)	)	PUNCT
ejpam-4923	155	12	,	,	PUNCT
ejpam-4923	155	13	and	and	CCONJ
ejpam-4923	155	14	the	the	DET
ejpam-4923	155	15	solution	solution	NOUN
ejpam-4923	155	16	of	of	ADP
ejpam-4923	155	17	(	(	PUNCT
ejpam-4923	155	18	38	38	NUM
ejpam-4923	155	19	)	)	PUNCT
ejpam-4923	155	20	is	be	AUX
ejpam-4923	155	21	ϕ(r2	ϕ(r2	NOUN
ejpam-4923	155	22	)	)	PUNCT
ejpam-4923	155	23	=	=	SYM
ejpam-4923	155	24	(	(	PUNCT
ejpam-4923	155	25	1−	1−	NUM
ejpam-4923	155	26	r2	r2	NOUN
ejpam-4923	155	27	)	)	PUNCT
ejpam-4923	156	1	1±	1±	NUM
ejpam-4923	156	2	√	√	NUM
ejpam-4923	156	3	1−µ	1−µ	NUM
ejpam-4923	156	4	2	2	NUM
ejpam-4923	156	5	f	f	X
ejpam-4923	156	6	(	(	PUNCT
ejpam-4923	156	7	a	a	PRON
ejpam-4923	156	8	,	,	PUNCT
ejpam-4923	156	9	b	b	NOUN
ejpam-4923	156	10	,	,	PUNCT
ejpam-4923	156	11	c	c	NOUN
ejpam-4923	156	12	,	,	PUNCT
ejpam-4923	156	13	r2	r2	PROPN
ejpam-4923	156	14	)	)	PUNCT
ejpam-4923	156	15	.	.	PUNCT
ejpam-4923	157	1	the	the	DET
ejpam-4923	157	2	hypergeometric	hypergeometric	ADJ
ejpam-4923	157	3	function	function	NOUN
ejpam-4923	157	4	is	be	AUX
ejpam-4923	157	5	given	give	VERB
ejpam-4923	157	6	by	by	ADP
ejpam-4923	157	7	f	f	PROPN
ejpam-4923	157	8	(	(	PUNCT
ejpam-4923	157	9	a	a	PRON
ejpam-4923	157	10	,	,	PUNCT
ejpam-4923	157	11	b	b	NOUN
ejpam-4923	157	12	,	,	PUNCT
ejpam-4923	157	13	c	c	X
ejpam-4923	157	14	,	,	PUNCT
ejpam-4923	157	15	r2	r2	PROPN
ejpam-4923	157	16	)	)	PUNCT
ejpam-4923	157	17	=	=	SYM
ejpam-4923	158	1	1	1	NUM
ejpam-4923	158	2	+	+	NUM
ejpam-4923	158	3	∞∑	∞∑	NUM
ejpam-4923	158	4	k=1	k=1	X
ejpam-4923	158	5	(	(	PUNCT
ejpam-4923	158	6	a)k(b)k	a)k(b)k	PROPN
ejpam-4923	158	7	(	(	PUNCT
ejpam-4923	158	8	c)k	c)k	X
ejpam-4923	158	9	(	(	PUNCT
ejpam-4923	158	10	r2)k	r2)k	NOUN
ejpam-4923	158	11	k	k	PROPN
ejpam-4923	158	12	!	!	PROPN
ejpam-4923	158	13	.	.	PUNCT
ejpam-4923	159	1	finally	finally	ADV
ejpam-4923	159	2	,	,	PUNCT
ejpam-4923	159	3	the	the	DET
ejpam-4923	159	4	eigenfunction	eigenfunction	NOUN
ejpam-4923	159	5	is	be	AUX
ejpam-4923	159	6	given	give	VERB
ejpam-4923	159	7	by	by	ADP
ejpam-4923	159	8	f−m	f−m	NOUN
ejpam-4923	159	9	2	2	NUM
ejpam-4923	159	10	,	,	PUNCT
ejpam-4923	159	11	n(w	n(w	NOUN
ejpam-4923	159	12	,	,	PUNCT
ejpam-4923	159	13	w	w	NOUN
ejpam-4923	159	14	)	)	PUNCT
ejpam-4923	159	15	=	=	PRON
ejpam-4923	159	16	w−m	w−m	ADJ
ejpam-4923	159	17	2	2	NUM
ejpam-4923	159	18	(	(	PUNCT
ejpam-4923	159	19	1−	1−	NUM
ejpam-4923	159	20	ww	ww	PROPN
ejpam-4923	159	21	)	)	PUNCT
ejpam-4923	159	22	1±	1±	NUM
ejpam-4923	159	23	√	√	NUM
ejpam-4923	159	24	1−µ	1−µ	NUM
ejpam-4923	159	25	2	2	NUM
ejpam-4923	159	26	f	f	NOUN
ejpam-4923	159	27	(	(	PUNCT
ejpam-4923	159	28	1	1	NUM
ejpam-4923	159	29	2	2	NUM
ejpam-4923	160	1	[	[	SYM
ejpam-4923	160	2	1	1	NUM
ejpam-4923	160	3	+	+	CCONJ
ejpam-4923	160	4	n−m±	n−m±	NUM
ejpam-4923	160	5	√	√	PROPN
ejpam-4923	160	6	1−	1−	NUM
ejpam-4923	160	7	µ	µ	X
ejpam-4923	160	8	]	]	X
ejpam-4923	160	9	,	,	PUNCT
ejpam-4923	160	10	1	1	NUM
ejpam-4923	160	11	2	2	NUM
ejpam-4923	160	12	[	[	X
ejpam-4923	160	13	1−	1−	NUM
ejpam-4923	160	14	n±	n±	ADV
ejpam-4923	160	15	√	√	PROPN
ejpam-4923	160	16	1−	1−	NUM
ejpam-4923	160	17	µ	µ	X
ejpam-4923	160	18	]	]	X
ejpam-4923	160	19	,	,	PUNCT
ejpam-4923	160	20	1−	1−	NUM
ejpam-4923	160	21	m	m	NOUN
ejpam-4923	160	22	2	2	NUM
ejpam-4923	160	23	,	,	PUNCT
ejpam-4923	160	24	ww	ww	PROPN
ejpam-4923	160	25	)	)	PUNCT
ejpam-4923	160	26	,	,	PUNCT
ejpam-4923	160	27	where	where	SCONJ
ejpam-4923	160	28	m	m	AUX
ejpam-4923	160	29	̸=	̸=	PROPN
ejpam-4923	160	30	2	2	NUM
ejpam-4923	160	31	,	,	PUNCT
ejpam-4923	160	32	4	4	NUM
ejpam-4923	160	33	,	,	PUNCT
ejpam-4923	160	34	6	6	NUM
ejpam-4923	160	35	,	,	PUNCT
ejpam-4923	160	36	8	8	NUM
ejpam-4923	160	37	.......	.......	PUNCT
ejpam-4923	160	38	following	follow	VERB
ejpam-4923	160	39	the	the	DET
ejpam-4923	160	40	same	same	ADJ
ejpam-4923	160	41	calculation	calculation	NOUN
ejpam-4923	160	42	for	for	ADP
ejpam-4923	160	43	the	the	DET
ejpam-4923	160	44	second	second	ADJ
ejpam-4923	160	45	solution	solution	NOUN
ejpam-4923	160	46	,	,	PUNCT
ejpam-4923	160	47	we	we	PRON
ejpam-4923	160	48	get	get	VERB
ejpam-4923	160	49	the	the	DET
ejpam-4923	160	50	eigenfunction	eigenfunction	NOUN
ejpam-4923	160	51	f̃−m	f̃−m	PROPN
ejpam-4923	160	52	2	2	NUM
ejpam-4923	160	53	,	,	PUNCT
ejpam-4923	160	54	n(w	n(w	NOUN
ejpam-4923	160	55	,	,	PUNCT
ejpam-4923	160	56	w	w	NOUN
ejpam-4923	160	57	)	)	PUNCT
ejpam-4923	160	58	=	=	PUNCT
ejpam-4923	161	1	w	w	PROPN
ejpam-4923	161	2	m	m	VERB
ejpam-4923	161	3	2	2	NUM
ejpam-4923	161	4	(	(	PUNCT
ejpam-4923	161	5	1−	1−	NUM
ejpam-4923	161	6	ww̄	ww̄	NOUN
ejpam-4923	161	7	)	)	PUNCT
ejpam-4923	161	8	1±	1±	NUM
ejpam-4923	161	9	√	√	NUM
ejpam-4923	161	10	1−µ	1−µ	NUM
ejpam-4923	161	11	2	2	NUM
ejpam-4923	161	12	f	f	NOUN
ejpam-4923	161	13	(	(	PUNCT
ejpam-4923	161	14	1	1	NUM
ejpam-4923	161	15	2	2	NUM
ejpam-4923	161	16	[	[	X
ejpam-4923	161	17	1−	1−	NUM
ejpam-4923	161	18	n+m±	n+m±	NUM
ejpam-4923	161	19	√	√	PROPN
ejpam-4923	161	20	1−	1−	NUM
ejpam-4923	161	21	µ	µ	X
ejpam-4923	161	22	]	]	X
ejpam-4923	161	23	,	,	PUNCT
ejpam-4923	161	24	1	1	NUM
ejpam-4923	161	25	2	2	NUM
ejpam-4923	162	1	[	[	SYM
ejpam-4923	162	2	1	1	NUM
ejpam-4923	162	3	+	+	CCONJ
ejpam-4923	162	4	n±	n±	ADV
ejpam-4923	163	1	√	√	PROPN
ejpam-4923	163	2	1−	1−	NUM
ejpam-4923	163	3	µ	µ	X
ejpam-4923	163	4	]	]	X
ejpam-4923	163	5	,	,	PUNCT
ejpam-4923	163	6	1	1	NUM
ejpam-4923	163	7	+	+	CCONJ
ejpam-4923	163	8	m	m	PROPN
ejpam-4923	163	9	2	2	NUM
ejpam-4923	163	10	,	,	PUNCT
ejpam-4923	163	11	ww	ww	PROPN
ejpam-4923	163	12	)	)	PUNCT
ejpam-4923	163	13	,	,	PUNCT
ejpam-4923	163	14	where	where	SCONJ
ejpam-4923	163	15	m	m	VERB
ejpam-4923	163	16	̸=	̸=	PROPN
ejpam-4923	163	17	−2,−4,−6,−8	−2,−4,−6,−8	NUM
ejpam-4923	163	18	.......	.......	PUNCT
ejpam-4923	163	19	the	the	DET
ejpam-4923	163	20	commutator	commutator	NOUN
ejpam-4923	163	21	relation	relation	NOUN
ejpam-4923	164	1	[	[	X
ejpam-4923	164	2	e	e	NOUN
ejpam-4923	164	3	,	,	PUNCT
ejpam-4923	164	4	l±	l±	X
ejpam-4923	164	5	]	]	X
ejpam-4923	164	6	=	=	SYM
ejpam-4923	164	7	±2il±	±2il±	ADJ
ejpam-4923	164	8	,	,	PUNCT
ejpam-4923	164	9	implies	imply	VERB
ejpam-4923	164	10	that	that	SCONJ
ejpam-4923	165	1	[	[	X
ejpam-4923	165	2	ef−m	ef−m	NOUN
ejpam-4923	165	3	2	2	NUM
ejpam-4923	165	4	,	,	PUNCT
ejpam-4923	165	5	n(w	n(w	NOUN
ejpam-4923	165	6	,	,	PUNCT
ejpam-4923	165	7	w̄	w̄	NOUN
ejpam-4923	165	8	)	)	PUNCT
ejpam-4923	165	9	]	]	PUNCT
ejpam-4923	165	10	=	=	PUNCT
ejpam-4923	165	11	e(m−n)iθf−m	e(m−n)iθf−m	PROPN
ejpam-4923	165	12	2	2	NUM
ejpam-4923	165	13	,	,	PUNCT
ejpam-4923	165	14	n(w	n(w	NOUN
ejpam-4923	165	15	,	,	PUNCT
ejpam-4923	165	16	w̄	w̄	NOUN
ejpam-4923	165	17	)	)	PUNCT
ejpam-4923	165	18	.	.	PUNCT
ejpam-4923	166	1	hence	hence	ADV
ejpam-4923	166	2	e	e	PROPN
ejpam-4923	166	3	=	=	PUNCT
ejpam-4923	166	4	(	(	PUNCT
ejpam-4923	166	5	m	m	NOUN
ejpam-4923	166	6	−	−	NOUN
ejpam-4923	166	7	n)i	n)i	NOUN
ejpam-4923	166	8	.	.	PUNCT
ejpam-4923	167	1	additionally	additionally	ADV
ejpam-4923	167	2	,	,	PUNCT
ejpam-4923	167	3	by	by	ADP
ejpam-4923	167	4	using	use	VERB
ejpam-4923	167	5	the	the	DET
ejpam-4923	167	6	relation	relation	NOUN
ejpam-4923	167	7	[	[	X
ejpam-4923	167	8	l+	l+	NOUN
ejpam-4923	167	9	,	,	PUNCT
ejpam-4923	167	10	l−	l−	PROPN
ejpam-4923	167	11	]	]	X
ejpam-4923	167	12	=	=	SYM
ejpam-4923	167	13	−ie	−ie	NOUN
ejpam-4923	167	14	,	,	PUNCT
ejpam-4923	167	15	and	and	CCONJ
ejpam-4923	167	16	(	(	PUNCT
ejpam-4923	167	17	31	31	NUM
ejpam-4923	167	18	)	)	PUNCT
ejpam-4923	167	19	,	,	PUNCT
ejpam-4923	167	20	we	we	PRON
ejpam-4923	167	21	get	get	VERB
ejpam-4923	167	22	the	the	DET
ejpam-4923	167	23	following	follow	VERB
ejpam-4923	167	24	identities	identity	NOUN
ejpam-4923	167	25	:	:	PUNCT
ejpam-4923	167	26	4l+l−	4l+l−	NUM
ejpam-4923	167	27	=	=	PROPN
ejpam-4923	167	28	e2	e2	PROPN
ejpam-4923	168	1	−	−	PROPN
ejpam-4923	168	2	2ie	2ie	ADJ
ejpam-4923	168	3	−	−	PROPN
ejpam-4923	168	4	dπn(c	dπn(c	PROPN
ejpam-4923	168	5	)	)	PUNCT
ejpam-4923	168	6	,	,	PUNCT
ejpam-4923	168	7	4l−l+	4l−l+	X
ejpam-4923	168	8	=	=	SYM
ejpam-4923	168	9	e2	e2	PROPN
ejpam-4923	168	10	+	+	CCONJ
ejpam-4923	168	11	2ie	2ie	ADJ
ejpam-4923	168	12	−	−	PROPN
ejpam-4923	168	13	dπn(c	dπn(c	PROPN
ejpam-4923	168	14	)	)	PUNCT
ejpam-4923	168	15	.	.	PUNCT
ejpam-4923	169	1	then	then	ADV
ejpam-4923	169	2	,	,	PUNCT
ejpam-4923	169	3	for	for	ADP
ejpam-4923	169	4	dπn(c	dπn(c	NOUN
ejpam-4923	169	5	)	)	PUNCT
ejpam-4923	169	6	=	=	SYM
ejpam-4923	169	7	µi	µi	PROPN
ejpam-4923	169	8	,	,	PUNCT
ejpam-4923	169	9	l+l−	l+l−	PROPN
ejpam-4923	169	10	=	=	NOUN
ejpam-4923	169	11	−1	−1	NOUN
ejpam-4923	169	12	4	4	NUM
ejpam-4923	169	13	[	[	X
ejpam-4923	169	14	(	(	PUNCT
ejpam-4923	169	15	m−	m−	PROPN
ejpam-4923	169	16	n−	n−	PROPN
ejpam-4923	169	17	1)2	1)2	NUM
ejpam-4923	169	18	+	+	CCONJ
ejpam-4923	169	19	µ−	µ−	PROPN
ejpam-4923	169	20	1	1	NUM
ejpam-4923	169	21	]	]	PUNCT
ejpam-4923	169	22	,	,	PUNCT
ejpam-4923	169	23	(	(	PUNCT
ejpam-4923	169	24	41	41	NUM
ejpam-4923	169	25	)	)	PUNCT
ejpam-4923	169	26	l−l+	l−l+	PROPN
ejpam-4923	169	27	=	=	PUNCT
ejpam-4923	169	28	−1	−1	NOUN
ejpam-4923	169	29	4	4	NUM
ejpam-4923	169	30	[	[	X
ejpam-4923	169	31	(	(	PUNCT
ejpam-4923	169	32	m−	m−	PROPN
ejpam-4923	169	33	n+	n+	ADP
ejpam-4923	169	34	1)2	1)2	NUM
ejpam-4923	170	1	+	+	CCONJ
ejpam-4923	170	2	µ−	µ−	PROPN
ejpam-4923	170	3	1	1	NUM
ejpam-4923	170	4	]	]	PUNCT
ejpam-4923	170	5	.	.	PUNCT
ejpam-4923	171	1	(	(	PUNCT
ejpam-4923	171	2	42	42	NUM
ejpam-4923	171	3	)	)	PUNCT
ejpam-4923	171	4	now	now	ADV
ejpam-4923	171	5	,	,	PUNCT
ejpam-4923	171	6	since	since	SCONJ
ejpam-4923	171	7	l∗	l∗	PROPN
ejpam-4923	171	8	+	+	CCONJ
ejpam-4923	171	9	=	=	SYM
ejpam-4923	171	10	−l−	−l−	NOUN
ejpam-4923	171	11	,	,	PUNCT
ejpam-4923	171	12	we	we	PRON
ejpam-4923	171	13	have	have	AUX
ejpam-4923	171	14	∥l−∥	∥l−∥	VERB
ejpam-4923	171	15	=	=	NUM
ejpam-4923	171	16	∥l∗	∥l∗	PUNCT
ejpam-4923	171	17	−l−∥	−l−∥	PROPN
ejpam-4923	171	18	1	1	NUM
ejpam-4923	171	19	2	2	NUM
ejpam-4923	171	20	=	=	SYM
ejpam-4923	171	21	∥	∥	NOUN
ejpam-4923	171	22	−	−	VERB
ejpam-4923	171	23	l+l−∥	l+l−∥	VERB
ejpam-4923	171	24	1	1	NUM
ejpam-4923	171	25	2	2	NUM
ejpam-4923	171	26	=	=	SYM
ejpam-4923	171	27	1	1	NUM
ejpam-4923	171	28	2	2	NUM
ejpam-4923	171	29	[	[	X
ejpam-4923	171	30	(	(	PUNCT
ejpam-4923	171	31	m−	m−	PROPN
ejpam-4923	171	32	n−	n−	PROPN
ejpam-4923	171	33	1)2	1)2	NUM
ejpam-4923	171	34	+	+	CCONJ
ejpam-4923	171	35	µ−	µ−	PROPN
ejpam-4923	171	36	1	1	NUM
ejpam-4923	171	37	]	]	SYM
ejpam-4923	171	38	1	1	NUM
ejpam-4923	171	39	2	2	NUM
ejpam-4923	171	40	.	.	PUNCT
ejpam-4923	172	1	(	(	PUNCT
ejpam-4923	172	2	43	43	NUM
ejpam-4923	172	3	)	)	PUNCT
ejpam-4923	172	4	a.	a.	NOUN
ejpam-4923	172	5	s.	s.	PROPN
ejpam-4923	172	6	alghamdi	alghamdi	PROPN
ejpam-4923	172	7	/	/	SYM
ejpam-4923	172	8	eur	eur	PROPN
ejpam-4923	172	9	.	.	PUNCT
ejpam-4923	173	1	j.	j.	PROPN
ejpam-4923	173	2	pure	pure	PROPN
ejpam-4923	173	3	appl	appl	PROPN
ejpam-4923	173	4	.	.	PROPN
ejpam-4923	173	5	math	math	PROPN
ejpam-4923	173	6	,	,	PUNCT
ejpam-4923	173	7	16	16	NUM
ejpam-4923	173	8	(	(	PUNCT
ejpam-4923	173	9	4	4	NUM
ejpam-4923	173	10	)	)	PUNCT
ejpam-4923	173	11	(	(	PUNCT
ejpam-4923	173	12	2023	2023	NUM
ejpam-4923	173	13	)	)	PUNCT
ejpam-4923	173	14	,	,	PUNCT
ejpam-4923	173	15	2348	2348	NUM
ejpam-4923	173	16	-	-	SYM
ejpam-4923	173	17	2367	2367	NUM
ejpam-4923	173	18	2357	2357	NUM
ejpam-4923	173	19	similarly	similarly	ADV
ejpam-4923	173	20	,	,	PUNCT
ejpam-4923	173	21	∥l+∥	∥l+∥	X
ejpam-4923	173	22	=	=	SYM
ejpam-4923	173	23	1	1	NUM
ejpam-4923	173	24	2	2	NUM
ejpam-4923	174	1	[	[	X
ejpam-4923	174	2	(	(	PUNCT
ejpam-4923	174	3	m−	m−	PROPN
ejpam-4923	174	4	n+	n+	ADP
ejpam-4923	174	5	1)2	1)2	NUM
ejpam-4923	174	6	+	+	CCONJ
ejpam-4923	174	7	µ−	µ−	PROPN
ejpam-4923	174	8	1	1	NUM
ejpam-4923	174	9	]	]	SYM
ejpam-4923	174	10	1	1	NUM
ejpam-4923	174	11	2	2	NUM
ejpam-4923	174	12	.	.	PUNCT
ejpam-4923	175	1	(	(	PUNCT
ejpam-4923	175	2	44	44	NUM
ejpam-4923	175	3	)	)	PUNCT
ejpam-4923	175	4	let	let	VERB
ejpam-4923	175	5	1−	1−	NUM
ejpam-4923	175	6	µ	µ	X
ejpam-4923	175	7	=	=	PUNCT
ejpam-4923	175	8	(	(	PUNCT
ejpam-4923	175	9	n−	n−	NOUN
ejpam-4923	175	10	1)2	1)2	NUM
ejpam-4923	175	11	,	,	PUNCT
ejpam-4923	175	12	where	where	SCONJ
ejpam-4923	175	13	n	n	PRON
ejpam-4923	175	14	is	be	AUX
ejpam-4923	175	15	an	an	DET
ejpam-4923	175	16	integer	integer	NOUN
ejpam-4923	175	17	.	.	PUNCT
ejpam-4923	176	1	the	the	DET
ejpam-4923	176	2	functions	function	NOUN
ejpam-4923	176	3	(	(	PUNCT
ejpam-4923	176	4	33	33	NUM
ejpam-4923	176	5	)	)	PUNCT
ejpam-4923	176	6	are	be	AUX
ejpam-4923	176	7	given	give	VERB
ejpam-4923	176	8	by	by	ADP
ejpam-4923	176	9	f−m	f−m	NOUN
ejpam-4923	176	10	2	2	NUM
ejpam-4923	176	11	,	,	PUNCT
ejpam-4923	176	12	n(w	n(w	NOUN
ejpam-4923	176	13	,	,	PUNCT
ejpam-4923	176	14	w	w	NOUN
ejpam-4923	176	15	)	)	PUNCT
ejpam-4923	176	16	=	=	SYM
ejpam-4923	176	17	w	w	PROPN
ejpam-4923	176	18	−m	−m	NOUN
ejpam-4923	176	19	2	2	NUM
ejpam-4923	176	20	(	(	PUNCT
ejpam-4923	176	21	1−	1−	NUM
ejpam-4923	176	22	ww	ww	PROPN
ejpam-4923	176	23	)	)	PUNCT
ejpam-4923	176	24	n	n	PRON
ejpam-4923	176	25	2	2	NUM
ejpam-4923	176	26	.	.	PUNCT
ejpam-4923	177	1	(	(	PUNCT
ejpam-4923	177	2	45	45	NUM
ejpam-4923	177	3	)	)	PUNCT
ejpam-4923	177	4	the	the	DET
ejpam-4923	177	5	functions	function	NOUN
ejpam-4923	177	6	f−m	f−m	VERB
ejpam-4923	177	7	2	2	NUM
ejpam-4923	177	8	,	,	PUNCT
ejpam-4923	177	9	n(w	n(w	NOUN
ejpam-4923	177	10	,	,	PUNCT
ejpam-4923	177	11	w	w	NOUN
ejpam-4923	177	12	)	)	PUNCT
ejpam-4923	177	13	=	=	SYM
ejpam-4923	178	1	w	w	PROPN
ejpam-4923	178	2	−m	−m	NOUN
ejpam-4923	178	3	2	2	NUM
ejpam-4923	178	4	(	(	PUNCT
ejpam-4923	178	5	1−ww	1−ww	NUM
ejpam-4923	178	6	)	)	PUNCT
ejpam-4923	178	7	n	n	PRON
ejpam-4923	178	8	2	2	NUM
ejpam-4923	178	9	,	,	PUNCT
ejpam-4923	178	10	are	be	AUX
ejpam-4923	178	11	l2	l2	NOUN
ejpam-4923	178	12	summable	summable	ADJ
ejpam-4923	178	13	for	for	ADP
ejpam-4923	178	14	n	n	X
ejpam-4923	178	15	>	>	SYM
ejpam-4923	178	16	1	1	NUM
ejpam-4923	178	17	and	and	CCONJ
ejpam-4923	178	18	m	m	PRON
ejpam-4923	178	19	≤	≤	ADJ
ejpam-4923	178	20	0	0	NUM
ejpam-4923	178	21	.	.	PUNCT
ejpam-4923	179	1	proof	proof	NOUN
ejpam-4923	179	2	.	.	PUNCT
ejpam-4923	180	1	let	let	VERB
ejpam-4923	180	2	w	w	PROPN
ejpam-4923	180	3	=	=	SYM
ejpam-4923	180	4	reiθ	reiθ	PROPN
ejpam-4923	180	5	,	,	PUNCT
ejpam-4923	180	6	then	then	ADV
ejpam-4923	180	7	f−m	f−m	VERB
ejpam-4923	180	8	2	2	NUM
ejpam-4923	180	9	,	,	PUNCT
ejpam-4923	180	10	n(re	n(re	NOUN
ejpam-4923	180	11	iθ	iθ	NOUN
ejpam-4923	180	12	,	,	PUNCT
ejpam-4923	180	13	re−iθ	re−iθ	NOUN
ejpam-4923	180	14	)	)	PUNCT
ejpam-4923	181	1	=	=	PRON
ejpam-4923	181	2	(	(	PUNCT
ejpam-4923	181	3	reiθ	reiθ	ADJ
ejpam-4923	181	4	)	)	PUNCT
ejpam-4923	181	5	−m	−m	NOUN
ejpam-4923	181	6	2	2	NUM
ejpam-4923	181	7	(	(	PUNCT
ejpam-4923	181	8	1	1	NUM
ejpam-4923	181	9	−	−	PROPN
ejpam-4923	181	10	r2	r2	NOUN
ejpam-4923	181	11	)	)	PUNCT
ejpam-4923	181	12	n	n	PRON
ejpam-4923	181	13	2	2	NUM
ejpam-4923	181	14	.	.	PUNCT
ejpam-4923	182	1	the	the	DET
ejpam-4923	182	2	measure	measure	NOUN
ejpam-4923	182	3	is	be	AUX
ejpam-4923	182	4	dµ	dµ	ADJ
ejpam-4923	182	5	=	=	PUNCT
ejpam-4923	182	6	rdr∧dθ	rdr∧dθ	X
ejpam-4923	182	7	(	(	PUNCT
ejpam-4923	182	8	1−r2)2	1−r2)2	NUM
ejpam-4923	182	9	.	.	PUNCT
ejpam-4923	183	1	then	then	ADV
ejpam-4923	183	2	,	,	PUNCT
ejpam-4923	183	3	∥f−m	∥f−m	PROPN
ejpam-4923	183	4	2	2	NUM
ejpam-4923	183	5	,	,	PUNCT
ejpam-4923	183	6	n∥2	n∥2	ADJ
ejpam-4923	183	7	=	=	SYM
ejpam-4923	183	8	∫	∫	PROPN
ejpam-4923	183	9	2π	2π	NOUN
ejpam-4923	183	10	0	0	NUM
ejpam-4923	184	1	∫	∫	PROPN
ejpam-4923	184	2	1	1	NUM
ejpam-4923	184	3	0	0	NUM
ejpam-4923	184	4	|f−m	|f−m	PROPN
ejpam-4923	184	5	2	2	NUM
ejpam-4923	184	6	,	,	PUNCT
ejpam-4923	184	7	n(re	n(re	PROPN
ejpam-4923	184	8	iθ	iθ	NOUN
ejpam-4923	184	9	,	,	PUNCT
ejpam-4923	184	10	re−iθ)|2	re−iθ)|2	PROPN
ejpam-4923	184	11	rdr	rdr	PROPN
ejpam-4923	184	12	∧	∧	PROPN
ejpam-4923	184	13	dθ	dθ	PROPN
ejpam-4923	184	14	(	(	PUNCT
ejpam-4923	184	15	1−	1−	NUM
ejpam-4923	184	16	r2)2	r2)2	NOUN
ejpam-4923	184	17	=	=	SYM
ejpam-4923	184	18	∫	∫	PROPN
ejpam-4923	184	19	2π	2π	PROPN
ejpam-4923	184	20	0	0	NUM
ejpam-4923	185	1	∫	∫	PROPN
ejpam-4923	185	2	1	1	NUM
ejpam-4923	185	3	0	0	NUM
ejpam-4923	185	4	∣∣∣∣(reiθ)−m	∣∣∣∣(reiθ)−m	NOUN
ejpam-4923	185	5	2	2	NUM
ejpam-4923	185	6	(	(	PUNCT
ejpam-4923	185	7	1−	1−	NUM
ejpam-4923	185	8	r2	r2	NOUN
ejpam-4923	185	9	)	)	PUNCT
ejpam-4923	185	10	n	n	CCONJ
ejpam-4923	185	11	2	2	NUM
ejpam-4923	185	12	∣∣∣∣2	∣∣∣∣2	NOUN
ejpam-4923	185	13	rdr	rdr	NOUN
ejpam-4923	185	14	∧	∧	PROPN
ejpam-4923	185	15	dθ(1−	dθ(1−	PROPN
ejpam-4923	185	16	r2)2	r2)2	NOUN
ejpam-4923	185	17	=	=	SYM
ejpam-4923	185	18	∫	∫	PROPN
ejpam-4923	185	19	2π	2π	PROPN
ejpam-4923	185	20	0	0	NUM
ejpam-4923	186	1	∫	∫	PROPN
ejpam-4923	186	2	1	1	NUM
ejpam-4923	186	3	0	0	NUM
ejpam-4923	186	4	r−m(1−	r−m(1−	NOUN
ejpam-4923	186	5	r2)n−2rdrdθ	r2)n−2rdrdθ	NOUN
ejpam-4923	186	6	≤	≤	PROPN
ejpam-4923	186	7	π	π	PROPN
ejpam-4923	186	8	∫	∫	PROPN
ejpam-4923	186	9	1	1	NUM
ejpam-4923	186	10	0	0	NUM
ejpam-4923	186	11	(	(	PUNCT
ejpam-4923	186	12	1−	1−	NUM
ejpam-4923	186	13	r2)n−22rdr	r2)n−22rdr	ADV
ejpam-4923	186	14	,	,	PUNCT
ejpam-4923	186	15	for	for	ADP
ejpam-4923	186	16	m	m	PROPN
ejpam-4923	186	17	≤	≤	NOUN
ejpam-4923	186	18	0	0	NUM
ejpam-4923	187	1	=	=	NOUN
ejpam-4923	187	2	−π	−π	PRON
ejpam-4923	187	3	(	(	PUNCT
ejpam-4923	187	4	1−	1−	NUM
ejpam-4923	187	5	r2)n−1	r2)n−1	PROPN
ejpam-4923	187	6	n−	n−	PROPN
ejpam-4923	187	7	1	1	NUM
ejpam-4923	187	8	∣∣∣∣1	∣∣∣∣1	NOUN
ejpam-4923	187	9	0	0	NUM
ejpam-4923	188	1	=	=	SYM
ejpam-4923	189	1	π	π	NOUN
ejpam-4923	189	2	n−	n−	NOUN
ejpam-4923	189	3	1	1	NUM
ejpam-4923	189	4	<	<	ADP
ejpam-4923	189	5	∞.	∞.	PROPN
ejpam-4923	189	6	hence	hence	ADV
ejpam-4923	189	7	,	,	PUNCT
ejpam-4923	189	8	f−m	f−m	NOUN
ejpam-4923	189	9	2	2	NUM
ejpam-4923	189	10	,	,	PUNCT
ejpam-4923	189	11	n	n	PRON
ejpam-4923	189	12	are	be	AUX
ejpam-4923	189	13	l2	l2	NOUN
ejpam-4923	189	14	summable	summable	ADJ
ejpam-4923	189	15	if	if	SCONJ
ejpam-4923	189	16	n	n	PROPN
ejpam-4923	189	17	>	>	X
ejpam-4923	189	18	1	1	NUM
ejpam-4923	189	19	and	and	CCONJ
ejpam-4923	189	20	m	m	PRON
ejpam-4923	189	21	≤	≤	ADJ
ejpam-4923	189	22	0	0	NUM
ejpam-4923	189	23	.	.	PUNCT
ejpam-4923	190	1	by	by	ADP
ejpam-4923	190	2	simple	simple	ADJ
ejpam-4923	190	3	calculation	calculation	NOUN
ejpam-4923	190	4	,	,	PUNCT
ejpam-4923	190	5	we	we	PRON
ejpam-4923	190	6	get	get	VERB
ejpam-4923	190	7	[	[	X
ejpam-4923	190	8	l+f−m	l+f−m	PROPN
ejpam-4923	190	9	2	2	NUM
ejpam-4923	190	10	,	,	PUNCT
ejpam-4923	190	11	n](w	n](w	NOUN
ejpam-4923	190	12	,	,	PUNCT
ejpam-4923	190	13	w	w	NOUN
ejpam-4923	190	14	)	)	PUNCT
ejpam-4923	190	15	=	=	SYM
ejpam-4923	191	1	(	(	PUNCT
ejpam-4923	191	2	n−	n−	NOUN
ejpam-4923	191	3	m	m	NOUN
ejpam-4923	191	4	2	2	NUM
ejpam-4923	191	5	)	)	PUNCT
ejpam-4923	191	6	f−m	f−m	NOUN
ejpam-4923	191	7	2	2	NUM
ejpam-4923	191	8	+1,n(w	+1,n(w	ADJ
ejpam-4923	191	9	,	,	PUNCT
ejpam-4923	191	10	w	w	NOUN
ejpam-4923	191	11	)	)	PUNCT
ejpam-4923	191	12	,	,	PUNCT
ejpam-4923	191	13	(	(	PUNCT
ejpam-4923	191	14	46	46	NUM
ejpam-4923	191	15	)	)	PUNCT
ejpam-4923	192	1	[	[	X
ejpam-4923	192	2	l−f−m	l−f−m	NOUN
ejpam-4923	192	3	2	2	NUM
ejpam-4923	192	4	,	,	PUNCT
ejpam-4923	192	5	n](w	n](w	NOUN
ejpam-4923	192	6	,	,	PUNCT
ejpam-4923	192	7	w	w	NOUN
ejpam-4923	192	8	)	)	PUNCT
ejpam-4923	192	9	=	=	SYM
ejpam-4923	192	10	m	m	VERB
ejpam-4923	192	11	2	2	NUM
ejpam-4923	192	12	f−m	f−m	NOUN
ejpam-4923	192	13	2	2	NUM
ejpam-4923	192	14	−1,n(w	−1,n(w	NOUN
ejpam-4923	192	15	,	,	PUNCT
ejpam-4923	192	16	w	w	NOUN
ejpam-4923	192	17	)	)	PUNCT
ejpam-4923	192	18	.	.	PUNCT
ejpam-4923	193	1	(	(	PUNCT
ejpam-4923	193	2	47	47	NUM
ejpam-4923	193	3	)	)	PUNCT
ejpam-4923	193	4	at	at	ADP
ejpam-4923	193	5	m	m	PROPN
ejpam-4923	193	6	=	=	SYM
ejpam-4923	193	7	0	0	NUM
ejpam-4923	193	8	,	,	PUNCT
ejpam-4923	193	9	we	we	PRON
ejpam-4923	193	10	have	have	VERB
ejpam-4923	193	11	the	the	DET
ejpam-4923	193	12	function	function	NOUN
ejpam-4923	193	13	f0,n(w	f0,n(w	ADP
ejpam-4923	193	14	,	,	PUNCT
ejpam-4923	193	15	w	w	NOUN
ejpam-4923	193	16	)	)	PUNCT
ejpam-4923	193	17	=	=	SYM
ejpam-4923	193	18	(	(	PUNCT
ejpam-4923	193	19	1	1	NUM
ejpam-4923	193	20	−	−	NUM
ejpam-4923	193	21	ww	ww	PROPN
ejpam-4923	193	22	)	)	PUNCT
ejpam-4923	193	23	n	n	PRON
ejpam-4923	193	24	2	2	NUM
ejpam-4923	193	25	.	.	PUNCT
ejpam-4923	194	1	then	then	ADV
ejpam-4923	194	2	,	,	PUNCT
ejpam-4923	194	3	l−f0,n(w	l−f0,n(w	PROPN
ejpam-4923	194	4	,	,	PUNCT
ejpam-4923	194	5	w	w	NOUN
ejpam-4923	194	6	)	)	PUNCT
ejpam-4923	194	7	=	=	SYM
ejpam-4923	194	8	0	0	NUM
ejpam-4923	194	9	,	,	PUNCT
ejpam-4923	194	10	which	which	PRON
ejpam-4923	194	11	means	mean	VERB
ejpam-4923	194	12	that	that	SCONJ
ejpam-4923	194	13	f0,n(w	f0,n(w	ADP
ejpam-4923	194	14	,	,	PUNCT
ejpam-4923	194	15	w	w	NOUN
ejpam-4923	194	16	)	)	PUNCT
ejpam-4923	194	17	is	be	AUX
ejpam-4923	194	18	the	the	DET
ejpam-4923	194	19	vacuum	vacuum	NOUN
ejpam-4923	194	20	of	of	ADP
ejpam-4923	194	21	the	the	DET
ejpam-4923	194	22	operator	operator	NOUN
ejpam-4923	194	23	l−.	l−.	PROPN
ejpam-4923	194	24	this	this	PRON
ejpam-4923	194	25	is	be	AUX
ejpam-4923	194	26	represented	represent	VERB
ejpam-4923	194	27	by	by	ADP
ejpam-4923	194	28	the	the	DET
ejpam-4923	194	29	following	follow	VERB
ejpam-4923	194	30	diagram	diagram	NOUN
ejpam-4923	194	31	:	:	PUNCT
ejpam-4923	194	32	next	next	ADV
ejpam-4923	194	33	,	,	PUNCT
ejpam-4923	194	34	let	let	VERB
ejpam-4923	194	35	1−	1−	NUM
ejpam-4923	194	36	µ	µ	X
ejpam-4923	194	37	=	=	PUNCT
ejpam-4923	194	38	(	(	PUNCT
ejpam-4923	194	39	n+	n+	NUM
ejpam-4923	194	40	1)2	1)2	NUM
ejpam-4923	194	41	.	.	PUNCT
ejpam-4923	195	1	then	then	ADV
ejpam-4923	195	2	,	,	PUNCT
ejpam-4923	195	3	the	the	DET
ejpam-4923	195	4	functions	function	NOUN
ejpam-4923	195	5	(	(	PUNCT
ejpam-4923	195	6	34	34	NUM
ejpam-4923	195	7	)	)	PUNCT
ejpam-4923	195	8	are	be	AUX
ejpam-4923	195	9	given	give	VERB
ejpam-4923	195	10	by	by	ADP
ejpam-4923	195	11	0	0	NUM
ejpam-4923	195	12	f0,n	f0,n	PROPN
ejpam-4923	195	13	f1,n	f1,n	PROPN
ejpam-4923	195	14	f2,n	f2,n	PROPN
ejpam-4923	195	15	·	·	PUNCT
ejpam-4923	195	16	·	·	PUNCT
ejpam-4923	195	17	·	·	PUNCT
ejpam-4923	196	1	l−	l−	NOUN
ejpam-4923	196	2	l+	l+	PUNCT
ejpam-4923	196	3	l−	l−	NOUN
ejpam-4923	196	4	l+	l+	PUNCT
ejpam-4923	196	5	l−	l−	NOUN
ejpam-4923	196	6	l+	l+	PUNCT
ejpam-4923	196	7	l−	l−	NOUN
ejpam-4923	196	8	f̃−m	f̃−m	PROPN
ejpam-4923	196	9	2	2	NUM
ejpam-4923	196	10	,	,	PUNCT
ejpam-4923	196	11	n(w	n(w	NOUN
ejpam-4923	196	12	,	,	PUNCT
ejpam-4923	196	13	w	w	NOUN
ejpam-4923	196	14	)	)	PUNCT
ejpam-4923	196	15	=	=	PUNCT
ejpam-4923	197	1	w	w	PROPN
ejpam-4923	197	2	m	m	VERB
ejpam-4923	197	3	2	2	NUM
ejpam-4923	197	4	(	(	PUNCT
ejpam-4923	197	5	1−	1−	NUM
ejpam-4923	197	6	ww	ww	PROPN
ejpam-4923	197	7	)	)	PUNCT
ejpam-4923	197	8	−n	−n	NOUN
ejpam-4923	197	9	2	2	NUM
ejpam-4923	197	10	,	,	PUNCT
ejpam-4923	197	11	(	(	PUNCT
ejpam-4923	197	12	48	48	NUM
ejpam-4923	197	13	)	)	PUNCT
ejpam-4923	197	14	a.	a.	NOUN
ejpam-4923	197	15	s.	s.	PROPN
ejpam-4923	197	16	alghamdi	alghamdi	PROPN
ejpam-4923	197	17	/	/	SYM
ejpam-4923	197	18	eur	eur	PROPN
ejpam-4923	197	19	.	.	PUNCT
ejpam-4923	198	1	j.	j.	PROPN
ejpam-4923	198	2	pure	pure	PROPN
ejpam-4923	198	3	appl	appl	PROPN
ejpam-4923	198	4	.	.	PROPN
ejpam-4923	198	5	math	math	PROPN
ejpam-4923	198	6	,	,	PUNCT
ejpam-4923	198	7	16	16	NUM
ejpam-4923	198	8	(	(	PUNCT
ejpam-4923	198	9	4	4	NUM
ejpam-4923	198	10	)	)	PUNCT
ejpam-4923	198	11	(	(	PUNCT
ejpam-4923	198	12	2023	2023	NUM
ejpam-4923	198	13	)	)	PUNCT
ejpam-4923	198	14	,	,	PUNCT
ejpam-4923	198	15	2348	2348	NUM
ejpam-4923	198	16	-	-	SYM
ejpam-4923	198	17	2367	2367	NUM
ejpam-4923	198	18	2358	2358	NUM
ejpam-4923	198	19	which	which	PRON
ejpam-4923	198	20	are	be	AUX
ejpam-4923	198	21	l2	l2	NOUN
ejpam-4923	198	22	summable	summable	ADJ
ejpam-4923	198	23	for	for	ADP
ejpam-4923	198	24	n	n	NOUN
ejpam-4923	198	25	<	<	X
ejpam-4923	198	26	−1	−1	NOUN
ejpam-4923	198	27	and	and	CCONJ
ejpam-4923	198	28	m	m	PROPN
ejpam-4923	198	29	≥	≥	NOUN
ejpam-4923	198	30	0	0	NUM
ejpam-4923	198	31	;	;	PUNCT
ejpam-4923	198	32	that	that	PRON
ejpam-4923	198	33	is	is	ADV
ejpam-4923	198	34	,	,	PUNCT
ejpam-4923	198	35	∥f̃−m	∥f̃−m	PROPN
ejpam-4923	198	36	2	2	NUM
ejpam-4923	198	37	,	,	PUNCT
ejpam-4923	198	38	n∥2	n∥2	ADV
ejpam-4923	198	39	=	=	SYM
ejpam-4923	198	40	∫	∫	PROPN
ejpam-4923	199	1	d	d	X
ejpam-4923	199	2	∣∣∣∣f̃−m	∣∣∣∣f̃−m	PROPN
ejpam-4923	199	3	2	2	NUM
ejpam-4923	199	4	,	,	PUNCT
ejpam-4923	199	5	n(w	n(w	NOUN
ejpam-4923	199	6	,	,	PUNCT
ejpam-4923	199	7	w	w	NOUN
ejpam-4923	199	8	)	)	PUNCT
ejpam-4923	199	9	∣∣∣∣2	∣∣∣∣2	NOUN
ejpam-4923	199	10	dw	dw	PROPN
ejpam-4923	199	11	∧	∧	PROPN
ejpam-4923	199	12	dw	dw	PROPN
ejpam-4923	199	13	(	(	PUNCT
ejpam-4923	199	14	1−	1−	NUM
ejpam-4923	199	15	|w|2	|w|2	NOUN
ejpam-4923	199	16	)	)	PUNCT
ejpam-4923	199	17	<	<	X
ejpam-4923	199	18	∞	∞	PROPN
ejpam-4923	199	19	,	,	PUNCT
ejpam-4923	199	20	n	n	CCONJ
ejpam-4923	199	21	<	<	X
ejpam-4923	199	22	−1	−1	NOUN
ejpam-4923	199	23	.	.	PUNCT
ejpam-4923	200	1	[	[	X
ejpam-4923	200	2	l+f̃−m	l+f̃−m	PROPN
ejpam-4923	200	3	2	2	NUM
ejpam-4923	200	4	,	,	PUNCT
ejpam-4923	200	5	n](w	n](w	NOUN
ejpam-4923	200	6	,	,	PUNCT
ejpam-4923	200	7	w	w	NOUN
ejpam-4923	200	8	)	)	PUNCT
ejpam-4923	200	9	=	=	SYM
ejpam-4923	200	10	−m	−m	ADJ
ejpam-4923	200	11	2	2	NUM
ejpam-4923	200	12	f̃−(m	f̃−(m	NOUN
ejpam-4923	200	13	2	2	NUM
ejpam-4923	200	14	+1),n(w	+1),n(w	ADP
ejpam-4923	200	15	,	,	PUNCT
ejpam-4923	200	16	w	w	NOUN
ejpam-4923	200	17	)	)	PUNCT
ejpam-4923	200	18	,	,	PUNCT
ejpam-4923	200	19	(	(	PUNCT
ejpam-4923	200	20	49	49	NUM
ejpam-4923	200	21	)	)	PUNCT
ejpam-4923	201	1	[	[	X
ejpam-4923	201	2	l−f̃−m	l−f̃−m	NOUN
ejpam-4923	201	3	2	2	NUM
ejpam-4923	201	4	,	,	PUNCT
ejpam-4923	201	5	n](w	n](w	NOUN
ejpam-4923	201	6	,	,	PUNCT
ejpam-4923	201	7	w	w	NOUN
ejpam-4923	201	8	)	)	PUNCT
ejpam-4923	201	9	=	=	SYM
ejpam-4923	201	10	(	(	PUNCT
ejpam-4923	201	11	m	m	PROPN
ejpam-4923	201	12	2	2	NUM
ejpam-4923	201	13	−	−	PROPN
ejpam-4923	201	14	n	n	CCONJ
ejpam-4923	201	15	)	)	PUNCT
ejpam-4923	201	16	f̃−(m	f̃−(m	NOUN
ejpam-4923	201	17	2	2	NUM
ejpam-4923	201	18	−1),n(w	−1),n(w	NOUN
ejpam-4923	201	19	,	,	PUNCT
ejpam-4923	201	20	w	w	NOUN
ejpam-4923	201	21	)	)	PUNCT
ejpam-4923	201	22	.	.	PUNCT
ejpam-4923	202	1	(	(	PUNCT
ejpam-4923	202	2	50	50	NUM
ejpam-4923	202	3	)	)	PUNCT
ejpam-4923	202	4	atm	atm	NOUN
ejpam-4923	202	5	=	=	SYM
ejpam-4923	202	6	0	0	NUM
ejpam-4923	202	7	,	,	PUNCT
ejpam-4923	202	8	we	we	PRON
ejpam-4923	202	9	get	get	VERB
ejpam-4923	202	10	the	the	DET
ejpam-4923	202	11	function	function	NOUN
ejpam-4923	202	12	f̃0,n(w	f̃0,n(w	PROPN
ejpam-4923	202	13	,	,	PUNCT
ejpam-4923	202	14	w	w	NOUN
ejpam-4923	202	15	)	)	PUNCT
ejpam-4923	202	16	=	=	SYM
ejpam-4923	202	17	(	(	PUNCT
ejpam-4923	202	18	1−ww	1−ww	NUM
ejpam-4923	202	19	)	)	PUNCT
ejpam-4923	202	20	−n	−n	ADV
ejpam-4923	202	21	2	2	NUM
ejpam-4923	202	22	.	.	PUNCT
ejpam-4923	203	1	we	we	PRON
ejpam-4923	203	2	can	can	AUX
ejpam-4923	203	3	then	then	ADV
ejpam-4923	203	4	see	see	VERB
ejpam-4923	203	5	that	that	SCONJ
ejpam-4923	203	6	[	[	X
ejpam-4923	203	7	l+f̃0,n](w	l+f̃0,n](w	PROPN
ejpam-4923	203	8	,	,	PUNCT
ejpam-4923	203	9	w	w	NOUN
ejpam-4923	203	10	)	)	PUNCT
ejpam-4923	203	11	=	=	SYM
ejpam-4923	203	12	0	0	NUM
ejpam-4923	203	13	,	,	PUNCT
ejpam-4923	203	14	which	which	PRON
ejpam-4923	203	15	means	mean	VERB
ejpam-4923	203	16	that	that	SCONJ
ejpam-4923	203	17	f̃0,n	f̃0,n	PROPN
ejpam-4923	203	18	is	be	AUX
ejpam-4923	203	19	the	the	DET
ejpam-4923	203	20	vacuum	vacuum	NOUN
ejpam-4923	203	21	of	of	ADP
ejpam-4923	203	22	the	the	DET
ejpam-4923	203	23	operator	operator	NOUN
ejpam-4923	203	24	l+	l+	NOUN
ejpam-4923	203	25	.	.	PUNCT
ejpam-4923	204	1	this	this	PRON
ejpam-4923	204	2	is	be	AUX
ejpam-4923	204	3	represented	represent	VERB
ejpam-4923	204	4	by	by	ADP
ejpam-4923	204	5	the	the	DET
ejpam-4923	204	6	following	follow	VERB
ejpam-4923	204	7	diagram	diagram	NOUN
ejpam-4923	204	8	:	:	PUNCT
ejpam-4923	204	9	the	the	DET
ejpam-4923	204	10	lie	lie	NOUN
ejpam-4923	204	11	derivatives	derivative	NOUN
ejpam-4923	204	12	of	of	ADP
ejpam-4923	204	13	the	the	DET
ejpam-4923	204	14	representation	representation	NOUN
ejpam-4923	204	15	πn	πn	VERB
ejpam-4923	204	16	are	be	AUX
ejpam-4923	204	17	·	·	PUNCT
ejpam-4923	204	18	·	·	PUNCT
ejpam-4923	204	19	·	·	PUNCT
ejpam-4923	204	20	f̃−2,n	f̃−2,n	NOUN
ejpam-4923	204	21	f̃−1,n	f̃−1,n	PROPN
ejpam-4923	204	22	f̃0,n	f̃0,n	X
ejpam-4923	204	23	0	0	NUM
ejpam-4923	204	24	l+	l+	AUX
ejpam-4923	204	25	l−	l−	NOUN
ejpam-4923	204	26	l+	l+	PUNCT
ejpam-4923	204	27	l−	l−	NOUN
ejpam-4923	204	28	l+	l+	PUNCT
ejpam-4923	204	29	l−	l−	NOUN
ejpam-4923	204	30	l+	l+	PUNCT
ejpam-4923	204	31	lz̃	lz̃	NOUN
ejpam-4923	204	32	=	=	PUNCT
ejpam-4923	204	33	−∂θ	−∂θ	PROPN
ejpam-4923	204	34	,	,	PUNCT
ejpam-4923	204	35	(	(	PUNCT
ejpam-4923	204	36	51	51	NUM
ejpam-4923	204	37	)	)	PUNCT
ejpam-4923	204	38	lã	lã	NOUN
ejpam-4923	204	39	=	=	SYM
ejpam-4923	204	40	−r	−r	ADJ
ejpam-4923	204	41	2	2	NUM
ejpam-4923	204	42	sin(ϕ−	sin(ϕ−	NOUN
ejpam-4923	204	43	2θ)∂θ	2θ)∂θ	NUM
ejpam-4923	204	44	−	−	NOUN
ejpam-4923	204	45	1	1	NUM
ejpam-4923	204	46	2	2	NUM
ejpam-4923	204	47	(	(	PUNCT
ejpam-4923	204	48	1−	1−	NUM
ejpam-4923	204	49	uū	uū	NOUN
ejpam-4923	204	50	)	)	PUNCT
ejpam-4923	204	51	[	[	PUNCT
ejpam-4923	204	52	e2iθ∂u	e2iθ∂u	NOUN
ejpam-4923	204	53	+	+	CCONJ
ejpam-4923	204	54	e−2iθ∂ū	e−2iθ∂ū	NOUN
ejpam-4923	204	55	]	]	PUNCT
ejpam-4923	204	56	,	,	PUNCT
ejpam-4923	204	57	(	(	PUNCT
ejpam-4923	204	58	52	52	NUM
ejpam-4923	204	59	)	)	PUNCT
ejpam-4923	204	60	lb̃	lb̃	NOUN
ejpam-4923	205	1	=	=	SYM
ejpam-4923	205	2	r	r	NOUN
ejpam-4923	205	3	2	2	NUM
ejpam-4923	205	4	cos(ϕ−	cos(ϕ−	NOUN
ejpam-4923	206	1	2θ)∂θ	2θ)∂θ	NUM
ejpam-4923	207	1	−	−	NOUN
ejpam-4923	208	1	i	i	PRON
ejpam-4923	208	2	2	2	NUM
ejpam-4923	208	3	(	(	PUNCT
ejpam-4923	208	4	1−	1−	NUM
ejpam-4923	208	5	uū	uū	NOUN
ejpam-4923	208	6	)	)	PUNCT
ejpam-4923	208	7	[	[	PUNCT
ejpam-4923	208	8	e2iθ∂u	e2iθ∂u	NOUN
ejpam-4923	208	9	−	−	NOUN
ejpam-4923	208	10	e−2iθ∂ū	e−2iθ∂ū	NOUN
ejpam-4923	208	11	]	]	PUNCT
ejpam-4923	208	12	.	.	PUNCT
ejpam-4923	209	1	(	(	PUNCT
ejpam-4923	209	2	53	53	NUM
ejpam-4923	209	3	)	)	PUNCT
ejpam-4923	209	4	the	the	DET
ejpam-4923	209	5	right	right	ADJ
ejpam-4923	209	6	ladder	ladder	NOUN
ejpam-4923	209	7	operators	operator	NOUN
ejpam-4923	209	8	are	be	AUX
ejpam-4923	209	9	then	then	ADV
ejpam-4923	209	10	represented	represent	VERB
ejpam-4923	209	11	by	by	ADP
ejpam-4923	209	12	l+	l+	X
ejpam-4923	210	1	=	=	SYM
ejpam-4923	210	2	lã+ib̃	lã+ib̃	PROPN
ejpam-4923	210	3	=	=	PUNCT
ejpam-4923	210	4	e−2iθ	e−2iθ	NOUN
ejpam-4923	210	5	[	[	PUNCT
ejpam-4923	210	6	i	i	NOUN
ejpam-4923	210	7	2	2	NUM
ejpam-4923	210	8	u∂θ	u∂θ	ADV
ejpam-4923	210	9	−	−	PROPN
ejpam-4923	210	10	(	(	PUNCT
ejpam-4923	210	11	1−	1−	NUM
ejpam-4923	210	12	uū)∂ū	uū)∂ū	X
ejpam-4923	210	13	]	]	PUNCT
ejpam-4923	210	14	,	,	PUNCT
ejpam-4923	210	15	(	(	PUNCT
ejpam-4923	210	16	54	54	NUM
ejpam-4923	210	17	)	)	PUNCT
ejpam-4923	210	18	l−	l−	NOUN
ejpam-4923	210	19	=	=	SYM
ejpam-4923	210	20	lã−ib̃	lã−ib̃	PROPN
ejpam-4923	210	21	=	=	SYM
ejpam-4923	210	22	−e2iθ	−e2iθ	NUM
ejpam-4923	211	1	[	[	PUNCT
ejpam-4923	211	2	i	i	NOUN
ejpam-4923	211	3	2	2	NUM
ejpam-4923	211	4	ū∂θ	ū∂θ	PROPN
ejpam-4923	211	5	+	+	CCONJ
ejpam-4923	211	6	(	(	PUNCT
ejpam-4923	211	7	1−	1−	NUM
ejpam-4923	211	8	uū)∂u	uū)∂u	ADJ
ejpam-4923	211	9	]	]	PUNCT
ejpam-4923	211	10	.	.	PUNCT
ejpam-4923	212	1	(	(	PUNCT
ejpam-4923	212	2	55	55	NUM
ejpam-4923	212	3	)	)	PUNCT
ejpam-4923	212	4	proof	proof	NOUN
ejpam-4923	212	5	.	.	PUNCT
ejpam-4923	213	1	the	the	DET
ejpam-4923	213	2	lie	lie	NOUN
ejpam-4923	213	3	derivative	derivative	ADJ
ejpam-4923	213	4	lx	lx	NOUN
ejpam-4923	213	5	for	for	ADP
ejpam-4923	213	6	an	an	DET
ejpam-4923	213	7	element	element	NOUN
ejpam-4923	213	8	x	x	PUNCT
ejpam-4923	213	9	of	of	ADP
ejpam-4923	213	10	the	the	DET
ejpam-4923	213	11	lie	lie	NOUN
ejpam-4923	213	12	algebra	algebra	PROPN
ejpam-4923	213	13	su(1	su(1	NOUN
ejpam-4923	213	14	,	,	PUNCT
ejpam-4923	213	15	1	1	NUM
ejpam-4923	213	16	)	)	PUNCT
ejpam-4923	213	17	is	be	AUX
ejpam-4923	213	18	given	give	VERB
ejpam-4923	213	19	by	by	ADP
ejpam-4923	213	20	[	[	X
ejpam-4923	213	21	lxf	lxf	X
ejpam-4923	213	22	]	]	X
ejpam-4923	213	23	(	(	PUNCT
ejpam-4923	213	24	g	g	NOUN
ejpam-4923	213	25	)	)	PUNCT
ejpam-4923	213	26	=	=	PUNCT
ejpam-4923	214	1	d	d	NOUN
ejpam-4923	214	2	dt	dt	X
ejpam-4923	214	3	f	f	X
ejpam-4923	214	4	(	(	PUNCT
ejpam-4923	214	5	g	g	PROPN
ejpam-4923	214	6	exp	exp	NOUN
ejpam-4923	214	7	tx)|t=0	tx)|t=0	PROPN
ejpam-4923	214	8	,	,	PUNCT
ejpam-4923	214	9	(	(	PUNCT
ejpam-4923	214	10	56	56	NUM
ejpam-4923	214	11	)	)	PUNCT
ejpam-4923	214	12	for	for	ADP
ejpam-4923	214	13	any	any	DET
ejpam-4923	214	14	differentiable	differentiable	ADJ
ejpam-4923	214	15	function	function	NOUN
ejpam-4923	214	16	f	f	PROPN
ejpam-4923	214	17	on	on	ADP
ejpam-4923	214	18	su(1	su(1	NOUN
ejpam-4923	214	19	,	,	PUNCT
ejpam-4923	214	20	1	1	NUM
ejpam-4923	214	21	)	)	PUNCT
ejpam-4923	214	22	and	and	CCONJ
ejpam-4923	214	23	g	g	NOUN
ejpam-4923	214	24	=	=	SYM
ejpam-4923	214	25	(	(	PUNCT
ejpam-4923	214	26	α	α	PROPN
ejpam-4923	214	27	β̄	β̄	PROPN
ejpam-4923	214	28	β	β	X
ejpam-4923	214	29	ᾱ	ᾱ	NOUN
ejpam-4923	214	30	)	)	PUNCT
ejpam-4923	214	31	.	.	PUNCT
ejpam-4923	215	1	we	we	PRON
ejpam-4923	215	2	know	know	VERB
ejpam-4923	215	3	that	that	SCONJ
ejpam-4923	215	4	the	the	DET
ejpam-4923	215	5	space	space	NOUN
ejpam-4923	215	6	lχn	lχn	ADV
ejpam-4923	215	7	2	2	NUM
ejpam-4923	215	8	(	(	PUNCT
ejpam-4923	215	9	su(1	su(1	NOUN
ejpam-4923	215	10	,	,	PUNCT
ejpam-4923	215	11	1	1	NUM
ejpam-4923	215	12	)	)	PUNCT
ejpam-4923	215	13	)	)	PUNCT
ejpam-4923	215	14	consists	consist	VERB
ejpam-4923	215	15	of	of	ADP
ejpam-4923	215	16	the	the	DET
ejpam-4923	215	17	functions	function	NOUN
ejpam-4923	216	1	fn	fn	NOUN
ejpam-4923	216	2	:	:	PUNCT
ejpam-4923	216	3	su(1	su(1	NOUN
ejpam-4923	216	4	,	,	PUNCT
ejpam-4923	216	5	1	1	NUM
ejpam-4923	216	6	)	)	PUNCT
ejpam-4923	216	7	→	→	PUNCT
ejpam-4923	216	8	c	c	NOUN
ejpam-4923	216	9	with	with	ADP
ejpam-4923	216	10	the	the	DET
ejpam-4923	216	11	property	property	NOUN
ejpam-4923	216	12	fn	fn	NOUN
ejpam-4923	217	1	[	[	X
ejpam-4923	217	2	(	(	PUNCT
ejpam-4923	217	3	α	α	X
ejpam-4923	217	4	β	β	X
ejpam-4923	217	5	β	β	X
ejpam-4923	217	6	α	α	NOUN
ejpam-4923	217	7	)	)	PUNCT
ejpam-4923	217	8	]	]	PUNCT
ejpam-4923	218	1	=	=	PUNCT
ejpam-4923	218	2	χn	χn	X
ejpam-4923	218	3	(	(	PUNCT
ejpam-4923	218	4	α	α	PROPN
ejpam-4923	218	5	|α|	|α|	PROPN
ejpam-4923	218	6	)	)	PUNCT
ejpam-4923	218	7	f	f	PROPN
ejpam-4923	218	8	(	(	PUNCT
ejpam-4923	218	9	β	β	X
ejpam-4923	218	10	α	α	NOUN
ejpam-4923	218	11	,	,	PUNCT
ejpam-4923	218	12	β	β	X
ejpam-4923	218	13	α	α	NOUN
ejpam-4923	218	14	)	)	PUNCT
ejpam-4923	218	15	,	,	PUNCT
ejpam-4923	218	16	where	where	SCONJ
ejpam-4923	218	17	f	f	PROPN
ejpam-4923	218	18	∈	∈	PROPN
ejpam-4923	218	19	l2(d	l2(d	PROPN
ejpam-4923	218	20	)	)	PUNCT
ejpam-4923	218	21	.	.	PUNCT
ejpam-4923	219	1	a.	a.	PROPN
ejpam-4923	219	2	s.	s.	PROPN
ejpam-4923	219	3	alghamdi	alghamdi	PROPN
ejpam-4923	219	4	/	/	SYM
ejpam-4923	219	5	eur	eur	PROPN
ejpam-4923	219	6	.	.	PUNCT
ejpam-4923	220	1	j.	j.	PROPN
ejpam-4923	220	2	pure	pure	PROPN
ejpam-4923	220	3	appl	appl	PROPN
ejpam-4923	220	4	.	.	PROPN
ejpam-4923	220	5	math	math	PROPN
ejpam-4923	220	6	,	,	PUNCT
ejpam-4923	220	7	16	16	NUM
ejpam-4923	220	8	(	(	PUNCT
ejpam-4923	220	9	4	4	NUM
ejpam-4923	220	10	)	)	PUNCT
ejpam-4923	220	11	(	(	PUNCT
ejpam-4923	220	12	2023	2023	NUM
ejpam-4923	220	13	)	)	PUNCT
ejpam-4923	220	14	,	,	PUNCT
ejpam-4923	220	15	2348	2348	NUM
ejpam-4923	220	16	-	-	SYM
ejpam-4923	220	17	2367	2367	NUM
ejpam-4923	220	18	2359	2359	NUM
ejpam-4923	220	19	hence	hence	ADV
ejpam-4923	220	20	,	,	PUNCT
ejpam-4923	220	21	for	for	ADP
ejpam-4923	220	22	v	v	NOUN
ejpam-4923	220	23	=	=	SYM
ejpam-4923	220	24	α	α	DET
ejpam-4923	220	25	|α|	|α|	PROPN
ejpam-4923	220	26	=	=	SYM
ejpam-4923	220	27	eiθ	eiθ	PROPN
ejpam-4923	220	28	and	and	CCONJ
ejpam-4923	220	29	u	u	NOUN
ejpam-4923	220	30	=	=	SYM
ejpam-4923	220	31	β	β	X
ejpam-4923	220	32	α	α	NOUN
ejpam-4923	220	33	=	=	NOUN
ejpam-4923	220	34	reiϕ	reiϕ	NOUN
ejpam-4923	220	35	,	,	PUNCT
ejpam-4923	220	36	we	we	PRON
ejpam-4923	220	37	have	have	VERB
ejpam-4923	220	38	[	[	X
ejpam-4923	220	39	lxfn](g	lxfn](g	X
ejpam-4923	220	40	)	)	PUNCT
ejpam-4923	220	41	=	=	PUNCT
ejpam-4923	221	1	d	d	NOUN
ejpam-4923	221	2	dt	dt	X
ejpam-4923	221	3	fn(g	fn(g	PUNCT
ejpam-4923	221	4	exp	exp	X
ejpam-4923	221	5	tx	tx	PROPN
ejpam-4923	221	6	)	)	PUNCT
ejpam-4923	221	7	∣∣∣∣	∣∣∣∣	NOUN
ejpam-4923	221	8	t=0	t=0	VERB
ejpam-4923	221	9	=	=	SYM
ejpam-4923	222	1	d	d	X
ejpam-4923	222	2	dt	dt	X
ejpam-4923	222	3	χn(v(t))f	χn(v(t))f	PUNCT
ejpam-4923	222	4	(	(	PUNCT
ejpam-4923	222	5	u(t	u(t	PROPN
ejpam-4923	222	6	)	)	PUNCT
ejpam-4923	222	7	,	,	PUNCT
ejpam-4923	222	8	ū(t	ū(t	NOUN
ejpam-4923	222	9	)	)	PUNCT
ejpam-4923	222	10	)	)	PUNCT
ejpam-4923	223	1	∣∣∣∣	∣∣∣∣	NOUN
ejpam-4923	223	2	t=0	t=0	VERB
ejpam-4923	223	3	=	=	PROPN
ejpam-4923	223	4	∂χn	∂χn	PROPN
ejpam-4923	223	5	∂v	∂v	PROPN
ejpam-4923	223	6	dv(t	dv(t	NOUN
ejpam-4923	223	7	)	)	PUNCT
ejpam-4923	223	8	dt	dt	ADP
ejpam-4923	223	9	∣∣∣∣	∣∣∣∣	PROPN
ejpam-4923	223	10	t=0	t=0	PROPN
ejpam-4923	223	11	+	+	PROPN
ejpam-4923	223	12	∂f	∂f	PROPN
ejpam-4923	223	13	∂u	∂u	PROPN
ejpam-4923	223	14	du(t	du(t	NOUN
ejpam-4923	223	15	)	)	PUNCT
ejpam-4923	223	16	dt	dt	PART
ejpam-4923	224	1	∣∣∣∣	∣∣∣∣	PROPN
ejpam-4923	224	2	t=0	t=0	PROPN
ejpam-4923	224	3	+	+	CCONJ
ejpam-4923	224	4	∂f	∂f	PROPN
ejpam-4923	224	5	∂ū	∂ū	PROPN
ejpam-4923	224	6	dū(t	dū(t	PROPN
ejpam-4923	224	7	)	)	PUNCT
ejpam-4923	224	8	dt	dt	PROPN
ejpam-4923	224	9	∣∣∣∣	∣∣∣∣	PROPN
ejpam-4923	224	10	t=0	t=0	PROPN
ejpam-4923	224	11	.	.	PUNCT
ejpam-4923	225	1	(	(	PUNCT
ejpam-4923	225	2	57	57	NUM
ejpam-4923	225	3	)	)	PUNCT
ejpam-4923	225	4	from	from	ADP
ejpam-4923	225	5	section	section	NOUN
ejpam-4923	225	6	2	2	NUM
ejpam-4923	225	7	we	we	PRON
ejpam-4923	225	8	have	have	VERB
ejpam-4923	225	9	z̃	z̃	PROPN
ejpam-4923	225	10	,	,	PUNCT
ejpam-4923	225	11	ã	ã	PROPN
ejpam-4923	225	12	and	and	CCONJ
ejpam-4923	225	13	b̃	b̃	PROPN
ejpam-4923	225	14	∈	∈	PROPN
ejpam-4923	225	15	su(1	su(1	NOUN
ejpam-4923	225	16	,	,	PUNCT
ejpam-4923	225	17	1	1	NUM
ejpam-4923	225	18	)	)	PUNCT
ejpam-4923	225	19	given	give	VERB
ejpam-4923	225	20	by	by	ADP
ejpam-4923	225	21	(	(	PUNCT
ejpam-4923	225	22	8)	8)	NUM
ejpam-4923	225	23	.	.	PUNCT
ejpam-4923	226	1	then	then	ADV
ejpam-4923	226	2	,	,	PUNCT
ejpam-4923	226	3	the	the	DET
ejpam-4923	226	4	lie	lie	NOUN
ejpam-4923	226	5	derivatives	derivative	NOUN
ejpam-4923	226	6	corresponding	correspond	VERB
ejpam-4923	226	7	to	to	ADP
ejpam-4923	226	8	the	the	DET
ejpam-4923	226	9	subgroups	subgroup	NOUN
ejpam-4923	226	10	exp	exp	NOUN
ejpam-4923	226	11	tz̃,(9	tz̃,(9	NOUN
ejpam-4923	226	12	)	)	PUNCT
ejpam-4923	226	13	,	,	PUNCT
ejpam-4923	226	14	exp	exp	NOUN
ejpam-4923	226	15	tã,(10	tã,(10	PROPN
ejpam-4923	226	16	)	)	PUNCT
ejpam-4923	226	17	and	and	CCONJ
ejpam-4923	226	18	exp	exp	NOUN
ejpam-4923	226	19	tb̃(11	tb̃(11	NOUN
ejpam-4923	226	20	)	)	PUNCT
ejpam-4923	226	21	are	be	AUX
ejpam-4923	226	22	obtained	obtain	VERB
ejpam-4923	226	23	through	through	ADP
ejpam-4923	226	24	the	the	DET
ejpam-4923	226	25	differentiation	differentiation	NOUN
ejpam-4923	226	26	of	of	ADP
ejpam-4923	226	27	the	the	DET
ejpam-4923	226	28	right	right	ADJ
ejpam-4923	226	29	action	action	NOUN
ejpam-4923	226	30	of	of	ADP
ejpam-4923	226	31	these	these	DET
ejpam-4923	226	32	subgroups	subgroup	NOUN
ejpam-4923	226	33	as	as	SCONJ
ejpam-4923	226	34	follows	follow	VERB
ejpam-4923	226	35	:	:	PUNCT
ejpam-4923	227	1	[	[	X
ejpam-4923	227	2	lz̃fn](g	lz̃fn](g	NOUN
ejpam-4923	227	3	)	)	PUNCT
ejpam-4923	227	4	=	=	PUNCT
ejpam-4923	228	1	d	d	NOUN
ejpam-4923	228	2	dt	dt	X
ejpam-4923	228	3	fn(g	fn(g	PUNCT
ejpam-4923	228	4	exp	exp	NOUN
ejpam-4923	228	5	tz̃	tz̃	NOUN
ejpam-4923	228	6	)	)	PUNCT
ejpam-4923	228	7	∣∣∣∣	∣∣∣∣	NOUN
ejpam-4923	228	8	t=0	t=0	VERB
ejpam-4923	228	9	=	=	SYM
ejpam-4923	229	1	d	d	NOUN
ejpam-4923	229	2	dt	dt	X
ejpam-4923	230	1	fn	fn	INTJ
ejpam-4923	230	2	(	(	PUNCT
ejpam-4923	230	3	αeit	αeit	PROPN
ejpam-4923	230	4	β̄e−it	β̄e−it	PUNCT
ejpam-4923	230	5	βeit	βeit	NOUN
ejpam-4923	230	6	ᾱe−it	ᾱe−it	PROPN
ejpam-4923	230	7	)	)	PUNCT
ejpam-4923	230	8	∣∣∣∣	∣∣∣∣	NOUN
ejpam-4923	230	9	t=0	t=0	VERB
ejpam-4923	230	10	=	=	SYM
ejpam-4923	231	1	d	d	X
ejpam-4923	231	2	dt	dt	X
ejpam-4923	231	3	χn	χn	X
ejpam-4923	231	4	(	(	PUNCT
ejpam-4923	231	5	αeit	αeit	PROPN
ejpam-4923	231	6	|αeit|	|αeit|	PROPN
ejpam-4923	231	7	)	)	PUNCT
ejpam-4923	231	8	f	f	PROPN
ejpam-4923	231	9	(	(	PUNCT
ejpam-4923	231	10	β̄e−it	β̄e−it	INTJ
ejpam-4923	231	11	ᾱe−it	ᾱe−it	PROPN
ejpam-4923	231	12	,	,	PUNCT
ejpam-4923	231	13	βe−it	βe−it	X
ejpam-4923	231	14	αe−it	αe−it	X
ejpam-4923	231	15	)	)	PUNCT
ejpam-4923	231	16	∣∣∣∣	∣∣∣∣	NOUN
ejpam-4923	231	17	t=0	t=0	VERB
ejpam-4923	231	18	=	=	SYM
ejpam-4923	232	1	d	d	NOUN
ejpam-4923	232	2	dt	dt	X
ejpam-4923	232	3	χn(e	χn(e	X
ejpam-4923	232	4	i(θ+t))f	i(θ+t))f	PROPN
ejpam-4923	232	5	(	(	PUNCT
ejpam-4923	232	6	u	u	NOUN
ejpam-4923	232	7	,	,	PUNCT
ejpam-4923	232	8	ū	ū	NOUN
ejpam-4923	232	9	)	)	PUNCT
ejpam-4923	233	1	∣∣∣∣	∣∣∣∣	NOUN
ejpam-4923	233	2	t=0	t=0	VERB
ejpam-4923	233	3	=	=	SYM
ejpam-4923	233	4	−∂f	−∂f	PROPN
ejpam-4923	233	5	∂θ	∂θ	PROPN
ejpam-4923	233	6	,	,	PUNCT
ejpam-4923	233	7	where	where	SCONJ
ejpam-4923	233	8	α	α	NOUN
ejpam-4923	233	9	=	=	PUNCT
ejpam-4923	233	10	eiθ√	eiθ√	VERB
ejpam-4923	233	11	1−|r|2	1−|r|2	NUM
ejpam-4923	233	12	and	and	CCONJ
ejpam-4923	233	13	β	β	X
ejpam-4923	233	14	=	=	SYM
ejpam-4923	233	15	rei(θ−ϕ)√	rei(θ−ϕ)√	ADJ
ejpam-4923	233	16	1−|r|2	1−|r|2	NUM
ejpam-4923	233	17	.	.	PUNCT
ejpam-4923	234	1	similarly	similarly	ADV
ejpam-4923	234	2	,	,	PUNCT
ejpam-4923	234	3	it	it	PRON
ejpam-4923	234	4	is	be	AUX
ejpam-4923	234	5	easy	easy	ADJ
ejpam-4923	234	6	to	to	PART
ejpam-4923	234	7	determine	determine	VERB
ejpam-4923	234	8	that	that	SCONJ
ejpam-4923	235	1	[	[	X
ejpam-4923	235	2	lãfn](g	lãfn](g	NOUN
ejpam-4923	235	3	)	)	PUNCT
ejpam-4923	235	4	=	=	PUNCT
ejpam-4923	236	1	d	d	NOUN
ejpam-4923	236	2	dt	dt	X
ejpam-4923	236	3	fn(g	fn(g	PUNCT
ejpam-4923	236	4	exp	exp	NOUN
ejpam-4923	236	5	tã	tã	NOUN
ejpam-4923	236	6	)	)	PUNCT
ejpam-4923	236	7	∣∣∣∣	∣∣∣∣	NOUN
ejpam-4923	236	8	t=0	t=0	VERB
ejpam-4923	236	9	=	=	SYM
ejpam-4923	236	10	−r	−r	ADJ
ejpam-4923	236	11	2	2	NUM
ejpam-4923	236	12	sin(ϕ−	sin(ϕ−	NOUN
ejpam-4923	236	13	2θ	2θ	NUM
ejpam-4923	236	14	)	)	PUNCT
ejpam-4923	237	1	∂f	∂f	PROPN
ejpam-4923	237	2	∂θ	∂θ	PROPN
ejpam-4923	238	1	−	−	NOUN
ejpam-4923	238	2	1	1	NUM
ejpam-4923	238	3	2	2	NUM
ejpam-4923	238	4	(	(	PUNCT
ejpam-4923	238	5	1−	1−	NUM
ejpam-4923	238	6	uū	uū	NOUN
ejpam-4923	238	7	)	)	PUNCT
ejpam-4923	238	8	[	[	PUNCT
ejpam-4923	238	9	e2iθ	e2iθ	X
ejpam-4923	238	10	∂f	∂f	PROPN
ejpam-4923	238	11	∂u	∂u	PROPN
ejpam-4923	239	1	+	+	NUM
ejpam-4923	239	2	e−2iθ	e−2iθ	NOUN
ejpam-4923	239	3	∂f	∂f	PROPN
ejpam-4923	239	4	∂ū	∂ū	PROPN
ejpam-4923	239	5	]	]	PUNCT
ejpam-4923	239	6	.	.	PUNCT
ejpam-4923	240	1	[	[	X
ejpam-4923	240	2	lb̃fn](g	lb̃fn](g	NOUN
ejpam-4923	240	3	)	)	PUNCT
ejpam-4923	240	4	=	=	PUNCT
ejpam-4923	241	1	d	d	NOUN
ejpam-4923	241	2	dt	dt	X
ejpam-4923	241	3	fn(g	fn(g	PUNCT
ejpam-4923	241	4	exp	exp	NOUN
ejpam-4923	241	5	tb̃	tb̃	ADJ
ejpam-4923	241	6	)	)	PUNCT
ejpam-4923	241	7	∣∣∣∣	∣∣∣∣	NOUN
ejpam-4923	241	8	t=0	t=0	VERB
ejpam-4923	241	9	=	=	SYM
ejpam-4923	242	1	r	r	NOUN
ejpam-4923	242	2	2	2	NUM
ejpam-4923	242	3	cos(ϕ−	cos(ϕ−	NUM
ejpam-4923	242	4	2θ	2θ	NUM
ejpam-4923	242	5	)	)	PUNCT
ejpam-4923	243	1	∂f	∂f	PROPN
ejpam-4923	243	2	∂θ	∂θ	PROPN
ejpam-4923	244	1	−	−	NOUN
ejpam-4923	245	1	i	i	PRON
ejpam-4923	245	2	2	2	NUM
ejpam-4923	245	3	(	(	PUNCT
ejpam-4923	245	4	1−	1−	NUM
ejpam-4923	245	5	uū	uū	NOUN
ejpam-4923	245	6	)	)	PUNCT
ejpam-4923	245	7	[	[	PUNCT
ejpam-4923	245	8	e2iθ	e2iθ	NUM
ejpam-4923	245	9	∂f	∂f	PROPN
ejpam-4923	245	10	∂u	∂u	PROPN
ejpam-4923	245	11	−	−	NOUN
ejpam-4923	245	12	e−2iθ	e−2iθ	NOUN
ejpam-4923	245	13	∂f	∂f	PROPN
ejpam-4923	245	14	∂ū	∂ū	PROPN
ejpam-4923	245	15	]	]	PUNCT
ejpam-4923	245	16	.	.	PUNCT
ejpam-4923	246	1	the	the	DET
ejpam-4923	246	2	function	function	NOUN
ejpam-4923	246	3	f−m	f−m	NOUN
ejpam-4923	246	4	2	2	NUM
ejpam-4923	246	5	,	,	PUNCT
ejpam-4923	246	6	n	n	CCONJ
ejpam-4923	246	7	given	give	VERB
ejpam-4923	246	8	by	by	ADP
ejpam-4923	246	9	(	(	PUNCT
ejpam-4923	246	10	45	45	NUM
ejpam-4923	246	11	)	)	PUNCT
ejpam-4923	246	12	is	be	AUX
ejpam-4923	246	13	an	an	DET
ejpam-4923	246	14	eigenfunction	eigenfunction	NOUN
ejpam-4923	246	15	with	with	ADP
ejpam-4923	246	16	an	an	DET
ejpam-4923	246	17	eigenvalue	eigenvalue	NOUN
ejpam-4923	246	18	in	in	ADP
ejpam-4923	246	19	for	for	ADP
ejpam-4923	246	20	the	the	DET
ejpam-4923	246	21	operator	operator	NOUN
ejpam-4923	246	22	lz̃	lz̃	VERB
ejpam-4923	246	23	.	.	PUNCT
ejpam-4923	247	1	that	that	PRON
ejpam-4923	247	2	is	be	AUX
ejpam-4923	247	3	,	,	PUNCT
ejpam-4923	247	4	for	for	ADP
ejpam-4923	247	5	fn(g	fn(g	PUNCT
ejpam-4923	247	6	)	)	PUNCT
ejpam-4923	247	7	=	=	PUNCT
ejpam-4923	247	8	eintf−m	eintf−m	ADP
ejpam-4923	247	9	2	2	NUM
ejpam-4923	247	10	,	,	PUNCT
ejpam-4923	247	11	n(w	n(w	NOUN
ejpam-4923	247	12	,	,	PUNCT
ejpam-4923	247	13	w	w	NOUN
ejpam-4923	247	14	)	)	PUNCT
ejpam-4923	247	15	,	,	PUNCT
ejpam-4923	247	16	a.	a.	PROPN
ejpam-4923	247	17	s.	s.	PROPN
ejpam-4923	247	18	alghamdi	alghamdi	PROPN
ejpam-4923	247	19	/	/	SYM
ejpam-4923	247	20	eur	eur	PROPN
ejpam-4923	247	21	.	.	PUNCT
ejpam-4923	248	1	j.	j.	PROPN
ejpam-4923	248	2	pure	pure	PROPN
ejpam-4923	248	3	appl	appl	PROPN
ejpam-4923	248	4	.	.	PROPN
ejpam-4923	248	5	math	math	PROPN
ejpam-4923	248	6	,	,	PUNCT
ejpam-4923	248	7	16	16	NUM
ejpam-4923	248	8	(	(	PUNCT
ejpam-4923	248	9	4	4	NUM
ejpam-4923	248	10	)	)	PUNCT
ejpam-4923	248	11	(	(	PUNCT
ejpam-4923	248	12	2023	2023	NUM
ejpam-4923	248	13	)	)	PUNCT
ejpam-4923	248	14	,	,	PUNCT
ejpam-4923	248	15	2348	2348	NUM
ejpam-4923	248	16	-	-	SYM
ejpam-4923	248	17	2367	2367	NUM
ejpam-4923	248	18	2360	2360	NUM
ejpam-4923	248	19	we	we	PRON
ejpam-4923	248	20	have	have	VERB
ejpam-4923	248	21	lz̃eintf−m	lz̃eintf−m	NOUN
ejpam-4923	248	22	2	2	NUM
ejpam-4923	248	23	,	,	PUNCT
ejpam-4923	248	24	n(w	n(w	NOUN
ejpam-4923	248	25	,	,	PUNCT
ejpam-4923	248	26	w	w	NOUN
ejpam-4923	248	27	)	)	PUNCT
ejpam-4923	248	28	=	=	SYM
ejpam-4923	249	1	ineintf−m	ineintf−m	PROPN
ejpam-4923	249	2	2	2	NUM
ejpam-4923	249	3	,	,	PUNCT
ejpam-4923	249	4	n(w	n(w	NOUN
ejpam-4923	249	5	,	,	PUNCT
ejpam-4923	249	6	w	w	NOUN
ejpam-4923	249	7	)	)	PUNCT
ejpam-4923	249	8	.	.	PUNCT
ejpam-4923	250	1	(	(	PUNCT
ejpam-4923	250	2	58	58	NUM
ejpam-4923	250	3	)	)	PUNCT
ejpam-4923	250	4	moreover	moreover	ADV
ejpam-4923	250	5	,	,	PUNCT
ejpam-4923	250	6	f̃−m	f̃−m	PROPN
ejpam-4923	250	7	2	2	NUM
ejpam-4923	250	8	,	,	PUNCT
ejpam-4923	250	9	n	n	CCONJ
ejpam-4923	250	10	(	(	PUNCT
ejpam-4923	250	11	48	48	NUM
ejpam-4923	250	12	)	)	PUNCT
ejpam-4923	250	13	is	be	AUX
ejpam-4923	250	14	an	an	DET
ejpam-4923	250	15	eigenfunction	eigenfunction	NOUN
ejpam-4923	250	16	with	with	ADP
ejpam-4923	250	17	an	an	DET
ejpam-4923	250	18	eigenvalue	eigenvalue	NOUN
ejpam-4923	250	19	in	in	ADP
ejpam-4923	250	20	for	for	ADP
ejpam-4923	250	21	the	the	DET
ejpam-4923	250	22	operator	operator	NOUN
ejpam-4923	250	23	lz̃	lz̃	PART
ejpam-4923	250	24	.	.	PUNCT
ejpam-4923	251	1	lemma	lemma	PROPN
ejpam-4923	251	2	2	2	X
ejpam-4923	251	3	.	.	X
ejpam-4923	252	1	we	we	PRON
ejpam-4923	252	2	have	have	VERB
ejpam-4923	252	3	lã±ib̃	lã±ib̃	NOUN
ejpam-4923	252	4	:	:	PUNCT
ejpam-4923	252	5	f−m	f−m	NOUN
ejpam-4923	252	6	2	2	NUM
ejpam-4923	252	7	,	,	PUNCT
ejpam-4923	252	8	n	n	CCONJ
ejpam-4923	252	9	→	→	SYM
ejpam-4923	252	10	f−m	f−m	NOUN
ejpam-4923	252	11	2	2	NUM
ejpam-4923	252	12	,	,	PUNCT
ejpam-4923	252	13	n±2	n±2	NOUN
ejpam-4923	252	14	,	,	PUNCT
ejpam-4923	252	15	and	and	CCONJ
ejpam-4923	252	16	lã±ib̃	lã±ib̃	NOUN
ejpam-4923	252	17	:	:	PUNCT
ejpam-4923	252	18	f̃−m	f̃−m	PROPN
ejpam-4923	252	19	2	2	NUM
ejpam-4923	252	20	,	,	PUNCT
ejpam-4923	252	21	n	n	PRON
ejpam-4923	252	22	→	→	SYM
ejpam-4923	252	23	f̃−m	f̃−m	PROPN
ejpam-4923	252	24	2	2	NUM
ejpam-4923	252	25	,	,	PUNCT
ejpam-4923	252	26	n±2	n±2	NOUN
ejpam-4923	252	27	.	.	PUNCT
ejpam-4923	253	1	proof	proof	NOUN
ejpam-4923	253	2	.	.	PUNCT
ejpam-4923	254	1	from	from	ADP
ejpam-4923	254	2	the	the	DET
ejpam-4923	254	3	commutator	commutator	NOUN
ejpam-4923	254	4	relations	relation	NOUN
ejpam-4923	254	5	[	[	X
ejpam-4923	254	6	lz̃	lz̃	X
ejpam-4923	254	7	,	,	PUNCT
ejpam-4923	254	8	lã±ib̃	lã±ib̃	PROPN
ejpam-4923	254	9	]	]	X
ejpam-4923	254	10	=	=	SYM
ejpam-4923	254	11	±2ilã±ib̃	±2ilã±ib̃	NUM
ejpam-4923	254	12	,	,	PUNCT
ejpam-4923	254	13	for	for	ADP
ejpam-4923	254	14	the	the	DET
ejpam-4923	254	15	eigenfunction	eigenfunction	NOUN
ejpam-4923	254	16	f−m	f−m	NOUN
ejpam-4923	254	17	2	2	NUM
ejpam-4923	254	18	,	,	PUNCT
ejpam-4923	254	19	n	n	CCONJ
ejpam-4923	254	20	given	give	VERB
ejpam-4923	254	21	by	by	ADP
ejpam-4923	254	22	(	(	PUNCT
ejpam-4923	254	23	45	45	NUM
ejpam-4923	254	24	)	)	PUNCT
ejpam-4923	254	25	,	,	PUNCT
ejpam-4923	254	26	we	we	PRON
ejpam-4923	254	27	can	can	AUX
ejpam-4923	254	28	see	see	VERB
ejpam-4923	254	29	that	that	SCONJ
ejpam-4923	255	1	[	[	X
ejpam-4923	255	2	lz̃lã±ib̃]eintf−m	lz̃lã±ib̃]eintf−m	NOUN
ejpam-4923	255	3	2	2	NUM
ejpam-4923	255	4	,	,	PUNCT
ejpam-4923	255	5	n	n	NOUN
ejpam-4923	255	6	=	=	SYM
ejpam-4923	255	7	lã±ib̃(lz̃eintf−m	lã±ib̃(lz̃eintf−m	PROPN
ejpam-4923	255	8	2	2	NUM
ejpam-4923	255	9	,	,	PUNCT
ejpam-4923	255	10	n)±	n)±	PROPN
ejpam-4923	255	11	2ilã±ib̃eintf−m	2ilã±ib̃eintf−m	NUM
ejpam-4923	255	12	2	2	NUM
ejpam-4923	255	13	,	,	PUNCT
ejpam-4923	255	14	n	n	NOUN
ejpam-4923	255	15	=	=	SYM
ejpam-4923	255	16	lã±ib̃(nieintf−m	lã±ib̃(nieintf−m	PROPN
ejpam-4923	255	17	2	2	NUM
ejpam-4923	255	18	,	,	PUNCT
ejpam-4923	255	19	n)±	n)±	PROPN
ejpam-4923	255	20	2ilã±ib̃eintf−m	2ilã±ib̃eintf−m	NUM
ejpam-4923	255	21	2	2	NUM
ejpam-4923	255	22	,	,	PUNCT
ejpam-4923	255	23	n	n	NOUN
ejpam-4923	255	24	=	=	PUNCT
ejpam-4923	255	25	(	(	PUNCT
ejpam-4923	255	26	n±	n±	PROPN
ejpam-4923	255	27	2)ilã±ib̃eintf−m	2)ilã±ib̃eintf−m	NUM
ejpam-4923	255	28	2	2	NUM
ejpam-4923	255	29	,	,	PUNCT
ejpam-4923	255	30	n.	n.	NOUN
ejpam-4923	255	31	(	(	PUNCT
ejpam-4923	255	32	59	59	NUM
ejpam-4923	255	33	)	)	PUNCT
ejpam-4923	255	34	similarly	similarly	ADV
ejpam-4923	255	35	,	,	PUNCT
ejpam-4923	255	36	for	for	ADP
ejpam-4923	255	37	the	the	DET
ejpam-4923	255	38	eigenfunction	eigenfunction	NOUN
ejpam-4923	255	39	f̃−m	f̃−m	PROPN
ejpam-4923	255	40	2	2	NUM
ejpam-4923	255	41	,	,	PUNCT
ejpam-4923	255	42	n	n	CCONJ
ejpam-4923	255	43	(	(	PUNCT
ejpam-4923	255	44	48	48	NUM
ejpam-4923	255	45	)	)	PUNCT
ejpam-4923	255	46	,	,	PUNCT
ejpam-4923	255	47	we	we	PRON
ejpam-4923	255	48	have	have	VERB
ejpam-4923	255	49	[	[	X
ejpam-4923	255	50	lz̃lã±ib̃]eintf̃−m	lz̃lã±ib̃]eintf̃−m	NOUN
ejpam-4923	255	51	2	2	NUM
ejpam-4923	255	52	,	,	PUNCT
ejpam-4923	255	53	n	n	NOUN
ejpam-4923	255	54	=	=	PUNCT
ejpam-4923	255	55	(	(	PUNCT
ejpam-4923	255	56	n±	n±	ADV
ejpam-4923	255	57	2)ilã±ib̃eintf̃−m	2)ilã±ib̃eintf̃−m	NUM
ejpam-4923	255	58	2	2	NUM
ejpam-4923	255	59	,	,	PUNCT
ejpam-4923	255	60	n.	n.	VERB
ejpam-4923	255	61	the	the	DET
ejpam-4923	255	62	vacuum	vacuum	NOUN
ejpam-4923	255	63	f0,n(w	f0,n(w	PROPN
ejpam-4923	255	64	,	,	PUNCT
ejpam-4923	255	65	w	w	NOUN
ejpam-4923	255	66	)	)	PUNCT
ejpam-4923	255	67	=	=	SYM
ejpam-4923	256	1	(	(	PUNCT
ejpam-4923	256	2	1	1	NUM
ejpam-4923	256	3	−	−	NUM
ejpam-4923	256	4	ww	ww	PROPN
ejpam-4923	256	5	)	)	PUNCT
ejpam-4923	256	6	n	n	PRON
ejpam-4923	256	7	2	2	NUM
ejpam-4923	256	8	is	be	AUX
ejpam-4923	256	9	annihilated	annihilate	VERB
ejpam-4923	256	10	by	by	ADP
ejpam-4923	256	11	the	the	DET
ejpam-4923	256	12	operator	operator	NOUN
ejpam-4923	256	13	lã+ib̃.	lã+ib̃.	ADJ
ejpam-4923	256	14	that	that	PRON
ejpam-4923	256	15	is	be	AUX
ejpam-4923	256	16	,	,	PUNCT
ejpam-4923	256	17	[	[	X
ejpam-4923	256	18	lã+ib̃eintf0,n](w	lã+ib̃eintf0,n](w	NOUN
ejpam-4923	256	19	,	,	PUNCT
ejpam-4923	256	20	w	w	NOUN
ejpam-4923	256	21	)	)	PUNCT
ejpam-4923	256	22	=	=	SYM
ejpam-4923	257	1	0	0	X
ejpam-4923	257	2	.	.	PUNCT
ejpam-4923	258	1	then	then	ADV
ejpam-4923	258	2	,	,	PUNCT
ejpam-4923	258	3	all	all	DET
ejpam-4923	258	4	the	the	DET
ejpam-4923	258	5	vectors	vector	NOUN
ejpam-4923	258	6	fj	fj	PROPN
ejpam-4923	258	7	,	,	PUNCT
ejpam-4923	258	8	n	n	PROPN
ejpam-4923	258	9	=	=	SYM
ejpam-4923	258	10	(	(	PUNCT
ejpam-4923	258	11	l+	l+	NOUN
ejpam-4923	258	12	)	)	PUNCT
ejpam-4923	258	13	jf0,n	jf0,n	NOUN
ejpam-4923	258	14	are	be	AUX
ejpam-4923	258	15	vacuums	vacuum	NOUN
ejpam-4923	258	16	of	of	ADP
ejpam-4923	258	17	the	the	DET
ejpam-4923	258	18	operator	operator	NOUN
ejpam-4923	258	19	lã+ib̃	lã+ib̃	PROPN
ejpam-4923	258	20	due	due	ADP
ejpam-4923	258	21	to	to	ADP
ejpam-4923	258	22	the	the	DET
ejpam-4923	258	23	commutation	commutation	NOUN
ejpam-4923	258	24	of	of	ADP
ejpam-4923	258	25	the	the	DET
ejpam-4923	258	26	left	left	ADJ
ejpam-4923	258	27	and	and	CCONJ
ejpam-4923	258	28	right	right	ADJ
ejpam-4923	258	29	actions	action	NOUN
ejpam-4923	258	30	:	:	PUNCT
ejpam-4923	258	31	lã+ib̃fj	lã+ib̃fj	NOUN
ejpam-4923	258	32	,	,	PUNCT
ejpam-4923	258	33	n	n	PROPN
ejpam-4923	258	34	=	=	SYM
ejpam-4923	258	35	lã+ib̃(l+	lã+ib̃(l+	PROPN
ejpam-4923	258	36	)	)	PUNCT
ejpam-4923	258	37	jf0,n	jf0,n	NOUN
ejpam-4923	259	1	=	=	PUNCT
ejpam-4923	259	2	(	(	PUNCT
ejpam-4923	259	3	l+	l+	NOUN
ejpam-4923	259	4	)	)	PUNCT
ejpam-4923	259	5	jlã+ib̃f0,n	jlã+ib̃f0,n	X
ejpam-4923	260	1	=	=	SYM
ejpam-4923	260	2	0	0	X
ejpam-4923	260	3	.	.	PUNCT
ejpam-4923	261	1	(	(	PUNCT
ejpam-4923	261	2	60	60	NUM
ejpam-4923	261	3	)	)	PUNCT
ejpam-4923	261	4	for	for	ADP
ejpam-4923	261	5	each	each	DET
ejpam-4923	261	6	vacuum	vacuum	NOUN
ejpam-4923	261	7	f0,n	f0,n	PROPN
ejpam-4923	261	8	,	,	PUNCT
ejpam-4923	261	9	the	the	DET
ejpam-4923	261	10	collection	collection	NOUN
ejpam-4923	261	11	of	of	ADP
ejpam-4923	261	12	vectors	vector	NOUN
ejpam-4923	261	13	fj	fj	PROPN
ejpam-4923	261	14	,	,	PUNCT
ejpam-4923	261	15	n	n	PROPN
ejpam-4923	261	16	=	=	SYM
ejpam-4923	261	17	(	(	PUNCT
ejpam-4923	261	18	l+	l+	NOUN
ejpam-4923	261	19	)	)	PUNCT
ejpam-4923	261	20	jf0,n	jf0,n	NOUN
ejpam-4923	261	21	forms	form	VERB
ejpam-4923	261	22	an	an	DET
ejpam-4923	261	23	orthogonal	orthogonal	ADJ
ejpam-4923	261	24	basis	basis	NOUN
ejpam-4923	261	25	of	of	ADP
ejpam-4923	261	26	an	an	DET
ejpam-4923	261	27	irreducible	irreducible	ADJ
ejpam-4923	261	28	component	component	NOUN
ejpam-4923	261	29	with	with	ADP
ejpam-4923	261	30	the	the	DET
ejpam-4923	261	31	respective	respective	ADJ
ejpam-4923	261	32	ladder	ladder	NOUN
ejpam-4923	261	33	operators	operator	NOUN
ejpam-4923	261	34	(	(	PUNCT
ejpam-4923	261	35	46	46	NUM
ejpam-4923	261	36	)	)	PUNCT
ejpam-4923	261	37	and	and	CCONJ
ejpam-4923	261	38	(	(	PUNCT
ejpam-4923	261	39	47	47	NUM
ejpam-4923	261	40	)	)	PUNCT
ejpam-4923	261	41	.	.	PUNCT
ejpam-4923	262	1	the	the	DET
ejpam-4923	262	2	left	left	NOUN
ejpam-4923	262	3	and	and	CCONJ
ejpam-4923	262	4	the	the	DET
ejpam-4923	262	5	right	right	ADJ
ejpam-4923	262	6	actions	action	NOUN
ejpam-4923	262	7	for	for	ADP
ejpam-4923	262	8	the	the	DET
ejpam-4923	262	9	eigenfunctions	eigenfunction	NOUN
ejpam-4923	262	10	fm	fm	PROPN
ejpam-4923	262	11	,	,	PUNCT
ejpam-4923	262	12	n	n	PROPN
ejpam-4923	262	13	(	(	PUNCT
ejpam-4923	262	14	45	45	NUM
ejpam-4923	262	15	)	)	PUNCT
ejpam-4923	262	16	jointly	jointly	ADV
ejpam-4923	262	17	create	create	VERB
ejpam-4923	262	18	the	the	DET
ejpam-4923	262	19	two	two	NUM
ejpam-4923	262	20	-	-	PUNCT
ejpam-4923	262	21	dimensional	dimensional	ADJ
ejpam-4923	262	22	lattice	lattice	NOUN
ejpam-4923	262	23	structure	structure	NOUN
ejpam-4923	262	24	that	that	PRON
ejpam-4923	262	25	can	can	AUX
ejpam-4923	262	26	be	be	AUX
ejpam-4923	262	27	seen	see	VERB
ejpam-4923	262	28	in	in	ADP
ejpam-4923	262	29	the	the	DET
ejpam-4923	262	30	following	follow	VERB
ejpam-4923	262	31	diagram	diagram	NOUN
ejpam-4923	262	32	:	:	PUNCT
ejpam-4923	262	33	a.	a.	PROPN
ejpam-4923	262	34	s.	s.	PROPN
ejpam-4923	262	35	alghamdi	alghamdi	PROPN
ejpam-4923	262	36	/	/	SYM
ejpam-4923	262	37	eur	eur	PROPN
ejpam-4923	262	38	.	.	PUNCT
ejpam-4923	263	1	j.	j.	PROPN
ejpam-4923	263	2	pure	pure	PROPN
ejpam-4923	263	3	appl	appl	PROPN
ejpam-4923	263	4	.	.	PROPN
ejpam-4923	263	5	math	math	PROPN
ejpam-4923	263	6	,	,	PUNCT
ejpam-4923	263	7	16	16	NUM
ejpam-4923	263	8	(	(	PUNCT
ejpam-4923	263	9	4	4	NUM
ejpam-4923	263	10	)	)	PUNCT
ejpam-4923	263	11	(	(	PUNCT
ejpam-4923	263	12	2023	2023	NUM
ejpam-4923	263	13	)	)	PUNCT
ejpam-4923	263	14	,	,	PUNCT
ejpam-4923	263	15	2348	2348	NUM
ejpam-4923	263	16	-	-	SYM
ejpam-4923	263	17	2367	2367	NUM
ejpam-4923	263	18	2361	2361	NUM
ejpam-4923	263	19	0	0	NUM
ejpam-4923	264	1	f0,2	f0,2	PROPN
ejpam-4923	264	2	f0,4	f0,4	PROPN
ejpam-4923	264	3	f0,6	f0,6	X
ejpam-4923	264	4	·	·	PUNCT
ejpam-4923	264	5	·	·	PUNCT
ejpam-4923	264	6	·	·	PUNCT
ejpam-4923	265	1	f1,2	f1,2	ADJ
ejpam-4923	265	2	f1,4	f1,4	PROPN
ejpam-4923	265	3	f1,6	f1,6	PROPN
ejpam-4923	265	4	·	·	PUNCT
ejpam-4923	265	5	·	·	PUNCT
ejpam-4923	265	6	·	·	PUNCT
ejpam-4923	265	7	0	0	NUM
ejpam-4923	265	8	f2,2	f2,2	PROPN
ejpam-4923	265	9	f2,4	f2,4	PROPN
ejpam-4923	265	10	f2,6	f2,6	PROPN
ejpam-4923	265	11	·	·	PUNCT
ejpam-4923	265	12	·	·	PUNCT
ejpam-4923	265	13	·	·	PUNCT
ejpam-4923	265	14	0	0	NUM
ejpam-4923	265	15	000	000	NUM
ejpam-4923	265	16	...	...	PUNCT
ejpam-4923	265	17	...	...	PUNCT
ejpam-4923	265	18	...	...	PUNCT
ejpam-4923	265	19	l+	l+	PUNCT
ejpam-4923	265	20	l−	l−	NOUN
ejpam-4923	265	21	l+	l+	PUNCT
ejpam-4923	265	22	l−	l−	NOUN
ejpam-4923	265	23	l+	l+	PUNCT
ejpam-4923	265	24	l−	l−	PROPN
ejpam-4923	265	25	l−	l−	PROPN
ejpam-4923	265	26	l+	l+	PUNCT
ejpam-4923	265	27	l−	l−	NOUN
ejpam-4923	265	28	l+	l+	PUNCT
ejpam-4923	265	29	l−	l−	NOUN
ejpam-4923	265	30	l+	l+	PUNCT
ejpam-4923	265	31	l−	l−	PROPN
ejpam-4923	265	32	l−	l−	PROPN
ejpam-4923	265	33	l+	l+	PUNCT
ejpam-4923	265	34	l−	l−	NOUN
ejpam-4923	265	35	l+	l+	PUNCT
ejpam-4923	265	36	l−	l−	NOUN
ejpam-4923	265	37	l+	l+	PUNCT
ejpam-4923	265	38	l−	l−	PROPN
ejpam-4923	265	39	l−	l−	PROPN
ejpam-4923	265	40	l−	l−	PROPN
ejpam-4923	265	41	l−	l−	PROPN
ejpam-4923	265	42	l−	l−	NOUN
ejpam-4923	265	43	l−l+	l−l+	VERB
ejpam-4923	265	44	l−l+	l−l+	INTJ
ejpam-4923	265	45	l−l+	l−l+	INTJ
ejpam-4923	265	46	l−l+	l−l+	INTJ
ejpam-4923	265	47	l−l+	l−l+	INTJ
ejpam-4923	265	48	l−l+	l−l+	INTJ
ejpam-4923	265	49	l−l+	l−l+	INTJ
ejpam-4923	265	50	l−l+	l−l+	PRON
ejpam-4923	265	51	l−l+	l−l+	PRON
ejpam-4923	265	52	figure	figure	NOUN
ejpam-4923	265	53	1	1	NUM
ejpam-4923	265	54	:	:	PUNCT
ejpam-4923	265	55	the	the	DET
ejpam-4923	265	56	left	left	NOUN
ejpam-4923	265	57	and	and	CCONJ
ejpam-4923	265	58	the	the	DET
ejpam-4923	265	59	right	right	ADJ
ejpam-4923	265	60	actions	action	NOUN
ejpam-4923	265	61	of	of	ADP
ejpam-4923	265	62	the	the	DET
ejpam-4923	265	63	ladder	ladder	NOUN
ejpam-4923	265	64	operators	operator	NOUN
ejpam-4923	265	65	for	for	ADP
ejpam-4923	265	66	f−m	f−m	NOUN
ejpam-4923	265	67	2	2	NUM
ejpam-4923	265	68	,	,	PUNCT
ejpam-4923	265	69	n	n	X
ejpam-4923	265	70	.	.	PUNCT
ejpam-4923	266	1	furthermore	furthermore	ADV
ejpam-4923	266	2	,	,	PUNCT
ejpam-4923	266	3	the	the	DET
ejpam-4923	266	4	function	function	NOUN
ejpam-4923	266	5	f̃0,n(w	f̃0,n(w	PROPN
ejpam-4923	266	6	,	,	PUNCT
ejpam-4923	266	7	w	w	NOUN
ejpam-4923	266	8	)	)	PUNCT
ejpam-4923	266	9	=	=	SYM
ejpam-4923	266	10	(	(	PUNCT
ejpam-4923	266	11	1−ww	1−ww	NUM
ejpam-4923	266	12	)	)	PUNCT
ejpam-4923	266	13	−n	−n	ADV
ejpam-4923	266	14	2	2	NUM
ejpam-4923	266	15	is	be	AUX
ejpam-4923	266	16	a	a	DET
ejpam-4923	266	17	vacuum	vacuum	NOUN
ejpam-4923	266	18	of	of	ADP
ejpam-4923	266	19	the	the	DET
ejpam-4923	266	20	operator	operator	NOUN
ejpam-4923	266	21	lã−ib̃.	lã−ib̃.	PUNCT
ejpam-4923	266	22	that	that	ADV
ejpam-4923	266	23	is	be	AUX
ejpam-4923	266	24	,	,	PUNCT
ejpam-4923	266	25	[	[	X
ejpam-4923	266	26	lã−ib̃eintf̃0,n](w	lã−ib̃eintf̃0,n](w	PROPN
ejpam-4923	266	27	,	,	PUNCT
ejpam-4923	266	28	w	w	NOUN
ejpam-4923	266	29	)	)	PUNCT
ejpam-4923	266	30	=	=	SYM
ejpam-4923	267	1	0	0	X
ejpam-4923	267	2	.	.	PUNCT
ejpam-4923	268	1	then	then	ADV
ejpam-4923	268	2	,	,	PUNCT
ejpam-4923	268	3	all	all	DET
ejpam-4923	268	4	the	the	DET
ejpam-4923	268	5	vectors	vector	NOUN
ejpam-4923	268	6	f̃k	f̃k	VERB
ejpam-4923	268	7	,	,	PUNCT
ejpam-4923	268	8	n	n	X
ejpam-4923	268	9	=	=	SYM
ejpam-4923	268	10	(	(	PUNCT
ejpam-4923	268	11	l−	l−	PROPN
ejpam-4923	268	12	)	)	PUNCT
ejpam-4923	269	1	kf̃0,n	kf̃0,n	PROPN
ejpam-4923	269	2	are	be	AUX
ejpam-4923	269	3	vacuums	vacuum	NOUN
ejpam-4923	269	4	of	of	ADP
ejpam-4923	269	5	the	the	DET
ejpam-4923	269	6	operator	operator	NOUN
ejpam-4923	269	7	lã−ib̃	lã−ib̃	PROPN
ejpam-4923	269	8	due	due	ADP
ejpam-4923	269	9	to	to	ADP
ejpam-4923	269	10	the	the	DET
ejpam-4923	269	11	commutation	commutation	NOUN
ejpam-4923	269	12	of	of	ADP
ejpam-4923	269	13	the	the	DET
ejpam-4923	269	14	left	left	ADJ
ejpam-4923	269	15	and	and	CCONJ
ejpam-4923	269	16	right	right	ADJ
ejpam-4923	269	17	actions	action	NOUN
ejpam-4923	269	18	:	:	PUNCT
ejpam-4923	269	19	lã−ib̃	lã−ib̃	PROPN
ejpam-4923	269	20	f̃k	f̃k	PROPN
ejpam-4923	269	21	,	,	PUNCT
ejpam-4923	269	22	n	n	PROPN
ejpam-4923	269	23	=	=	SYM
ejpam-4923	269	24	lã−ib̃(l−	lã−ib̃(l−	NUM
ejpam-4923	269	25	)	)	PUNCT
ejpam-4923	269	26	kf0,n	kf0,n	NOUN
ejpam-4923	269	27	=	=	SYM
ejpam-4923	269	28	(	(	PUNCT
ejpam-4923	269	29	l−	l−	PROPN
ejpam-4923	269	30	)	)	PUNCT
ejpam-4923	269	31	klã−ib̃	klã−ib̃	PROPN
ejpam-4923	269	32	f̃0,n	f̃0,n	PROPN
ejpam-4923	270	1	=	=	SYM
ejpam-4923	270	2	0	0	X
ejpam-4923	270	3	.	.	PUNCT
ejpam-4923	270	4	(	(	PUNCT
ejpam-4923	270	5	61	61	NUM
ejpam-4923	270	6	)	)	PUNCT
ejpam-4923	270	7	for	for	ADP
ejpam-4923	270	8	each	each	DET
ejpam-4923	270	9	f̃0,n	f̃0,n	NOUN
ejpam-4923	270	10	,	,	PUNCT
ejpam-4923	270	11	the	the	DET
ejpam-4923	270	12	collection	collection	NOUN
ejpam-4923	270	13	of	of	ADP
ejpam-4923	270	14	vectors	vector	NOUN
ejpam-4923	270	15	f̃k	f̃k	VERB
ejpam-4923	270	16	,	,	PUNCT
ejpam-4923	270	17	n	n	X
ejpam-4923	270	18	=	=	SYM
ejpam-4923	270	19	(	(	PUNCT
ejpam-4923	270	20	l−	l−	PROPN
ejpam-4923	270	21	)	)	PUNCT
ejpam-4923	270	22	kf0,n	kf0,n	NOUN
ejpam-4923	270	23	forms	form	VERB
ejpam-4923	270	24	an	an	DET
ejpam-4923	270	25	orthogonal	orthogonal	ADJ
ejpam-4923	270	26	basis	basis	NOUN
ejpam-4923	270	27	of	of	ADP
ejpam-4923	270	28	an	an	DET
ejpam-4923	270	29	irreducible	irreducible	ADJ
ejpam-4923	270	30	component	component	NOUN
ejpam-4923	270	31	with	with	ADP
ejpam-4923	270	32	the	the	DET
ejpam-4923	270	33	respective	respective	ADJ
ejpam-4923	270	34	ladder	ladder	NOUN
ejpam-4923	270	35	operators	operator	NOUN
ejpam-4923	270	36	(	(	PUNCT
ejpam-4923	270	37	49	49	NUM
ejpam-4923	270	38	)	)	PUNCT
ejpam-4923	270	39	and	and	CCONJ
ejpam-4923	270	40	(	(	PUNCT
ejpam-4923	270	41	50	50	NUM
ejpam-4923	270	42	)	)	PUNCT
ejpam-4923	270	43	.	.	PUNCT
ejpam-4923	271	1	the	the	DET
ejpam-4923	271	2	left	left	NOUN
ejpam-4923	271	3	and	and	CCONJ
ejpam-4923	271	4	the	the	DET
ejpam-4923	271	5	right	right	ADJ
ejpam-4923	271	6	actions	action	NOUN
ejpam-4923	271	7	for	for	ADP
ejpam-4923	271	8	the	the	DET
ejpam-4923	271	9	functions	function	NOUN
ejpam-4923	271	10	f̃m	f̃m	PROPN
ejpam-4923	271	11	,	,	PUNCT
ejpam-4923	271	12	n	n	CCONJ
ejpam-4923	271	13	(	(	PUNCT
ejpam-4923	271	14	48	48	NUM
ejpam-4923	271	15	)	)	PUNCT
ejpam-4923	271	16	jointly	jointly	ADV
ejpam-4923	271	17	create	create	VERB
ejpam-4923	271	18	the	the	DET
ejpam-4923	271	19	two	two	NUM
ejpam-4923	271	20	-	-	PUNCT
ejpam-4923	271	21	dimensional	dimensional	ADJ
ejpam-4923	271	22	lattice	lattice	NOUN
ejpam-4923	271	23	structure	structure	NOUN
ejpam-4923	271	24	that	that	PRON
ejpam-4923	271	25	can	can	AUX
ejpam-4923	271	26	be	be	AUX
ejpam-4923	271	27	seen	see	VERB
ejpam-4923	271	28	in	in	ADP
ejpam-4923	271	29	the	the	DET
ejpam-4923	271	30	following	follow	VERB
ejpam-4923	271	31	diagram	diagram	NOUN
ejpam-4923	271	32	:	:	PUNCT
ejpam-4923	271	33	a.	a.	PROPN
ejpam-4923	271	34	s.	s.	PROPN
ejpam-4923	271	35	alghamdi	alghamdi	PROPN
ejpam-4923	271	36	/	/	SYM
ejpam-4923	271	37	eur	eur	PROPN
ejpam-4923	271	38	.	.	PUNCT
ejpam-4923	272	1	j.	j.	PROPN
ejpam-4923	272	2	pure	pure	PROPN
ejpam-4923	272	3	appl	appl	PROPN
ejpam-4923	272	4	.	.	PROPN
ejpam-4923	272	5	math	math	PROPN
ejpam-4923	272	6	,	,	PUNCT
ejpam-4923	272	7	16	16	NUM
ejpam-4923	272	8	(	(	PUNCT
ejpam-4923	272	9	4	4	NUM
ejpam-4923	272	10	)	)	PUNCT
ejpam-4923	272	11	(	(	PUNCT
ejpam-4923	272	12	2023	2023	NUM
ejpam-4923	272	13	)	)	PUNCT
ejpam-4923	272	14	,	,	PUNCT
ejpam-4923	272	15	2348	2348	NUM
ejpam-4923	272	16	-	-	SYM
ejpam-4923	272	17	2367	2367	NUM
ejpam-4923	272	18	2362	2362	NUM
ejpam-4923	272	19	·	·	PUNCT
ejpam-4923	272	20	·	·	PUNCT
ejpam-4923	272	21	·	·	PUNCT
ejpam-4923	273	1	f̃0,6	f̃0,6	NOUN
ejpam-4923	273	2	f̃0,4	f̃0,4	NOUN
ejpam-4923	273	3	f̃0,2	f̃0,2	VERB
ejpam-4923	273	4	0	0	NUM
ejpam-4923	273	5	0	0	NUM
ejpam-4923	273	6	f̃−1,6	f̃−1,6	PROPN
ejpam-4923	273	7	0	0	NUM
ejpam-4923	273	8	f̃−1,4	f̃−1,4	ADV
ejpam-4923	273	9	0	0	NUM
ejpam-4923	273	10	f̃−1,2	f̃−1,2	NOUN
ejpam-4923	273	11	0	0	NUM
ejpam-4923	273	12	·	·	PUNCT
ejpam-4923	273	13	·	·	PUNCT
ejpam-4923	273	14	·	·	PUNCT
ejpam-4923	274	1	f̃−2,6	f̃−2,6	PROPN
ejpam-4923	274	2	f̃−2,4	f̃−2,4	PROPN
ejpam-4923	274	3	f̃−2,2	f̃−2,2	PROPN
ejpam-4923	274	4	·	·	PUNCT
ejpam-4923	274	5	·	·	PUNCT
ejpam-4923	274	6	·	·	PUNCT
ejpam-4923	274	7	0	0	NUM
ejpam-4923	274	8	...	...	PUNCT
ejpam-4923	274	9	...	...	PUNCT
ejpam-4923	274	10	...	...	PUNCT
ejpam-4923	275	1	l+	l+	PUNCT
ejpam-4923	275	2	l−	l−	NOUN
ejpam-4923	275	3	l+	l+	PUNCT
ejpam-4923	275	4	l−	l−	NOUN
ejpam-4923	275	5	l+	l+	PUNCT
ejpam-4923	275	6	l−	l−	NOUN
ejpam-4923	275	7	l+	l+	PUNCT
ejpam-4923	275	8	l+	l+	X
ejpam-4923	275	9	l−l+	l−l+	PROPN
ejpam-4923	275	10	l+	l+	X
ejpam-4923	275	11	l−l+	l−l+	PROPN
ejpam-4923	275	12	l+	l+	PUNCT
ejpam-4923	275	13	l−l+	l−l+	ADP
ejpam-4923	275	14	l−	l−	NOUN
ejpam-4923	275	15	l+	l+	PUNCT
ejpam-4923	275	16	l+	l+	PUNCT
ejpam-4923	275	17	l−	l−	NOUN
ejpam-4923	275	18	l+	l+	PUNCT
ejpam-4923	275	19	l−	l−	NOUN
ejpam-4923	275	20	l+	l+	PUNCT
ejpam-4923	275	21	l−	l−	NOUN
ejpam-4923	275	22	l+	l+	PUNCT
ejpam-4923	275	23	l+	l+	PUNCT
ejpam-4923	275	24	l−	l−	NOUN
ejpam-4923	275	25	l+	l+	PUNCT
ejpam-4923	275	26	l−	l−	NOUN
ejpam-4923	275	27	l+	l+	X
ejpam-4923	275	28	l−l+	l−l+	VERB
ejpam-4923	275	29	l−l+	l−l+	AUX
ejpam-4923	275	30	l−l+	l−l+	INTJ
ejpam-4923	275	31	l−l+	l−l+	INTJ
ejpam-4923	275	32	l−l+	l−l+	PRON
ejpam-4923	275	33	l−l+	l−l+	PRON
ejpam-4923	275	34	figure	figure	NOUN
ejpam-4923	275	35	2	2	NUM
ejpam-4923	275	36	:	:	PUNCT
ejpam-4923	275	37	the	the	DET
ejpam-4923	275	38	left	left	NOUN
ejpam-4923	275	39	and	and	CCONJ
ejpam-4923	275	40	the	the	DET
ejpam-4923	275	41	right	right	ADJ
ejpam-4923	275	42	actions	action	NOUN
ejpam-4923	275	43	of	of	ADP
ejpam-4923	275	44	the	the	DET
ejpam-4923	275	45	ladder	ladder	NOUN
ejpam-4923	275	46	operators	operator	NOUN
ejpam-4923	275	47	for	for	ADP
ejpam-4923	275	48	f̃−m	f̃−m	PROPN
ejpam-4923	275	49	2	2	NUM
ejpam-4923	275	50	,	,	PUNCT
ejpam-4923	275	51	n	n	NOUN
ejpam-4923	275	52	.	.	PUNCT
ejpam-4923	276	1	5	5	X
ejpam-4923	276	2	.	.	X
ejpam-4923	276	3	representation	representation	NOUN
ejpam-4923	276	4	on	on	ADP
ejpam-4923	276	5	the	the	DET
ejpam-4923	276	6	dirichlet	dirichlet	PROPN
ejpam-4923	276	7	space	space	NOUN
ejpam-4923	276	8	the	the	DET
ejpam-4923	276	9	dirichlet	dirichlet	PROPN
ejpam-4923	276	10	space	space	NOUN
ejpam-4923	276	11	,	,	PUNCT
ejpam-4923	276	12	the	the	DET
ejpam-4923	276	13	hardy	hardy	ADJ
ejpam-4923	276	14	space	space	NOUN
ejpam-4923	276	15	and	and	CCONJ
ejpam-4923	276	16	the	the	DET
ejpam-4923	276	17	bergman	bergman	PROPN
ejpam-4923	276	18	space	space	NOUN
ejpam-4923	276	19	are	be	AUX
ejpam-4923	276	20	the	the	DET
ejpam-4923	276	21	three	three	NUM
ejpam-4923	276	22	classical	classical	ADJ
ejpam-4923	276	23	spaces	space	NOUN
ejpam-4923	276	24	of	of	ADP
ejpam-4923	276	25	holomorphic	holomorphic	ADJ
ejpam-4923	276	26	functions	function	NOUN
ejpam-4923	276	27	in	in	ADP
ejpam-4923	276	28	the	the	DET
ejpam-4923	276	29	unit	unit	NOUN
ejpam-4923	276	30	disc	disc	NOUN
ejpam-4923	276	31	.	.	PUNCT
ejpam-4923	277	1	in	in	ADP
ejpam-4923	277	2	the	the	DET
ejpam-4923	277	3	present	present	ADJ
ejpam-4923	277	4	section	section	NOUN
ejpam-4923	277	5	,	,	PUNCT
ejpam-4923	277	6	we	we	PRON
ejpam-4923	277	7	find	find	VERB
ejpam-4923	277	8	the	the	DET
ejpam-4923	277	9	su(1	su(1	NOUN
ejpam-4923	277	10	,	,	PUNCT
ejpam-4923	277	11	1	1	NUM
ejpam-4923	277	12	)	)	PUNCT
ejpam-4923	277	13	module	module	NOUN
ejpam-4923	277	14	(	(	PUNCT
ejpam-4923	277	15	which	which	PRON
ejpam-4923	277	16	is	be	AUX
ejpam-4923	277	17	the	the	DET
ejpam-4923	277	18	space	space	NOUN
ejpam-4923	277	19	of	of	ADP
ejpam-4923	277	20	the	the	DET
ejpam-4923	277	21	derived	derive	VERB
ejpam-4923	277	22	representation	representation	NOUN
ejpam-4923	277	23	)	)	PUNCT
ejpam-4923	277	24	on	on	ADP
ejpam-4923	277	25	the	the	DET
ejpam-4923	277	26	dirichlet	dirichlet	PROPN
ejpam-4923	277	27	space	space	NOUN
ejpam-4923	277	28	.	.	PUNCT
ejpam-4923	278	1	[	[	X
ejpam-4923	278	2	4	4	X
ejpam-4923	278	3	]	]	PUNCT
ejpam-4923	278	4	the	the	DET
ejpam-4923	278	5	dirichlet	dirichlet	PROPN
ejpam-4923	278	6	space	space	NOUN
ejpam-4923	278	7	d	d	PROPN
ejpam-4923	278	8	on	on	ADP
ejpam-4923	278	9	the	the	DET
ejpam-4923	278	10	unit	unit	NOUN
ejpam-4923	278	11	disc	disc	VERB
ejpam-4923	278	12	d	d	PROPN
ejpam-4923	278	13	=	=	PRON
ejpam-4923	278	14	{	{	PUNCT
ejpam-4923	278	15	w	w	NOUN
ejpam-4923	278	16	:	:	PUNCT
ejpam-4923	278	17	|w|	|w|	VERB
ejpam-4923	278	18	<	<	NOUN
ejpam-4923	278	19	1	1	NUM
ejpam-4923	278	20	}	}	PUNCT
ejpam-4923	278	21	consists	consist	VERB
ejpam-4923	278	22	of	of	ADP
ejpam-4923	278	23	the	the	DET
ejpam-4923	278	24	holomorphic	holomorphic	ADJ
ejpam-4923	278	25	functions	function	NOUN
ejpam-4923	278	26	f(w	f(w	PROPN
ejpam-4923	278	27	)	)	PUNCT
ejpam-4923	278	28	on	on	ADP
ejpam-4923	278	29	d	d	NOUN
ejpam-4923	278	30	,	,	PUNCT
ejpam-4923	278	31	for	for	ADP
ejpam-4923	278	32	which	which	PRON
ejpam-4923	278	33	the	the	DET
ejpam-4923	278	34	following	follow	VERB
ejpam-4923	278	35	semi	semi	ADJ
ejpam-4923	278	36	-	-	ADJ
ejpam-4923	278	37	norm	norm	ADJ
ejpam-4923	278	38	is	be	AUX
ejpam-4923	278	39	finite	finite	ADJ
ejpam-4923	278	40	:	:	PUNCT
ejpam-4923	278	41	d(f	d(f	NOUN
ejpam-4923	278	42	)	)	PUNCT
ejpam-4923	278	43	:	:	PUNCT
ejpam-4923	279	1	=	=	SYM
ejpam-4923	279	2	(	(	PUNCT
ejpam-4923	279	3	1	1	NUM
ejpam-4923	279	4	π	π	PROPN
ejpam-4923	279	5	∫	∫	PROPN
ejpam-4923	279	6	d	d	X
ejpam-4923	279	7	|f	|f	PROPN
ejpam-4923	279	8	′(w)|2dxdy	′(w)|2dxdy	PROPN
ejpam-4923	279	9	)	)	PUNCT
ejpam-4923	279	10	1	1	NUM
ejpam-4923	279	11	2	2	NUM
ejpam-4923	279	12	,	,	PUNCT
ejpam-4923	279	13	w	w	NOUN
ejpam-4923	279	14	=	=	SYM
ejpam-4923	279	15	x+	x+	PROPN
ejpam-4923	279	16	iy	iy	X
ejpam-4923	279	17	.	.	PUNCT
ejpam-4923	280	1	(	(	PUNCT
ejpam-4923	280	2	62	62	NUM
ejpam-4923	280	3	)	)	PUNCT
ejpam-4923	280	4	for	for	ADP
ejpam-4923	280	5	g	g	NOUN
ejpam-4923	280	6	=	=	SYM
ejpam-4923	280	7	(	(	PUNCT
ejpam-4923	280	8	α	α	X
ejpam-4923	280	9	β	β	X
ejpam-4923	280	10	β	β	X
ejpam-4923	280	11	α	α	NOUN
ejpam-4923	280	12	)	)	PUNCT
ejpam-4923	280	13	∈	∈	PROPN
ejpam-4923	280	14	su(1	su(1	NOUN
ejpam-4923	280	15	,	,	PUNCT
ejpam-4923	280	16	1	1	NUM
ejpam-4923	280	17	)	)	PUNCT
ejpam-4923	280	18	,	,	PUNCT
ejpam-4923	280	19	the	the	DET
ejpam-4923	280	20	su(1	su(1	NOUN
ejpam-4923	280	21	,	,	PUNCT
ejpam-4923	280	22	1	1	X
ejpam-4923	280	23	)	)	PUNCT
ejpam-4923	280	24	representation	representation	NOUN
ejpam-4923	280	25	on	on	ADP
ejpam-4923	280	26	the	the	DET
ejpam-4923	280	27	dirichlet	dirichlet	PROPN
ejpam-4923	280	28	space	space	NOUN
ejpam-4923	280	29	is	be	AUX
ejpam-4923	280	30	defined	define	VERB
ejpam-4923	280	31	as	as	SCONJ
ejpam-4923	280	32	follows	follow	VERB
ejpam-4923	280	33	:	:	PUNCT
ejpam-4923	281	1	[	[	X
ejpam-4923	281	2	π̆0(g)f	π̆0(g)f	X
ejpam-4923	281	3	]	]	X
ejpam-4923	281	4	(	(	PUNCT
ejpam-4923	281	5	w	w	NOUN
ejpam-4923	281	6	)	)	PUNCT
ejpam-4923	281	7	=	=	SYM
ejpam-4923	281	8	f	f	X
ejpam-4923	281	9	(	(	PUNCT
ejpam-4923	281	10	αw	αw	ADP
ejpam-4923	281	11	−	−	PROPN
ejpam-4923	281	12	β	β	X
ejpam-4923	281	13	α−	α−	ADP
ejpam-4923	281	14	βz	βz	ADP
ejpam-4923	281	15	)	)	PUNCT
ejpam-4923	281	16	.	.	PUNCT
ejpam-4923	282	1	(	(	PUNCT
ejpam-4923	282	2	63	63	NUM
ejpam-4923	282	3	)	)	PUNCT
ejpam-4923	282	4	the	the	DET
ejpam-4923	282	5	semi	semi	ADJ
ejpam-4923	282	6	-	-	ADJ
ejpam-4923	282	7	norm	norm	ADJ
ejpam-4923	282	8	d(f	d(f	NOUN
ejpam-4923	282	9	)	)	PUNCT
ejpam-4923	282	10	is	be	AUX
ejpam-4923	282	11	not	not	PART
ejpam-4923	282	12	a	a	DET
ejpam-4923	282	13	norm	norm	NOUN
ejpam-4923	282	14	because	because	SCONJ
ejpam-4923	282	15	d(f	d(f	NOUN
ejpam-4923	282	16	)	)	PUNCT
ejpam-4923	283	1	=	=	SYM
ejpam-4923	283	2	0	0	PUNCT
ejpam-4923	284	1	whenever	whenever	SCONJ
ejpam-4923	284	2	f	f	PROPN
ejpam-4923	284	3	is	be	AUX
ejpam-4923	284	4	a	a	DET
ejpam-4923	284	5	constant	constant	ADJ
ejpam-4923	284	6	.	.	PUNCT
ejpam-4923	285	1	then	then	ADV
ejpam-4923	285	2	,	,	PUNCT
ejpam-4923	285	3	π̆0	π̆0	X
ejpam-4923	285	4	is	be	AUX
ejpam-4923	285	5	a	a	DET
ejpam-4923	285	6	non	non	ADJ
ejpam-4923	285	7	-	-	ADJ
ejpam-4923	285	8	unitary	unitary	ADJ
ejpam-4923	285	9	representation	representation	NOUN
ejpam-4923	285	10	.	.	PUNCT
ejpam-4923	286	1	lemma	lemma	PROPN
ejpam-4923	286	2	3	3	NUM
ejpam-4923	286	3	.	.	PUNCT
ejpam-4923	287	1	the	the	DET
ejpam-4923	287	2	dirichlet	dirichlet	PROPN
ejpam-4923	287	3	space	space	NOUN
ejpam-4923	287	4	has	have	VERB
ejpam-4923	287	5	two	two	NUM
ejpam-4923	287	6	su(1	su(1	NOUN
ejpam-4923	287	7	,	,	PUNCT
ejpam-4923	287	8	1	1	X
ejpam-4923	287	9	)	)	PUNCT
ejpam-4923	287	10	vector	vector	NOUN
ejpam-4923	287	11	module	module	NOUN
ejpam-4923	287	12	:	:	PUNCT
ejpam-4923	287	13	•	•	ADP
ejpam-4923	287	14	the	the	DET
ejpam-4923	287	15	lowest	low	ADJ
ejpam-4923	287	16	weight	weight	NOUN
ejpam-4923	287	17	vector	vector	NOUN
ejpam-4923	287	18	module	module	NOUN
ejpam-4923	287	19	v0	v0	NOUN
ejpam-4923	287	20	+	+	PROPN
ejpam-4923	287	21	2	2	NUM
ejpam-4923	287	22	m	m	NOUN
ejpam-4923	287	23	=	=	PUNCT
ejpam-4923	287	24	{	{	PUNCT
ejpam-4923	287	25	w0,m	w0,m	ADV
ejpam-4923	287	26	:	:	PUNCT
ejpam-4923	287	27	m	m	VERB
ejpam-4923	287	28	=	=	SYM
ejpam-4923	287	29	0	0	NUM
ejpam-4923	287	30	,	,	PUNCT
ejpam-4923	287	31	1	1	NUM
ejpam-4923	287	32	,	,	PUNCT
ejpam-4923	287	33	2	2	NUM
ejpam-4923	287	34	,	,	PUNCT
ejpam-4923	287	35	3	3	NUM
ejpam-4923	287	36	.....	.....	PUNCT
ejpam-4923	287	37	}	}	PUNCT
ejpam-4923	287	38	,	,	PUNCT
ejpam-4923	287	39	with	with	ADP
ejpam-4923	287	40	the	the	DET
ejpam-4923	287	41	following	follow	VERB
ejpam-4923	287	42	ladder	ladder	NOUN
ejpam-4923	287	43	operators	operator	NOUN
ejpam-4923	287	44	l+w0,m	l+w0,m	NOUN
ejpam-4923	287	45	=	=	SYM
ejpam-4923	287	46	imw0,m+1	imw0,m+1	PROPN
ejpam-4923	287	47	,	,	PUNCT
ejpam-4923	287	48	m	m	VERB
ejpam-4923	287	49	∈	∈	NOUN
ejpam-4923	287	50	z+	z+	NUM
ejpam-4923	287	51	−	−	PROPN
ejpam-4923	287	52	{	{	PUNCT
ejpam-4923	287	53	0	0	NUM
ejpam-4923	287	54	}	}	PUNCT
ejpam-4923	287	55	,	,	PUNCT
ejpam-4923	287	56	l−w0,m	l−w0,m	X
ejpam-4923	287	57	=	=	SYM
ejpam-4923	287	58	imw0,m−1	imw0,m−1	PROPN
ejpam-4923	287	59	,	,	PUNCT
ejpam-4923	287	60	m	m	PROPN
ejpam-4923	287	61	∈	∈	PROPN
ejpam-4923	287	62	z+	z+	NUM
ejpam-4923	287	63	−	−	PROPN
ejpam-4923	287	64	{	{	PUNCT
ejpam-4923	287	65	0	0	NUM
ejpam-4923	287	66	}	}	PUNCT
ejpam-4923	287	67	,	,	PUNCT
ejpam-4923	287	68	a.	a.	PROPN
ejpam-4923	287	69	s.	s.	PROPN
ejpam-4923	287	70	alghamdi	alghamdi	PROPN
ejpam-4923	287	71	/	/	SYM
ejpam-4923	287	72	eur	eur	PROPN
ejpam-4923	287	73	.	.	PUNCT
ejpam-4923	288	1	j.	j.	PROPN
ejpam-4923	288	2	pure	pure	PROPN
ejpam-4923	288	3	appl	appl	PROPN
ejpam-4923	288	4	.	.	PROPN
ejpam-4923	288	5	math	math	PROPN
ejpam-4923	288	6	,	,	PUNCT
ejpam-4923	288	7	16	16	NUM
ejpam-4923	288	8	(	(	PUNCT
ejpam-4923	288	9	4	4	NUM
ejpam-4923	288	10	)	)	PUNCT
ejpam-4923	288	11	(	(	PUNCT
ejpam-4923	288	12	2023	2023	NUM
ejpam-4923	288	13	)	)	PUNCT
ejpam-4923	288	14	,	,	PUNCT
ejpam-4923	288	15	2348	2348	NUM
ejpam-4923	288	16	-	-	SYM
ejpam-4923	288	17	2367	2367	NUM
ejpam-4923	288	18	2363	2363	NUM
ejpam-4923	288	19	l+w0,0	l+w0,0	NOUN
ejpam-4923	288	20	=	=	SYM
ejpam-4923	288	21	0	0	NUM
ejpam-4923	288	22	,	,	PUNCT
ejpam-4923	288	23	•	•	ADP
ejpam-4923	288	24	the	the	DET
ejpam-4923	288	25	highest	high	ADJ
ejpam-4923	288	26	weight	weight	NOUN
ejpam-4923	288	27	vector	vector	NOUN
ejpam-4923	288	28	module	module	NOUN
ejpam-4923	288	29	v̄0	v̄0	NOUN
ejpam-4923	288	30	+	+	PROPN
ejpam-4923	288	31	2	2	NUM
ejpam-4923	288	32	m	m	NOUN
ejpam-4923	288	33	=	=	PUNCT
ejpam-4923	288	34	{	{	PUNCT
ejpam-4923	288	35	w0,m	w0,m	ADV
ejpam-4923	288	36	:	:	PUNCT
ejpam-4923	288	37	m	m	VERB
ejpam-4923	288	38	=	=	SYM
ejpam-4923	288	39	0	0	NUM
ejpam-4923	288	40	,	,	PUNCT
ejpam-4923	288	41	1	1	NUM
ejpam-4923	288	42	,	,	PUNCT
ejpam-4923	288	43	2	2	NUM
ejpam-4923	288	44	,	,	PUNCT
ejpam-4923	288	45	3	3	NUM
ejpam-4923	288	46	.....	.....	PUNCT
ejpam-4923	288	47	},with	},with	ADP
ejpam-4923	288	48	the	the	DET
ejpam-4923	288	49	following	follow	VERB
ejpam-4923	288	50	ladder	ladder	NOUN
ejpam-4923	288	51	operators	operator	NOUN
ejpam-4923	288	52	l+w0,m	l+w0,m	NOUN
ejpam-4923	288	53	=	=	SYM
ejpam-4923	288	54	imw0,m+1	imw0,m+1	PROPN
ejpam-4923	288	55	,	,	PUNCT
ejpam-4923	288	56	m	m	VERB
ejpam-4923	288	57	∈	∈	NOUN
ejpam-4923	288	58	z+	z+	NUM
ejpam-4923	288	59	−	−	PROPN
ejpam-4923	288	60	{	{	PUNCT
ejpam-4923	288	61	0	0	NUM
ejpam-4923	288	62	}	}	PUNCT
ejpam-4923	288	63	,	,	PUNCT
ejpam-4923	288	64	l−w0,m	l−w0,m	X
ejpam-4923	288	65	=	=	SYM
ejpam-4923	288	66	imw0,m−1	imw0,m−1	PROPN
ejpam-4923	288	67	,	,	PUNCT
ejpam-4923	288	68	m	m	PROPN
ejpam-4923	288	69	∈	∈	PROPN
ejpam-4923	288	70	z+	z+	NUM
ejpam-4923	288	71	−	−	PROPN
ejpam-4923	288	72	{	{	PUNCT
ejpam-4923	288	73	0	0	NUM
ejpam-4923	288	74	}	}	PUNCT
ejpam-4923	288	75	,	,	PUNCT
ejpam-4923	288	76	l−w0,0	l−w0,0	NOUN
ejpam-4923	288	77	=	=	SYM
ejpam-4923	288	78	0	0	NUM
ejpam-4923	288	79	,	,	PUNCT
ejpam-4923	288	80	proof	proof	NOUN
ejpam-4923	288	81	.	.	PUNCT
ejpam-4923	289	1	the	the	DET
ejpam-4923	289	2	representation	representation	NOUN
ejpam-4923	289	3	π̆0	π̆0	X
ejpam-4923	289	4	(	(	PUNCT
ejpam-4923	289	5	63	63	NUM
ejpam-4923	289	6	)	)	PUNCT
ejpam-4923	289	7	is	be	AUX
ejpam-4923	289	8	the	the	DET
ejpam-4923	289	9	su(1	su(1	NOUN
ejpam-4923	289	10	,	,	PUNCT
ejpam-4923	289	11	1	1	NUM
ejpam-4923	289	12	)	)	PUNCT
ejpam-4923	289	13	representation	representation	NOUN
ejpam-4923	289	14	π̆n	π̆n	PROPN
ejpam-4923	289	15	,	,	PUNCT
ejpam-4923	289	16	for	for	ADP
ejpam-4923	289	17	n	n	NOUN
ejpam-4923	289	18	=	=	SYM
ejpam-4923	289	19	0	0	NUM
ejpam-4923	289	20	.	.	PUNCT
ejpam-4923	290	1	the	the	DET
ejpam-4923	290	2	representation	representation	NOUN
ejpam-4923	290	3	π̆n	π̆n	PROPN
ejpam-4923	290	4	is	be	AUX
ejpam-4923	290	5	defined	define	VERB
ejpam-4923	290	6	as	as	SCONJ
ejpam-4923	290	7	follows	follow	VERB
ejpam-4923	290	8	:	:	PUNCT
ejpam-4923	290	9	[	[	X
ejpam-4923	290	10	π̆n(g)f	π̆n(g)f	X
ejpam-4923	290	11	]	]	X
ejpam-4923	290	12	(	(	PUNCT
ejpam-4923	290	13	w	w	NOUN
ejpam-4923	290	14	)	)	PUNCT
ejpam-4923	291	1	=	=	SYM
ejpam-4923	291	2	f	f	X
ejpam-4923	291	3	(	(	PUNCT
ejpam-4923	291	4	αw	αw	ADP
ejpam-4923	291	5	−	−	PROPN
ejpam-4923	291	6	β	β	X
ejpam-4923	291	7	α−	α−	ADP
ejpam-4923	291	8	βw	βw	ADP
ejpam-4923	291	9	)	)	PUNCT
ejpam-4923	291	10	(	(	PUNCT
ejpam-4923	291	11	α−	α−	ADP
ejpam-4923	291	12	βw)−n	βw)−n	NUM
ejpam-4923	291	13	,	,	PUNCT
ejpam-4923	291	14	(	(	PUNCT
ejpam-4923	291	15	64	64	NUM
ejpam-4923	291	16	)	)	PUNCT
ejpam-4923	291	17	where	where	SCONJ
ejpam-4923	291	18	n	n	X
ejpam-4923	291	19	∈	∈	PROPN
ejpam-4923	291	20	z.	z.	X
ejpam-4923	292	1	the	the	DET
ejpam-4923	292	2	derived	derive	VERB
ejpam-4923	292	3	representations	representation	NOUN
ejpam-4923	292	4	for	for	ADP
ejpam-4923	292	5	the	the	DET
ejpam-4923	292	6	basis	basis	NOUN
ejpam-4923	292	7	{	{	PUNCT
ejpam-4923	292	8	z̃	z̃	PROPN
ejpam-4923	292	9	,	,	PUNCT
ejpam-4923	292	10	ã	ã	PROPN
ejpam-4923	292	11	,	,	PUNCT
ejpam-4923	292	12	b̃	b̃	PROPN
ejpam-4923	292	13	}	}	PUNCT
ejpam-4923	292	14	(	(	PUNCT
ejpam-4923	292	15	8)	8)	NUM
ejpam-4923	292	16	are	be	AUX
ejpam-4923	292	17	as	as	SCONJ
ejpam-4923	292	18	follows	follow	VERB
ejpam-4923	292	19	:	:	PUNCT
ejpam-4923	293	1	e	e	NOUN
ejpam-4923	293	2	=	=	PROPN
ejpam-4923	293	3	dπ̆z̃n	dπ̆z̃n	PROPN
ejpam-4923	293	4	=	=	SYM
ejpam-4923	293	5	d	d	NOUN
ejpam-4923	293	6	dt	dt	X
ejpam-4923	293	7	π̆n(e	π̆n(e	PROPN
ejpam-4923	293	8	tz̃)f(w)|t=0	tz̃)f(w)|t=0	PROPN
ejpam-4923	294	1	=	=	PUNCT
ejpam-4923	295	1	[	[	X
ejpam-4923	295	2	−ini	−ini	X
ejpam-4923	295	3	−	−	PROPN
ejpam-4923	295	4	2iw∂w]f(w	2iw∂w]f(w	NUM
ejpam-4923	295	5	)	)	PUNCT
ejpam-4923	295	6	,	,	PUNCT
ejpam-4923	295	7	a1	a1	NOUN
ejpam-4923	295	8	=	=	SYM
ejpam-4923	295	9	dπ̆ãn	dπ̆ãn	PROPN
ejpam-4923	295	10	=	=	PUNCT
ejpam-4923	296	1	d	d	NOUN
ejpam-4923	296	2	dt	dt	X
ejpam-4923	297	1	π̆n(e	π̆n(e	PROPN
ejpam-4923	297	2	tã)f(w)|t=0	tã)f(w)|t=0	PROPN
ejpam-4923	298	1	=	=	X
ejpam-4923	298	2	i	i	PRON
ejpam-4923	298	3	2	2	NUM
ejpam-4923	299	1	[	[	X
ejpam-4923	299	2	nwi	nwi	NOUN
ejpam-4923	299	3	+	+	CCONJ
ejpam-4923	299	4	(	(	PUNCT
ejpam-4923	299	5	1	1	NUM
ejpam-4923	299	6	+	+	CCONJ
ejpam-4923	299	7	w2)∂w]f(w	w2)∂w]f(w	PROPN
ejpam-4923	299	8	)	)	PUNCT
ejpam-4923	299	9	,	,	PUNCT
ejpam-4923	299	10	b1	b1	NOUN
ejpam-4923	299	11	=	=	SYM
ejpam-4923	299	12	dπ̆b̃n	dπ̆b̃n	PROPN
ejpam-4923	299	13	=	=	SYM
ejpam-4923	300	1	d	d	PROPN
ejpam-4923	300	2	dt	dt	X
ejpam-4923	301	1	π̆n(e	π̆n(e	PROPN
ejpam-4923	301	2	tb̃)f(w)|t=0	tb̃)f(w)|t=0	PROPN
ejpam-4923	301	3	=	=	SYM
ejpam-4923	302	1	1	1	NUM
ejpam-4923	302	2	2	2	NUM
ejpam-4923	302	3	[	[	X
ejpam-4923	302	4	nwi	nwi	NOUN
ejpam-4923	302	5	+	+	CCONJ
ejpam-4923	302	6	(	(	PUNCT
ejpam-4923	302	7	w2	w2	NOUN
ejpam-4923	302	8	−	−	PROPN
ejpam-4923	302	9	1)∂w]f(w	1)∂w]f(w	NUM
ejpam-4923	302	10	)	)	PUNCT
ejpam-4923	302	11	.	.	PUNCT
ejpam-4923	303	1	the	the	DET
ejpam-4923	303	2	commutator	commutator	NOUN
ejpam-4923	303	3	relations	relation	NOUN
ejpam-4923	303	4	are	be	AUX
ejpam-4923	303	5	[	[	X
ejpam-4923	303	6	e	e	NOUN
ejpam-4923	303	7	,	,	PUNCT
ejpam-4923	303	8	a1	a1	NOUN
ejpam-4923	303	9	]	]	PUNCT
ejpam-4923	303	10	=	=	SYM
ejpam-4923	303	11	2b1	2b1	NUM
ejpam-4923	303	12	,	,	PUNCT
ejpam-4923	303	13	[	[	X
ejpam-4923	303	14	e	e	NOUN
ejpam-4923	303	15	,	,	PUNCT
ejpam-4923	303	16	b1	b1	NOUN
ejpam-4923	303	17	]	]	PUNCT
ejpam-4923	303	18	=	=	SYM
ejpam-4923	303	19	−2a1	−2a1	X
ejpam-4923	303	20	,	,	PUNCT
ejpam-4923	303	21	[	[	X
ejpam-4923	303	22	a1	a1	NOUN
ejpam-4923	303	23	,	,	PUNCT
ejpam-4923	303	24	b1	b1	NOUN
ejpam-4923	303	25	]	]	PUNCT
ejpam-4923	304	1	=	=	SYM
ejpam-4923	304	2	−1	−1	NOUN
ejpam-4923	304	3	2	2	NUM
ejpam-4923	304	4	e.	e.	PROPN
ejpam-4923	305	1	the	the	DET
ejpam-4923	305	2	ladder	ladder	NOUN
ejpam-4923	305	3	operators	operator	NOUN
ejpam-4923	305	4	are	be	AUX
ejpam-4923	305	5	defined	define	VERB
ejpam-4923	305	6	as	as	ADP
ejpam-4923	305	7	l+	l+	NOUN
ejpam-4923	305	8	=	=	SYM
ejpam-4923	305	9	a1	a1	NOUN
ejpam-4923	305	10	+	+	CCONJ
ejpam-4923	305	11	ib1	ib1	NOUN
ejpam-4923	305	12	=	=	NOUN
ejpam-4923	305	13	inwi	inwi	NOUN
ejpam-4923	305	14	+	+	CCONJ
ejpam-4923	305	15	iw2∂w	iw2∂w	PROPN
ejpam-4923	305	16	,	,	PUNCT
ejpam-4923	305	17	l−	l−	NOUN
ejpam-4923	305	18	=	=	NOUN
ejpam-4923	305	19	a1	a1	NOUN
ejpam-4923	305	20	−	−	NOUN
ejpam-4923	305	21	ib1	ib1	NOUN
ejpam-4923	305	22	=	=	PUNCT
ejpam-4923	305	23	i∂w	i∂w	NOUN
ejpam-4923	305	24	,	,	PUNCT
ejpam-4923	305	25	and	and	CCONJ
ejpam-4923	305	26	[	[	X
ejpam-4923	305	27	e	e	NOUN
ejpam-4923	305	28	,	,	PUNCT
ejpam-4923	305	29	l+	l+	NOUN
ejpam-4923	305	30	]	]	X
ejpam-4923	305	31	=	=	SYM
ejpam-4923	305	32	−2il+	−2il+	PROPN
ejpam-4923	305	33	,	,	PUNCT
ejpam-4923	305	34	[	[	X
ejpam-4923	305	35	e	e	NOUN
ejpam-4923	305	36	,	,	PUNCT
ejpam-4923	305	37	l−	l−	PROPN
ejpam-4923	305	38	]	]	X
ejpam-4923	305	39	=	=	SYM
ejpam-4923	305	40	2il−	2il−	NUM
ejpam-4923	305	41	and	and	CCONJ
ejpam-4923	305	42	[	[	X
ejpam-4923	305	43	l+	l+	NOUN
ejpam-4923	305	44	,	,	PUNCT
ejpam-4923	305	45	l−	l−	PROPN
ejpam-4923	305	46	]	]	X
ejpam-4923	305	47	=	=	PUNCT
ejpam-4923	305	48	ie	ie	X
ejpam-4923	305	49	.	.	PUNCT
ejpam-4923	306	1	(	(	PUNCT
ejpam-4923	306	2	65	65	NUM
ejpam-4923	306	3	)	)	PUNCT
ejpam-4923	306	4	the	the	DET
ejpam-4923	306	5	casimir	casimir	NOUN
ejpam-4923	306	6	operator	operator	NOUN
ejpam-4923	306	7	is	be	AUX
ejpam-4923	306	8	dπ̆n(c	dπ̆n(c	NOUN
ejpam-4923	306	9	)	)	PUNCT
ejpam-4923	307	1	=	=	VERB
ejpam-4923	307	2	dπ̆n(z̃	dπ̆n(z̃	VERB
ejpam-4923	307	3	2	2	NUM
ejpam-4923	307	4	−	−	PROPN
ejpam-4923	307	5	4ã2	4ã2	NUM
ejpam-4923	307	6	−	−	NOUN
ejpam-4923	307	7	4b̃2	4b̃2	NUM
ejpam-4923	307	8	)	)	PUNCT
ejpam-4923	307	9	=	=	SYM
ejpam-4923	308	1	−n2	−n2	PROPN
ejpam-4923	308	2	+	+	NUM
ejpam-4923	308	3	2n	2n	NUM
ejpam-4923	308	4	.	.	PUNCT
ejpam-4923	309	1	(	(	PUNCT
ejpam-4923	309	2	66	66	NUM
ejpam-4923	309	3	)	)	PUNCT
ejpam-4923	309	4	the	the	DET
ejpam-4923	309	5	representation	representation	NOUN
ejpam-4923	309	6	π̆n	π̆n	PROPN
ejpam-4923	309	7	on	on	ADP
ejpam-4923	309	8	l2(d	l2(d	PROPN
ejpam-4923	309	9	)	)	PUNCT
ejpam-4923	309	10	is	be	AUX
ejpam-4923	309	11	irreducible	irreducible	ADJ
ejpam-4923	309	12	,	,	PUNCT
ejpam-4923	309	13	and	and	CCONJ
ejpam-4923	309	14	vn+2	vn+2	NOUN
ejpam-4923	309	15	m	m	NOUN
ejpam-4923	309	16	is	be	AUX
ejpam-4923	309	17	the	the	DET
ejpam-4923	309	18	one	one	NUM
ejpam-4923	309	19	-	-	PUNCT
ejpam-4923	309	20	dimensional	dimensional	ADJ
ejpam-4923	309	21	subspace	subspace	NOUN
ejpam-4923	309	22	generated	generate	VERB
ejpam-4923	309	23	by	by	ADP
ejpam-4923	309	24	wn	wn	PROPN
ejpam-4923	309	25	,	,	PUNCT
ejpam-4923	309	26	m	m	VERB
ejpam-4923	309	27	[	[	X
ejpam-4923	309	28	13	13	NUM
ejpam-4923	309	29	]	]	PUNCT
ejpam-4923	309	30	.	.	PUNCT
ejpam-4923	310	1	indeed	indeed	ADV
ejpam-4923	310	2	,	,	PUNCT
ejpam-4923	310	3	π̆n	π̆n	PROPN
ejpam-4923	310	4	(	(	PUNCT
ejpam-4923	310	5	(	(	PUNCT
ejpam-4923	310	6	eiθ	eiθ	NOUN
ejpam-4923	310	7	0	0	NUM
ejpam-4923	310	8	0	0	NUM
ejpam-4923	310	9	e−iθ	e−iθ	NOUN
ejpam-4923	310	10	)	)	PUNCT
ejpam-4923	310	11	)	)	PUNCT
ejpam-4923	311	1	(	(	PUNCT
ejpam-4923	311	2	wn	wn	PROPN
ejpam-4923	311	3	,	,	PUNCT
ejpam-4923	311	4	m	m	PROPN
ejpam-4923	311	5	)	)	PUNCT
ejpam-4923	311	6	=	=	SYM
ejpam-4923	311	7	e−iθ(n+2m)wn	e−iθ(n+2m)wn	PROPN
ejpam-4923	311	8	,	,	PUNCT
ejpam-4923	311	9	m.	m.	NOUN
ejpam-4923	311	10	a.	a.	PROPN
ejpam-4923	311	11	s.	s.	PROPN
ejpam-4923	311	12	alghamdi	alghamdi	PROPN
ejpam-4923	311	13	/	/	SYM
ejpam-4923	311	14	eur	eur	PROPN
ejpam-4923	311	15	.	.	PUNCT
ejpam-4923	312	1	j.	j.	PROPN
ejpam-4923	312	2	pure	pure	PROPN
ejpam-4923	312	3	appl	appl	PROPN
ejpam-4923	312	4	.	.	PROPN
ejpam-4923	312	5	math	math	PROPN
ejpam-4923	312	6	,	,	PUNCT
ejpam-4923	312	7	16	16	NUM
ejpam-4923	312	8	(	(	PUNCT
ejpam-4923	312	9	4	4	NUM
ejpam-4923	312	10	)	)	PUNCT
ejpam-4923	312	11	(	(	PUNCT
ejpam-4923	312	12	2023	2023	NUM
ejpam-4923	312	13	)	)	PUNCT
ejpam-4923	312	14	,	,	PUNCT
ejpam-4923	312	15	2348	2348	NUM
ejpam-4923	312	16	-	-	SYM
ejpam-4923	312	17	2367	2367	NUM
ejpam-4923	312	18	2364	2364	NUM
ejpam-4923	312	19	hence	hence	ADV
ejpam-4923	312	20	,	,	PUNCT
ejpam-4923	312	21	vn+2	vn+2	PROPN
ejpam-4923	312	22	m	m	VERB
ejpam-4923	312	23	is	be	AUX
ejpam-4923	312	24	an	an	DET
ejpam-4923	312	25	eigenspace	eigenspace	NOUN
ejpam-4923	312	26	of	of	ADP
ejpam-4923	312	27	k	k	PROPN
ejpam-4923	312	28	with	with	ADP
ejpam-4923	312	29	an	an	DET
ejpam-4923	312	30	eigenvalue	eigenvalue	PROPN
ejpam-4923	312	31	e−iθ(n+2	e−iθ(n+2	PROPN
ejpam-4923	312	32	m	m	PROPN
ejpam-4923	312	33	)	)	PUNCT
ejpam-4923	312	34	,	,	PUNCT
ejpam-4923	312	35	which	which	PRON
ejpam-4923	312	36	is	be	AUX
ejpam-4923	312	37	the	the	DET
ejpam-4923	312	38	character	character	NOUN
ejpam-4923	312	39	of	of	ADP
ejpam-4923	312	40	the	the	DET
ejpam-4923	312	41	subgroup	subgroup	PROPN
ejpam-4923	312	42	k.	k.	PROPN
ejpam-4923	312	43	then	then	ADV
ejpam-4923	312	44	π̆n(exp	π̆n(exp	PROPN
ejpam-4923	312	45	tz̃	tz̃	NOUN
ejpam-4923	312	46	)	)	PUNCT
ejpam-4923	312	47	=	=	SYM
ejpam-4923	312	48	e−i(n+2m)ti	e−i(n+2m)ti	NOUN
ejpam-4923	312	49	on	on	ADP
ejpam-4923	312	50	vn+2	vn+2	PROPN
ejpam-4923	312	51	m	m	PROPN
ejpam-4923	312	52	,	,	PUNCT
ejpam-4923	312	53	and	and	CCONJ
ejpam-4923	312	54	the	the	DET
ejpam-4923	312	55	derived	derived	ADJ
ejpam-4923	312	56	representation	representation	NOUN
ejpam-4923	312	57	is	be	AUX
ejpam-4923	312	58	given	give	VERB
ejpam-4923	312	59	by	by	ADP
ejpam-4923	312	60	e	e	NOUN
ejpam-4923	312	61	=	=	NOUN
ejpam-4923	312	62	−i(n+	−i(n+	X
ejpam-4923	312	63	2m)i	2m)i	NUM
ejpam-4923	312	64	on	on	ADP
ejpam-4923	312	65	vn+2	vn+2	NOUN
ejpam-4923	312	66	m.	m.	NOUN
ejpam-4923	312	67	from	from	ADP
ejpam-4923	312	68	the	the	DET
ejpam-4923	312	69	commutator	commutator	NOUN
ejpam-4923	312	70	relation	relation	NOUN
ejpam-4923	312	71	(	(	PUNCT
ejpam-4923	312	72	65	65	NUM
ejpam-4923	312	73	)	)	PUNCT
ejpam-4923	312	74	,	,	PUNCT
ejpam-4923	312	75	we	we	PRON
ejpam-4923	312	76	have	have	VERB
ejpam-4923	312	77	e(l+wn	e(l+wn	NOUN
ejpam-4923	312	78	,	,	PUNCT
ejpam-4923	312	79	m	m	NOUN
ejpam-4923	312	80	)	)	PUNCT
ejpam-4923	312	81	=	=	PUNCT
ejpam-4923	312	82	l+(ewn	l+(ewn	PROPN
ejpam-4923	312	83	,	,	PUNCT
ejpam-4923	312	84	m)−	m)−	PROPN
ejpam-4923	312	85	2il+wn	2il+wn	NUM
ejpam-4923	312	86	,	,	PUNCT
ejpam-4923	312	87	m	m	VERB
ejpam-4923	312	88	=	=	NOUN
ejpam-4923	313	1	l+(−i(n+	l+(−i(n+	PROPN
ejpam-4923	313	2	2m))−	2m))−	NUM
ejpam-4923	313	3	2il+	2il+	NUM
ejpam-4923	313	4	=	=	PUNCT
ejpam-4923	313	5	−i(n+	−i(n+	X
ejpam-4923	313	6	2m+	2m+	NUM
ejpam-4923	313	7	2)l+	2)l+	NUM
ejpam-4923	313	8	,	,	PUNCT
ejpam-4923	313	9	e(l−wn	e(l−wn	PROPN
ejpam-4923	313	10	,	,	PUNCT
ejpam-4923	313	11	m	m	NOUN
ejpam-4923	313	12	)	)	PUNCT
ejpam-4923	313	13	=	=	SYM
ejpam-4923	314	1	l−(ewn	l−(ewn	PROPN
ejpam-4923	314	2	,	,	PUNCT
ejpam-4923	314	3	m	m	PROPN
ejpam-4923	314	4	)	)	PUNCT
ejpam-4923	315	1	+	+	CCONJ
ejpam-4923	315	2	2il−wn	2il−wn	NUM
ejpam-4923	315	3	,	,	PUNCT
ejpam-4923	315	4	m	m	NOUN
ejpam-4923	315	5	=	=	NOUN
ejpam-4923	315	6	l−(−i(n+	l−(−i(n+	NOUN
ejpam-4923	315	7	2	2	NUM
ejpam-4923	315	8	m	m	NOUN
ejpam-4923	315	9	)	)	PUNCT
ejpam-4923	315	10	)	)	PUNCT
ejpam-4923	316	1	+	+	CCONJ
ejpam-4923	316	2	2il+	2il+	NUM
ejpam-4923	316	3	=	=	PUNCT
ejpam-4923	316	4	−i(n+	−i(n+	PROPN
ejpam-4923	316	5	2m−	2m−	NUM
ejpam-4923	316	6	2)l−.	2)l−.	NUM
ejpam-4923	316	7	therefore	therefore	ADV
ejpam-4923	316	8	,	,	PUNCT
ejpam-4923	316	9	the	the	DET
ejpam-4923	316	10	ladder	ladder	NOUN
ejpam-4923	316	11	operator	operator	NOUN
ejpam-4923	316	12	l±	l±	VERB
ejpam-4923	316	13	acts	act	VERB
ejpam-4923	316	14	as	as	SCONJ
ejpam-4923	316	15	follows	follow	VERB
ejpam-4923	316	16	:	:	PUNCT
ejpam-4923	316	17	l+	l+	NOUN
ejpam-4923	316	18	:	:	PUNCT
ejpam-4923	317	1	vn+2	vn+2	NUM
ejpam-4923	317	2	m	m	PROPN
ejpam-4923	317	3	→	→	SYM
ejpam-4923	317	4	vn+2m+2	vn+2m+2	PROPN
ejpam-4923	317	5	,	,	PUNCT
ejpam-4923	317	6	l−	l−	NOUN
ejpam-4923	317	7	:	:	PUNCT
ejpam-4923	317	8	vn+2	vn+2	NUM
ejpam-4923	317	9	m	m	NOUN
ejpam-4923	317	10	→	→	SYM
ejpam-4923	317	11	vn+2m−2	vn+2m−2	X
ejpam-4923	317	12	.	.	PUNCT
ejpam-4923	317	13	·	·	PUNCT
ejpam-4923	317	14	·	·	PUNCT
ejpam-4923	317	15	·	·	PUNCT
ejpam-4923	318	1	vn+2m−2	vn+2m−2	ADP
ejpam-4923	318	2	vn+2	vn+2	X
ejpam-4923	318	3	m	m	PROPN
ejpam-4923	318	4	vn+2m+2	vn+2m+2	PROPN
ejpam-4923	318	5	·	·	PUNCT
ejpam-4923	318	6	·	·	PUNCT
ejpam-4923	318	7	·	·	PUNCT
ejpam-4923	318	8	l+	l+	PUNCT
ejpam-4923	318	9	l−	l−	NOUN
ejpam-4923	318	10	l+	l+	PUNCT
ejpam-4923	318	11	l−	l−	NOUN
ejpam-4923	318	12	l+	l+	PUNCT
ejpam-4923	318	13	l−	l−	NOUN
ejpam-4923	318	14	l+	l+	PUNCT
ejpam-4923	318	15	l−	l−	NOUN
ejpam-4923	318	16	vn+2	vn+2	NOUN
ejpam-4923	318	17	m	m	VERB
ejpam-4923	318	18	=	=	SYM
ejpam-4923	318	19	{	{	PUNCT
ejpam-4923	318	20	wn	wn	PROPN
ejpam-4923	318	21	,	,	PUNCT
ejpam-4923	318	22	m	m	VERB
ejpam-4923	318	23	:	:	PUNCT
ejpam-4923	318	24	m	m	VERB
ejpam-4923	318	25	=	=	SYM
ejpam-4923	318	26	0	0	NUM
ejpam-4923	318	27	,	,	PUNCT
ejpam-4923	318	28	1	1	NUM
ejpam-4923	318	29	,	,	PUNCT
ejpam-4923	318	30	2	2	NUM
ejpam-4923	318	31	,	,	PUNCT
ejpam-4923	318	32	3	3	NUM
ejpam-4923	318	33	.....	.....	PUNCT
ejpam-4923	318	34	}	}	PUNCT
ejpam-4923	318	35	is	be	AUX
ejpam-4923	318	36	the	the	DET
ejpam-4923	318	37	lowest	low	ADJ
ejpam-4923	318	38	weight	weight	NOUN
ejpam-4923	318	39	module	module	NOUN
ejpam-4923	318	40	and	and	CCONJ
ejpam-4923	318	41	is	be	AUX
ejpam-4923	318	42	given	give	VERB
ejpam-4923	318	43	as	as	SCONJ
ejpam-4923	318	44	follows	follow	VERB
ejpam-4923	318	45	:	:	PUNCT
ejpam-4923	318	46	ewn	ewn	PROPN
ejpam-4923	318	47	,	,	PUNCT
ejpam-4923	318	48	m	m	VERB
ejpam-4923	318	49	=	=	PUNCT
ejpam-4923	318	50	−(n+	−(n+	PROPN
ejpam-4923	318	51	2m)iwn	2m)iwn	NUM
ejpam-4923	318	52	,	,	PUNCT
ejpam-4923	318	53	m	m	PROPN
ejpam-4923	318	54	,	,	PUNCT
ejpam-4923	318	55	l+wn	l+wn	PROPN
ejpam-4923	318	56	,	,	PUNCT
ejpam-4923	318	57	m	m	VERB
ejpam-4923	318	58	=	=	PUNCT
ejpam-4923	318	59	a1wn	a1wn	X
ejpam-4923	318	60	,	,	PUNCT
ejpam-4923	318	61	m	m	VERB
ejpam-4923	318	62	+	+	NOUN
ejpam-4923	318	63	ib1wn	ib1wn	NUM
ejpam-4923	318	64	,	,	PUNCT
ejpam-4923	318	65	m	m	VERB
ejpam-4923	318	66	=	=	X
ejpam-4923	318	67	(	(	PUNCT
ejpam-4923	318	68	n+m)iwn	n+m)iwn	NOUN
ejpam-4923	318	69	,	,	PUNCT
ejpam-4923	318	70	m+1	m+1	NUM
ejpam-4923	318	71	,	,	PUNCT
ejpam-4923	318	72	m	m	NOUN
ejpam-4923	318	73	∈	∈	NOUN
ejpam-4923	318	74	z+	z+	NUM
ejpam-4923	318	75	−	−	PROPN
ejpam-4923	318	76	{	{	PUNCT
ejpam-4923	318	77	0	0	NUM
ejpam-4923	318	78	}	}	PUNCT
ejpam-4923	318	79	,	,	PUNCT
ejpam-4923	318	80	l−wn	l−wn	PROPN
ejpam-4923	318	81	,	,	PUNCT
ejpam-4923	318	82	m	m	VERB
ejpam-4923	318	83	=	=	PUNCT
ejpam-4923	318	84	a1wn	a1wn	X
ejpam-4923	318	85	,	,	PUNCT
ejpam-4923	318	86	m	m	VERB
ejpam-4923	318	87	−	−	NOUN
ejpam-4923	318	88	ib1wn	ib1wn	NOUN
ejpam-4923	318	89	,	,	PUNCT
ejpam-4923	318	90	m	m	NOUN
ejpam-4923	318	91	=	=	NOUN
ejpam-4923	318	92	miwn	miwn	NOUN
ejpam-4923	318	93	,	,	PUNCT
ejpam-4923	318	94	m−1	m−1	PROPN
ejpam-4923	318	95	,	,	PUNCT
ejpam-4923	318	96	m	m	PROPN
ejpam-4923	318	97	∈	∈	PROPN
ejpam-4923	318	98	z+	z+	NUM
ejpam-4923	318	99	−	−	PROPN
ejpam-4923	318	100	{	{	PUNCT
ejpam-4923	318	101	0	0	NUM
ejpam-4923	318	102	}	}	PUNCT
ejpam-4923	318	103	l−wn,0	l−wn,0	NOUN
ejpam-4923	319	1	=	=	SYM
ejpam-4923	319	2	0	0	NUM
ejpam-4923	319	3	,	,	PUNCT
ejpam-4923	319	4	dπ̆n(c)w	dπ̆n(c)w	NOUN
ejpam-4923	319	5	=	=	SYM
ejpam-4923	319	6	(	(	PUNCT
ejpam-4923	319	7	−n2	−n2	PROPN
ejpam-4923	319	8	+	+	NUM
ejpam-4923	319	9	2n)w	2n)w	NUM
ejpam-4923	319	10	,	,	PUNCT
ejpam-4923	319	11	w	w	PROPN
ejpam-4923	319	12	∈	∈	PROPN
ejpam-4923	319	13	vn+2	vn+2	NOUN
ejpam-4923	319	14	m.	m.	NOUN
ejpam-4923	319	15	the	the	DET
ejpam-4923	319	16	vector	vector	NOUN
ejpam-4923	319	17	wn,0	wn,0	PROPN
ejpam-4923	319	18	is	be	AUX
ejpam-4923	319	19	called	call	VERB
ejpam-4923	319	20	the	the	DET
ejpam-4923	319	21	lowest	low	ADJ
ejpam-4923	319	22	weight	weight	NOUN
ejpam-4923	319	23	vector	vector	NOUN
ejpam-4923	319	24	.	.	PUNCT
ejpam-4923	319	25	0	0	NUM
ejpam-4923	320	1	wn,0	wn,0	PROPN
ejpam-4923	320	2	wn,1	wn,1	PROPN
ejpam-4923	320	3	wn,2	wn,2	VERB
ejpam-4923	320	4	·	·	PUNCT
ejpam-4923	320	5	·	·	PUNCT
ejpam-4923	320	6	·	·	PUNCT
ejpam-4923	321	1	l−	l−	NOUN
ejpam-4923	321	2	l+	l+	PUNCT
ejpam-4923	321	3	l−	l−	NOUN
ejpam-4923	321	4	l+	l+	PUNCT
ejpam-4923	321	5	l−	l−	NOUN
ejpam-4923	321	6	l+	l+	PUNCT
ejpam-4923	321	7	l−	l−	PROPN
ejpam-4923	321	8	v̄n+2	v̄n+2	PROPN
ejpam-4923	321	9	m	m	NOUN
ejpam-4923	321	10	=	=	SYM
ejpam-4923	321	11	{	{	PUNCT
ejpam-4923	321	12	wn	wn	PROPN
ejpam-4923	321	13	,	,	PUNCT
ejpam-4923	321	14	m	m	VERB
ejpam-4923	321	15	:	:	PUNCT
ejpam-4923	321	16	m	m	VERB
ejpam-4923	321	17	=	=	SYM
ejpam-4923	321	18	0	0	NUM
ejpam-4923	321	19	,	,	PUNCT
ejpam-4923	321	20	1	1	NUM
ejpam-4923	321	21	,	,	PUNCT
ejpam-4923	321	22	2	2	NUM
ejpam-4923	321	23	,	,	PUNCT
ejpam-4923	321	24	3	3	NUM
ejpam-4923	321	25	.....	.....	PUNCT
ejpam-4923	321	26	}	}	PUNCT
ejpam-4923	321	27	is	be	AUX
ejpam-4923	321	28	the	the	DET
ejpam-4923	321	29	highest	high	ADJ
ejpam-4923	321	30	weight	weight	NOUN
ejpam-4923	321	31	module	module	NOUN
ejpam-4923	321	32	and	and	CCONJ
ejpam-4923	321	33	is	be	AUX
ejpam-4923	321	34	given	give	VERB
ejpam-4923	321	35	as	as	SCONJ
ejpam-4923	321	36	follows	follow	VERB
ejpam-4923	321	37	:	:	PUNCT
ejpam-4923	321	38	ewn	ewn	PROPN
ejpam-4923	321	39	,	,	PUNCT
ejpam-4923	321	40	m	m	NOUN
ejpam-4923	321	41	=	=	NOUN
ejpam-4923	321	42	−(n−	−(n−	NOUN
ejpam-4923	321	43	2m)iwn	2m)iwn	NUM
ejpam-4923	321	44	,	,	PUNCT
ejpam-4923	321	45	m	m	PROPN
ejpam-4923	321	46	,	,	PUNCT
ejpam-4923	321	47	l−wn	l−wn	PROPN
ejpam-4923	321	48	,	,	PUNCT
ejpam-4923	321	49	m	m	VERB
ejpam-4923	321	50	=	=	PUNCT
ejpam-4923	321	51	a1wn	a1wn	X
ejpam-4923	321	52	,	,	PUNCT
ejpam-4923	321	53	m	m	VERB
ejpam-4923	321	54	+	+	NOUN
ejpam-4923	321	55	ib1wn	ib1wn	NUM
ejpam-4923	321	56	,	,	PUNCT
ejpam-4923	321	57	m	m	VERB
ejpam-4923	321	58	=	=	PUNCT
ejpam-4923	321	59	i(n+m)wn	i(n+m)wn	ADP
ejpam-4923	321	60	,	,	PUNCT
ejpam-4923	321	61	m−1	m−1	PROPN
ejpam-4923	321	62	,	,	PUNCT
ejpam-4923	321	63	m	m	PROPN
ejpam-4923	321	64	∈	∈	PROPN
ejpam-4923	321	65	z+	z+	NUM
ejpam-4923	321	66	−	−	PROPN
ejpam-4923	321	67	{	{	PUNCT
ejpam-4923	321	68	0	0	NUM
ejpam-4923	321	69	}	}	PUNCT
ejpam-4923	321	70	,	,	PUNCT
ejpam-4923	321	71	l+wn	l+wn	NOUN
ejpam-4923	321	72	,	,	PUNCT
ejpam-4923	321	73	m	m	VERB
ejpam-4923	321	74	=	=	PUNCT
ejpam-4923	321	75	a1wn	a1wn	X
ejpam-4923	321	76	,	,	PUNCT
ejpam-4923	321	77	m	m	VERB
ejpam-4923	321	78	−	−	NOUN
ejpam-4923	321	79	ib1wn	ib1wn	NOUN
ejpam-4923	321	80	,	,	PUNCT
ejpam-4923	321	81	m	m	NOUN
ejpam-4923	321	82	=	=	ADJ
ejpam-4923	321	83	imwn	imwn	NOUN
ejpam-4923	321	84	,	,	PUNCT
ejpam-4923	321	85	m+1	m+1	PROPN
ejpam-4923	321	86	,	,	PUNCT
ejpam-4923	321	87	m	m	NOUN
ejpam-4923	321	88	∈	∈	NOUN
ejpam-4923	321	89	z+	z+	NUM
ejpam-4923	321	90	−	−	PROPN
ejpam-4923	321	91	{	{	PUNCT
ejpam-4923	321	92	0	0	NUM
ejpam-4923	321	93	}	}	PUNCT
ejpam-4923	321	94	a.	a.	NOUN
ejpam-4923	321	95	s.	s.	PROPN
ejpam-4923	321	96	alghamdi	alghamdi	PROPN
ejpam-4923	321	97	/	/	SYM
ejpam-4923	321	98	eur	eur	PROPN
ejpam-4923	321	99	.	.	PUNCT
ejpam-4923	322	1	j.	j.	PROPN
ejpam-4923	322	2	pure	pure	PROPN
ejpam-4923	322	3	appl	appl	PROPN
ejpam-4923	322	4	.	.	PROPN
ejpam-4923	322	5	math	math	PROPN
ejpam-4923	322	6	,	,	PUNCT
ejpam-4923	322	7	16	16	NUM
ejpam-4923	322	8	(	(	PUNCT
ejpam-4923	322	9	4	4	NUM
ejpam-4923	322	10	)	)	PUNCT
ejpam-4923	322	11	(	(	PUNCT
ejpam-4923	322	12	2023	2023	NUM
ejpam-4923	322	13	)	)	PUNCT
ejpam-4923	322	14	,	,	PUNCT
ejpam-4923	322	15	2348	2348	NUM
ejpam-4923	322	16	-	-	SYM
ejpam-4923	322	17	2367	2367	NUM
ejpam-4923	322	18	2365	2365	NUM
ejpam-4923	322	19	·	·	PUNCT
ejpam-4923	322	20	·	·	PUNCT
ejpam-4923	322	21	·	·	PUNCT
ejpam-4923	323	1	wn,2	wn,2	VERB
ejpam-4923	323	2	wn,1	wn,1	PROPN
ejpam-4923	323	3	wn,0	wn,0	PROPN
ejpam-4923	323	4	0	0	NUM
ejpam-4923	323	5	l+	l+	X
ejpam-4923	323	6	l+	l+	PUNCT
ejpam-4923	323	7	l−	l−	NOUN
ejpam-4923	323	8	l+	l+	PUNCT
ejpam-4923	323	9	l−	l−	NOUN
ejpam-4923	323	10	l+	l+	PUNCT
ejpam-4923	323	11	l−	l−	NOUN
ejpam-4923	323	12	l+wn,0	l+wn,0	NOUN
ejpam-4923	323	13	=	=	SYM
ejpam-4923	323	14	0	0	NUM
ejpam-4923	323	15	,	,	PUNCT
ejpam-4923	323	16	dπ̆n(c)w	dπ̆n(c)w	NOUN
ejpam-4923	323	17	=	=	SYM
ejpam-4923	323	18	(	(	PUNCT
ejpam-4923	323	19	−n2	−n2	PROPN
ejpam-4923	323	20	+	+	NUM
ejpam-4923	323	21	2n)w	2n)w	NUM
ejpam-4923	323	22	,	,	PUNCT
ejpam-4923	323	23	w	w	PROPN
ejpam-4923	323	24	∈	∈	PROPN
ejpam-4923	323	25	vn−2	vn−2	PROPN
ejpam-4923	323	26	m.	m.	NOUN
ejpam-4923	323	27	the	the	DET
ejpam-4923	323	28	vector	vector	NOUN
ejpam-4923	323	29	wn,0	wn,0	PROPN
ejpam-4923	323	30	is	be	AUX
ejpam-4923	323	31	called	call	VERB
ejpam-4923	323	32	the	the	DET
ejpam-4923	323	33	highest	high	ADJ
ejpam-4923	323	34	weight	weight	NOUN
ejpam-4923	323	35	vector	vector	NOUN
ejpam-4923	323	36	.	.	PUNCT
ejpam-4923	324	1	the	the	DET
ejpam-4923	324	2	vector	vector	NOUN
ejpam-4923	324	3	module	module	NOUN
ejpam-4923	324	4	vn+2	vn+2	NOUN
ejpam-4923	324	5	m	m	VERB
ejpam-4923	324	6	is	be	AUX
ejpam-4923	324	7	unitarisable	unitarisable	ADJ
ejpam-4923	324	8	if	if	SCONJ
ejpam-4923	324	9	and	and	CCONJ
ejpam-4923	324	10	only	only	ADV
ejpam-4923	324	11	if	if	SCONJ
ejpam-4923	324	12	n	n	PROPN
ejpam-4923	324	13	>	>	X
ejpam-4923	324	14	0	0	NUM
ejpam-4923	324	15	,	,	PUNCT
ejpam-4923	324	16	and	and	CCONJ
ejpam-4923	324	17	v̄n+2	v̄n+2	NUM
ejpam-4923	324	18	m	m	NOUN
ejpam-4923	324	19	is	be	AUX
ejpam-4923	324	20	unitarisable	unitarisable	ADJ
ejpam-4923	324	21	if	if	SCONJ
ejpam-4923	324	22	and	and	CCONJ
ejpam-4923	324	23	only	only	ADV
ejpam-4923	324	24	if	if	SCONJ
ejpam-4923	324	25	n	n	PRON
ejpam-4923	324	26	<	<	X
ejpam-4923	324	27	0	0	PUNCT
ejpam-4923	325	1	[	[	X
ejpam-4923	325	2	7	7	NUM
ejpam-4923	325	3	,	,	PUNCT
ejpam-4923	325	4	p.96	p.96	ADP
ejpam-4923	325	5	]	]	PUNCT
ejpam-4923	325	6	.	.	PUNCT
ejpam-4923	326	1	next	next	ADV
ejpam-4923	326	2	,	,	PUNCT
ejpam-4923	326	3	for	for	ADP
ejpam-4923	326	4	the	the	DET
ejpam-4923	326	5	dirichlet	dirichlet	PROPN
ejpam-4923	326	6	space	space	NOUN
ejpam-4923	326	7	the	the	DET
ejpam-4923	326	8	su(1	su(1	NOUN
ejpam-4923	326	9	,	,	PUNCT
ejpam-4923	326	10	1	1	X
ejpam-4923	326	11	)	)	PUNCT
ejpam-4923	326	12	vector	vector	NOUN
ejpam-4923	326	13	module	module	NOUN
ejpam-4923	326	14	is	be	AUX
ejpam-4923	326	15	v0	v0	NOUN
ejpam-4923	326	16	+	+	PROPN
ejpam-4923	326	17	2	2	NUM
ejpam-4923	326	18	m	m	NOUN
ejpam-4923	326	19	,	,	PUNCT
ejpam-4923	326	20	which	which	PRON
ejpam-4923	326	21	is	be	AUX
ejpam-4923	326	22	given	give	VERB
ejpam-4923	326	23	as	as	SCONJ
ejpam-4923	326	24	follows	follow	VERB
ejpam-4923	326	25	:	:	PUNCT
ejpam-4923	326	26	ew0,m	ew0,m	PROPN
ejpam-4923	326	27	=	=	SYM
ejpam-4923	326	28	−2imw0,m	−2imw0,m	PROPN
ejpam-4923	326	29	,	,	PUNCT
ejpam-4923	326	30	l+w0,m	l+w0,m	NOUN
ejpam-4923	326	31	=	=	SYM
ejpam-4923	326	32	imw0,m+1	imw0,m+1	PROPN
ejpam-4923	326	33	,	,	PUNCT
ejpam-4923	326	34	m	m	VERB
ejpam-4923	326	35	∈	∈	NOUN
ejpam-4923	326	36	z+	z+	NUM
ejpam-4923	326	37	−	−	PROPN
ejpam-4923	326	38	{	{	PUNCT
ejpam-4923	326	39	0	0	NUM
ejpam-4923	326	40	}	}	PUNCT
ejpam-4923	326	41	,	,	PUNCT
ejpam-4923	326	42	l−w0,m	l−w0,m	X
ejpam-4923	326	43	=	=	SYM
ejpam-4923	326	44	imw0,m−1	imw0,m−1	PROPN
ejpam-4923	326	45	,	,	PUNCT
ejpam-4923	326	46	m	m	PROPN
ejpam-4923	326	47	∈	∈	PROPN
ejpam-4923	326	48	z+	z+	NUM
ejpam-4923	326	49	−	−	PROPN
ejpam-4923	326	50	{	{	PUNCT
ejpam-4923	326	51	0	0	NUM
ejpam-4923	326	52	}	}	PUNCT
ejpam-4923	326	53	,	,	PUNCT
ejpam-4923	326	54	l+w0,0	l+w0,0	NOUN
ejpam-4923	326	55	=	=	SYM
ejpam-4923	326	56	0	0	NUM
ejpam-4923	326	57	,	,	PUNCT
ejpam-4923	326	58	dπ̆0(c	dπ̆0(c	ADJ
ejpam-4923	326	59	)	)	PUNCT
ejpam-4923	326	60	=	=	SYM
ejpam-4923	327	1	0	0	X
ejpam-4923	327	2	.	.	PUNCT
ejpam-4923	328	1	this	this	PRON
ejpam-4923	328	2	is	be	AUX
ejpam-4923	328	3	shown	show	VERB
ejpam-4923	328	4	in	in	ADP
ejpam-4923	328	5	the	the	DET
ejpam-4923	328	6	following	follow	VERB
ejpam-4923	328	7	figure	figure	NOUN
ejpam-4923	328	8	:	:	PUNCT
ejpam-4923	328	9	0	0	PUNCT
ejpam-4923	329	1	[	[	X
ejpam-4923	329	2	w0,0	w0,0	X
ejpam-4923	329	3	]	]	X
ejpam-4923	329	4	w0,1	w0,1	NOUN
ejpam-4923	329	5	w0,2	w0,2	PROPN
ejpam-4923	329	6	·	·	PUNCT
ejpam-4923	329	7	·	·	PUNCT
ejpam-4923	329	8	·	·	PUNCT
ejpam-4923	329	9	l−	l−	NOUN
ejpam-4923	329	10	l−	l−	NOUN
ejpam-4923	329	11	l+	l+	PUNCT
ejpam-4923	329	12	l−	l−	NOUN
ejpam-4923	329	13	l+	l+	PUNCT
ejpam-4923	329	14	l−	l−	NOUN
ejpam-4923	329	15	in	in	ADP
ejpam-4923	329	16	addition	addition	NOUN
ejpam-4923	329	17	,	,	PUNCT
ejpam-4923	329	18	w0,0	w0,0	NOUN
ejpam-4923	329	19	is	be	AUX
ejpam-4923	329	20	the	the	DET
ejpam-4923	329	21	highest	high	ADJ
ejpam-4923	329	22	weight	weight	NOUN
ejpam-4923	329	23	vector	vector	NOUN
ejpam-4923	329	24	for	for	ADP
ejpam-4923	329	25	the	the	DET
ejpam-4923	329	26	vector	vector	NOUN
ejpam-4923	329	27	module	module	NOUN
ejpam-4923	329	28	v̄0	v̄0	NOUN
ejpam-4923	329	29	+	+	PROPN
ejpam-4923	329	30	2	2	NUM
ejpam-4923	329	31	m	m	NOUN
ejpam-4923	329	32	which	which	PRON
ejpam-4923	329	33	is	be	AUX
ejpam-4923	329	34	given	give	VERB
ejpam-4923	329	35	by	by	ADP
ejpam-4923	329	36	ew0,m	ew0,m	PROPN
ejpam-4923	329	37	=	=	SYM
ejpam-4923	329	38	−2imw0,m	−2imw0,m	PROPN
ejpam-4923	329	39	,	,	PUNCT
ejpam-4923	329	40	l+w0,m	l+w0,m	NOUN
ejpam-4923	329	41	=	=	SYM
ejpam-4923	329	42	imw0,m+1	imw0,m+1	PROPN
ejpam-4923	329	43	,	,	PUNCT
ejpam-4923	329	44	m	m	VERB
ejpam-4923	329	45	∈	∈	NOUN
ejpam-4923	329	46	z+	z+	NUM
ejpam-4923	329	47	−	−	PROPN
ejpam-4923	329	48	{	{	PUNCT
ejpam-4923	329	49	0	0	NUM
ejpam-4923	329	50	}	}	PUNCT
ejpam-4923	329	51	,	,	PUNCT
ejpam-4923	329	52	l−w0,m	l−w0,m	X
ejpam-4923	329	53	=	=	SYM
ejpam-4923	329	54	imw0,m−1	imw0,m−1	PROPN
ejpam-4923	329	55	,	,	PUNCT
ejpam-4923	329	56	m	m	PROPN
ejpam-4923	329	57	∈	∈	PROPN
ejpam-4923	329	58	z+	z+	NUM
ejpam-4923	329	59	−	−	PROPN
ejpam-4923	329	60	{	{	PUNCT
ejpam-4923	329	61	0	0	NUM
ejpam-4923	329	62	}	}	PUNCT
ejpam-4923	329	63	,	,	PUNCT
ejpam-4923	329	64	l−w0,0	l−w0,0	NOUN
ejpam-4923	329	65	=	=	SYM
ejpam-4923	329	66	0	0	NUM
ejpam-4923	329	67	,	,	PUNCT
ejpam-4923	329	68	dπ̆0(c	dπ̆0(c	ADJ
ejpam-4923	329	69	)	)	PUNCT
ejpam-4923	329	70	=	=	SYM
ejpam-4923	329	71	0	0	X
ejpam-4923	329	72	.	.	PUNCT
ejpam-4923	329	73	and	and	CCONJ
ejpam-4923	329	74	presented	present	VERB
ejpam-4923	329	75	in	in	ADP
ejpam-4923	329	76	the	the	DET
ejpam-4923	329	77	following	follow	VERB
ejpam-4923	329	78	figure	figure	NOUN
ejpam-4923	329	79	:	:	PUNCT
ejpam-4923	329	80	·	·	PUNCT
ejpam-4923	329	81	·	·	PUNCT
ejpam-4923	329	82	·	·	PUNCT
ejpam-4923	330	1	w0,2	w0,2	VERB
ejpam-4923	330	2	w0,1	w0,1	PROPN
ejpam-4923	331	1	[	[	X
ejpam-4923	331	2	w0,0	w0,0	X
ejpam-4923	331	3	]	]	SYM
ejpam-4923	331	4	0	0	NUM
ejpam-4923	331	5	l+	l+	X
ejpam-4923	331	6	l+	l+	PUNCT
ejpam-4923	331	7	l−	l−	NOUN
ejpam-4923	331	8	l+	l+	PUNCT
ejpam-4923	331	9	l−	l−	PROPN
ejpam-4923	331	10	l+	l+	AUX
ejpam-4923	331	11	references	reference	NOUN
ejpam-4923	331	12	2366	2366	NUM
ejpam-4923	331	13	6	6	NUM
ejpam-4923	331	14	.	.	PUNCT
ejpam-4923	332	1	conclusion	conclusion	NOUN
ejpam-4923	332	2	this	this	DET
ejpam-4923	332	3	paper	paper	NOUN
ejpam-4923	332	4	considers	consider	VERB
ejpam-4923	332	5	the	the	DET
ejpam-4923	332	6	discrete	discrete	ADJ
ejpam-4923	332	7	series	series	NOUN
ejpam-4923	332	8	representation	representation	NOUN
ejpam-4923	332	9	of	of	ADP
ejpam-4923	332	10	the	the	DET
ejpam-4923	332	11	sl2(r	sl2(r	PROPN
ejpam-4923	332	12	)	)	PUNCT
ejpam-4923	332	13	group	group	NOUN
ejpam-4923	332	14	πn	πn	PUNCT
ejpam-4923	332	15	defined	define	VERB
ejpam-4923	332	16	by	by	ADP
ejpam-4923	332	17	(	(	PUNCT
ejpam-4923	332	18	1	1	NUM
ejpam-4923	332	19	)	)	PUNCT
ejpam-4923	332	20	on	on	ADP
ejpam-4923	332	21	spaces	space	NOUN
ejpam-4923	332	22	of	of	ADP
ejpam-4923	332	23	holomorphic	holomorphic	ADJ
ejpam-4923	332	24	functions	function	NOUN
ejpam-4923	332	25	on	on	ADP
ejpam-4923	332	26	the	the	DET
ejpam-4923	332	27	unit	unit	NOUN
ejpam-4923	332	28	disc	disc	NOUN
ejpam-4923	332	29	.	.	PUNCT
ejpam-4923	333	1	the	the	DET
ejpam-4923	333	2	group	group	NOUN
ejpam-4923	333	3	sl2(r	sl2(r	PROPN
ejpam-4923	333	4	)	)	PUNCT
ejpam-4923	333	5	is	be	AUX
ejpam-4923	333	6	more	more	ADV
ejpam-4923	333	7	convenient	convenient	ADJ
ejpam-4923	333	8	for	for	ADP
ejpam-4923	333	9	complex	complex	ADJ
ejpam-4923	333	10	analysis	analysis	NOUN
ejpam-4923	333	11	in	in	ADP
ejpam-4923	333	12	the	the	DET
ejpam-4923	333	13	upper	upper	ADJ
ejpam-4923	333	14	half	half	ADJ
ejpam-4923	333	15	-	-	PUNCT
ejpam-4923	333	16	plane	plane	NOUN
ejpam-4923	333	17	.	.	PUNCT
ejpam-4923	334	1	however	however	ADV
ejpam-4923	334	2	,	,	PUNCT
ejpam-4923	334	3	the	the	DET
ejpam-4923	334	4	group	group	NOUN
ejpam-4923	334	5	su(1	su(1	NOUN
ejpam-4923	334	6	,	,	PUNCT
ejpam-4923	334	7	1	1	NUM
ejpam-4923	334	8	)	)	PUNCT
ejpam-4923	334	9	of	of	ADP
ejpam-4923	334	10	2	2	NUM
ejpam-4923	334	11	×	×	NOUN
ejpam-4923	334	12	2	2	NUM
ejpam-4923	334	13	matrices	matrix	NOUN
ejpam-4923	334	14	,	,	PUNCT
ejpam-4923	334	15	with	with	ADP
ejpam-4923	334	16	complex	complex	ADJ
ejpam-4923	334	17	entries	entry	NOUN
ejpam-4923	334	18	and	and	CCONJ
ejpam-4923	334	19	a	a	DET
ejpam-4923	334	20	determinant	determinant	ADJ
ejpam-4923	334	21	equal	equal	ADJ
ejpam-4923	334	22	to	to	ADP
ejpam-4923	334	23	one	one	NUM
ejpam-4923	334	24	,	,	PUNCT
ejpam-4923	334	25	is	be	AUX
ejpam-4923	334	26	well	well	ADV
ejpam-4923	334	27	suited	suited	ADJ
ejpam-4923	334	28	in	in	ADP
ejpam-4923	334	29	unit	unit	NOUN
ejpam-4923	334	30	disc	disc	VERB
ejpam-4923	334	31	d.	d.	PROPN
ejpam-4923	334	32	the	the	DET
ejpam-4923	334	33	cayley	cayley	ADJ
ejpam-4923	334	34	transform	transform	NOUN
ejpam-4923	334	35	(	(	PUNCT
ejpam-4923	334	36	4	4	NUM
ejpam-4923	334	37	)	)	PUNCT
ejpam-4923	334	38	defines	define	VERB
ejpam-4923	334	39	an	an	DET
ejpam-4923	334	40	isomorphism	isomorphism	NOUN
ejpam-4923	334	41	of	of	ADP
ejpam-4923	334	42	the	the	DET
ejpam-4923	334	43	group	group	NOUN
ejpam-4923	334	44	sl2(r	sl2(r	PROPN
ejpam-4923	334	45	)	)	PUNCT
ejpam-4923	334	46	with	with	ADP
ejpam-4923	334	47	the	the	DET
ejpam-4923	334	48	group	group	NOUN
ejpam-4923	334	49	su(1	su(1	NOUN
ejpam-4923	334	50	,	,	PUNCT
ejpam-4923	334	51	1	1	NUM
ejpam-4923	334	52	)	)	PUNCT
ejpam-4923	334	53	.	.	PUNCT
ejpam-4923	335	1	we	we	PRON
ejpam-4923	335	2	present	present	VERB
ejpam-4923	335	3	the	the	DET
ejpam-4923	335	4	action	action	NOUN
ejpam-4923	335	5	of	of	ADP
ejpam-4923	335	6	the	the	DET
ejpam-4923	335	7	ladder	ladder	NOUN
ejpam-4923	335	8	operator	operator	NOUN
ejpam-4923	335	9	of	of	ADP
ejpam-4923	335	10	representation	representation	NOUN
ejpam-4923	335	11	on	on	ADP
ejpam-4923	335	12	the	the	DET
ejpam-4923	335	13	su(1	su(1	NOUN
ejpam-4923	335	14	,	,	PUNCT
ejpam-4923	335	15	1	1	NUM
ejpam-4923	335	16	)	)	PUNCT
ejpam-4923	335	17	lie	lie	NOUN
ejpam-4923	335	18	algebra	algebra	NOUN
ejpam-4923	335	19	.	.	PUNCT
ejpam-4923	336	1	this	this	DET
ejpam-4923	336	2	action	action	NOUN
ejpam-4923	336	3	can	can	AUX
ejpam-4923	336	4	be	be	AUX
ejpam-4923	336	5	realised	realise	VERB
ejpam-4923	336	6	on	on	ADP
ejpam-4923	336	7	the	the	DET
ejpam-4923	336	8	bergman	bergman	PROPN
ejpam-4923	336	9	space	space	NOUN
ejpam-4923	336	10	for	for	ADP
ejpam-4923	336	11	n	n	X
ejpam-4923	336	12	≥	≥	NOUN
ejpam-4923	336	13	2	2	NUM
ejpam-4923	336	14	,	,	PUNCT
ejpam-4923	336	15	on	on	ADP
ejpam-4923	336	16	the	the	DET
ejpam-4923	336	17	hardy	hardy	ADJ
ejpam-4923	336	18	space	space	NOUN
ejpam-4923	336	19	for	for	ADP
ejpam-4923	336	20	n	n	NOUN
ejpam-4923	336	21	=	=	SYM
ejpam-4923	336	22	1	1	NUM
ejpam-4923	336	23	and	and	CCONJ
ejpam-4923	336	24	on	on	ADP
ejpam-4923	336	25	the	the	DET
ejpam-4923	336	26	dirichlet	dirichlet	PROPN
ejpam-4923	336	27	space	space	NOUN
ejpam-4923	336	28	for	for	ADP
ejpam-4923	336	29	n	n	NOUN
ejpam-4923	336	30	=	=	SYM
ejpam-4923	336	31	0	0	NUM
ejpam-4923	336	32	.	.	PUNCT
ejpam-4923	337	1	the	the	DET
ejpam-4923	337	2	vector	vector	NOUN
ejpam-4923	337	3	module	module	NOUN
ejpam-4923	337	4	of	of	ADP
ejpam-4923	337	5	the	the	DET
ejpam-4923	337	6	representation	representation	NOUN
ejpam-4923	337	7	on	on	ADP
ejpam-4923	337	8	the	the	DET
ejpam-4923	337	9	dirichlet	dirichlet	PROPN
ejpam-4923	337	10	space	space	NOUN
ejpam-4923	337	11	has	have	AUX
ejpam-4923	337	12	been	be	AUX
ejpam-4923	337	13	described	describe	VERB
ejpam-4923	337	14	.	.	PUNCT
ejpam-4923	338	1	it	it	PRON
ejpam-4923	338	2	is	be	AUX
ejpam-4923	338	3	worth	worth	ADJ
ejpam-4923	338	4	to	to	ADP
ejpam-4923	338	5	studying	study	VERB
ejpam-4923	338	6	the	the	DET
ejpam-4923	338	7	su(1	su(1	NOUN
ejpam-4923	338	8	,	,	PUNCT
ejpam-4923	338	9	1	1	X
ejpam-4923	338	10	)	)	PUNCT
ejpam-4923	338	11	vector	vector	NOUN
ejpam-4923	338	12	module	module	NOUN
ejpam-4923	338	13	on	on	ADP
ejpam-4923	338	14	other	other	ADJ
ejpam-4923	338	15	spaces	space	NOUN
ejpam-4923	338	16	of	of	ADP
ejpam-4923	338	17	holomorphic	holomorphic	ADJ
ejpam-4923	338	18	function	function	NOUN
ejpam-4923	338	19	,	,	PUNCT
ejpam-4923	338	20	for	for	ADP
ejpam-4923	338	21	instance	instance	NOUN
ejpam-4923	338	22	the	the	DET
ejpam-4923	338	23	polybergman	polybergman	NOUN
ejpam-4923	338	24	space	space	NOUN
ejpam-4923	339	1	[	[	X
ejpam-4923	339	2	16	16	NUM
ejpam-4923	339	3	]	]	PUNCT
ejpam-4923	339	4	.	.	PUNCT
ejpam-4923	340	1	acknowledgements	acknowledgement	NOUN
ejpam-4923	340	2	i	i	PRON
ejpam-4923	340	3	would	would	AUX
ejpam-4923	340	4	like	like	VERB
ejpam-4923	340	5	to	to	PART
ejpam-4923	340	6	thank	thank	VERB
ejpam-4923	340	7	dr	dr	PROPN
ejpam-4923	340	8	.	.	PROPN
ejpam-4923	340	9	vladimir	vladimir	PROPN
ejpam-4923	340	10	kisil	kisil	PROPN
ejpam-4923	340	11	for	for	ADP
ejpam-4923	340	12	all	all	DET
ejpam-4923	340	13	his	his	PRON
ejpam-4923	340	14	guidance	guidance	NOUN
ejpam-4923	340	15	,	,	PUNCT
ejpam-4923	340	16	valuable	valuable	ADJ
ejpam-4923	340	17	advises	advise	NOUN
ejpam-4923	340	18	and	and	CCONJ
ejpam-4923	340	19	comments	comment	NOUN
ejpam-4923	340	20	.	.	PUNCT
ejpam-4923	341	1	also	also	ADV
ejpam-4923	341	2	,	,	PUNCT
ejpam-4923	341	3	my	my	PRON
ejpam-4923	341	4	deep	deep	ADJ
ejpam-4923	341	5	gratitude	gratitude	NOUN
ejpam-4923	341	6	to	to	ADP
ejpam-4923	341	7	my	my	PRON
ejpam-4923	341	8	family	family	NOUN
ejpam-4923	341	9	for	for	ADP
ejpam-4923	341	10	their	their	PRON
ejpam-4923	341	11	continuous	continuous	ADJ
ejpam-4923	341	12	love	love	NOUN
ejpam-4923	341	13	,	,	PUNCT
ejpam-4923	341	14	help	help	NOUN
ejpam-4923	341	15	and	and	CCONJ
ejpam-4923	341	16	support	support	VERB
ejpam-4923	341	17	.	.	PUNCT
ejpam-4923	342	1	i	i	PRON
ejpam-4923	342	2	would	would	AUX
ejpam-4923	342	3	like	like	VERB
ejpam-4923	342	4	to	to	PART
ejpam-4923	342	5	thank	thank	VERB
ejpam-4923	342	6	my	my	PRON
ejpam-4923	342	7	husband	husband	NOUN
ejpam-4923	342	8	for	for	ADP
ejpam-4923	342	9	his	his	PRON
ejpam-4923	342	10	patience	patience	NOUN
ejpam-4923	342	11	and	and	CCONJ
ejpam-4923	342	12	kindness	kindness	NOUN
ejpam-4923	342	13	.	.	PUNCT
ejpam-4923	343	1	thanks	thank	NOUN
ejpam-4923	343	2	for	for	ADP
ejpam-4923	343	3	my	my	PRON
ejpam-4923	343	4	kids	kid	NOUN
ejpam-4923	343	5	who	who	PRON
ejpam-4923	343	6	have	have	AUX
ejpam-4923	343	7	made	make	VERB
ejpam-4923	343	8	me	i	PRON
ejpam-4923	343	9	stronger	strong	ADJ
ejpam-4923	343	10	and	and	CCONJ
ejpam-4923	343	11	filled	fill	VERB
ejpam-4923	343	12	me	i	PRON
ejpam-4923	343	13	with	with	ADP
ejpam-4923	343	14	happiness	happiness	NOUN
ejpam-4923	343	15	.	.	PUNCT
ejpam-4923	344	1	references	reference	NOUN
ejpam-4923	344	2	[	[	X
ejpam-4923	344	3	1	1	NUM
ejpam-4923	344	4	]	]	PUNCT
ejpam-4923	344	5	dehbia	dehbia	NOUN
ejpam-4923	344	6	achab	achab	PROPN
ejpam-4923	344	7	.	.	PUNCT
ejpam-4923	345	1	analysis	analysis	NOUN
ejpam-4923	345	2	of	of	ADP
ejpam-4923	345	3	minimal	minimal	ADJ
ejpam-4923	345	4	representations	representation	NOUN
ejpam-4923	345	5	of	of	ADP
ejpam-4923	345	6	sl2(r	sl2(r	NOUN
ejpam-4923	345	7	)	)	PUNCT
ejpam-4923	345	8	.	.	PUNCT
ejpam-4923	346	1	journal	journal	PROPN
ejpam-4923	346	2	of	of	ADP
ejpam-4923	346	3	geometry	geometry	NOUN
ejpam-4923	346	4	and	and	CCONJ
ejpam-4923	346	5	physics	physics	NOUN
ejpam-4923	346	6	,	,	PUNCT
ejpam-4923	346	7	146:103520	146:103520	NUM
ejpam-4923	346	8	,	,	PUNCT
ejpam-4923	346	9	2019	2019	NUM
ejpam-4923	346	10	.	.	PUNCT
ejpam-4923	347	1	[	[	X
ejpam-4923	347	2	2	2	X
ejpam-4923	347	3	]	]	PUNCT
ejpam-4923	347	4	j.	j.	PROPN
ejpam-4923	347	5	arazy	arazy	PROPN
ejpam-4923	347	6	and	and	CCONJ
ejpam-4923	347	7	s.	s.	PROPN
ejpam-4923	347	8	d.	d.	PROPN
ejpam-4923	347	9	fisher	fisher	PROPN
ejpam-4923	347	10	.	.	PUNCT
ejpam-4923	348	1	the	the	DET
ejpam-4923	348	2	uniqueness	uniqueness	NOUN
ejpam-4923	348	3	of	of	ADP
ejpam-4923	348	4	the	the	DET
ejpam-4923	348	5	dirichlet	dirichlet	PROPN
ejpam-4923	348	6	space	space	NOUN
ejpam-4923	348	7	among	among	ADP
ejpam-4923	348	8	mobiusinvariant	mobiusinvariant	ADJ
ejpam-4923	348	9	hilbert	hilbert	PROPN
ejpam-4923	348	10	spaces	space	NOUN
ejpam-4923	348	11	.	.	PUNCT
ejpam-4923	349	1	illinois	illinois	PROPN
ejpam-4923	349	2	journal	journal	PROPN
ejpam-4923	349	3	of	of	ADP
ejpam-4923	349	4	mathematics	mathematics	PROPN
ejpam-4923	349	5	,	,	PUNCT
ejpam-4923	349	6	29(3):449	29(3):449	PROPN
ejpam-4923	349	7	–	–	PUNCT
ejpam-4923	349	8	462	462	NUM
ejpam-4923	349	9	,	,	PUNCT
ejpam-4923	349	10	1985	1985	NUM
ejpam-4923	349	11	.	.	PUNCT
ejpam-4923	350	1	[	[	X
ejpam-4923	350	2	3	3	NUM
ejpam-4923	350	3	]	]	X
ejpam-4923	350	4	francesca	francesca	PROPN
ejpam-4923	350	5	astengo	astengo	PROPN
ejpam-4923	350	6	,	,	PUNCT
ejpam-4923	350	7	michael	michael	PROPN
ejpam-4923	350	8	g.	g.	PROPN
ejpam-4923	350	9	cowling	cowling	PROPN
ejpam-4923	350	10	,	,	PUNCT
ejpam-4923	350	11	and	and	CCONJ
ejpam-4923	350	12	bianca	bianca	PROPN
ejpam-4923	350	13	di	di	PROPN
ejpam-4923	350	14	blasio	blasio	PROPN
ejpam-4923	350	15	.	.	PUNCT
ejpam-4923	351	1	uniformly	uniformly	ADV
ejpam-4923	351	2	bounded	bound	VERB
ejpam-4923	351	3	representations	representation	NOUN
ejpam-4923	351	4	of	of	ADP
ejpam-4923	351	5	sl(2	sl(2	PROPN
ejpam-4923	351	6	,	,	PUNCT
ejpam-4923	351	7	r	r	NOUN
ejpam-4923	351	8	)	)	PUNCT
ejpam-4923	351	9	.	.	PUNCT
ejpam-4923	352	1	journal	journal	NOUN
ejpam-4923	352	2	of	of	ADP
ejpam-4923	352	3	functional	functional	ADJ
ejpam-4923	352	4	analysis	analysis	NOUN
ejpam-4923	352	5	,	,	PUNCT
ejpam-4923	352	6	276(1):127–147	276(1):127–147	NUM
ejpam-4923	352	7	,	,	PUNCT
ejpam-4923	352	8	2019	2019	NUM
ejpam-4923	352	9	.	.	PUNCT
ejpam-4923	353	1	[	[	X
ejpam-4923	353	2	4	4	X
ejpam-4923	353	3	]	]	X
ejpam-4923	353	4	o.	o.	PROPN
ejpam-4923	353	5	el	el	PROPN
ejpam-4923	353	6	-	-	PROPN
ejpam-4923	353	7	fallah	fallah	PROPN
ejpam-4923	353	8	,	,	PUNCT
ejpam-4923	353	9	k.	k.	PROPN
ejpam-4923	353	10	kellay	kellay	PROPN
ejpam-4923	353	11	,	,	PUNCT
ejpam-4923	353	12	j.	j.	PROPN
ejpam-4923	353	13	mashreghi	mashreghi	PROPN
ejpam-4923	353	14	,	,	PUNCT
ejpam-4923	353	15	and	and	CCONJ
ejpam-4923	353	16	t.	t.	PROPN
ejpam-4923	353	17	ransford	ransford	NOUN
ejpam-4923	353	18	.	.	PUNCT
ejpam-4923	354	1	a	a	DET
ejpam-4923	354	2	primer	primer	NOUN
ejpam-4923	354	3	on	on	ADP
ejpam-4923	354	4	the	the	DET
ejpam-4923	354	5	dirichlet	dirichlet	PROPN
ejpam-4923	354	6	space	space	NOUN
ejpam-4923	354	7	.	.	PUNCT
ejpam-4923	355	1	cambridge	cambridge	PROPN
ejpam-4923	355	2	tracts	tract	NOUN
ejpam-4923	355	3	in	in	ADP
ejpam-4923	355	4	mathematics	mathematics	PROPN
ejpam-4923	355	5	.	.	PUNCT
ejpam-4923	356	1	cambridge	cambridge	PROPN
ejpam-4923	356	2	university	university	PROPN
ejpam-4923	356	3	press	press	NOUN
ejpam-4923	356	4	,	,	PUNCT
ejpam-4923	356	5	2014	2014	NUM
ejpam-4923	356	6	.	.	PUNCT
ejpam-4923	357	1	[	[	X
ejpam-4923	357	2	5	5	X
ejpam-4923	357	3	]	]	PUNCT
ejpam-4923	357	4	g.	g.	PROPN
ejpam-4923	357	5	b.	b.	PROPN
ejpam-4923	357	6	folland	folland	PROPN
ejpam-4923	357	7	.	.	PUNCT
ejpam-4923	358	1	a	a	DET
ejpam-4923	358	2	course	course	NOUN
ejpam-4923	358	3	in	in	ADP
ejpam-4923	358	4	abstract	abstract	ADJ
ejpam-4923	358	5	harmonic	harmonic	ADJ
ejpam-4923	358	6	analysis	analysis	NOUN
ejpam-4923	358	7	.	.	PUNCT
ejpam-4923	359	1	studies	study	NOUN
ejpam-4923	359	2	in	in	ADP
ejpam-4923	359	3	advanced	advanced	ADJ
ejpam-4923	359	4	mathematics	mathematic	NOUN
ejpam-4923	359	5	.	.	PUNCT
ejpam-4923	360	1	crc	crc	PROPN
ejpam-4923	360	2	press	press	PROPN
ejpam-4923	360	3	,	,	PUNCT
ejpam-4923	360	4	boca	boca	PROPN
ejpam-4923	360	5	raton	raton	PROPN
ejpam-4923	360	6	,	,	PUNCT
ejpam-4923	360	7	fl	fl	PROPN
ejpam-4923	360	8	,	,	PUNCT
ejpam-4923	360	9	1995	1995	NUM
ejpam-4923	360	10	.	.	PUNCT
ejpam-4923	361	1	[	[	X
ejpam-4923	361	2	6	6	NUM
ejpam-4923	361	3	]	]	PUNCT
ejpam-4923	361	4	l.	l.	PROPN
ejpam-4923	361	5	heping	heping	PROPN
ejpam-4923	361	6	and	and	CCONJ
ejpam-4923	361	7	p.	p.	PROPN
ejpam-4923	361	8	lizhong	lizhong	PROPN
ejpam-4923	361	9	.	.	PUNCT
ejpam-4923	362	1	weighted	weight	VERB
ejpam-4923	362	2	plancherel	plancherel	NOUN
ejpam-4923	362	3	formula	formula	NOUN
ejpam-4923	362	4	.	.	PUNCT
ejpam-4923	363	1	irreducible	irreducible	ADJ
ejpam-4923	363	2	unitary	unitary	ADJ
ejpam-4923	363	3	representations	representation	NOUN
ejpam-4923	363	4	and	and	CCONJ
ejpam-4923	363	5	eigenspace	eigenspace	NOUN
ejpam-4923	363	6	representations	representation	NOUN
ejpam-4923	363	7	.	.	PUNCT
ejpam-4923	364	1	mathematica	mathematica	PROPN
ejpam-4923	364	2	scandinavica	scandinavica	PROPN
ejpam-4923	364	3	,	,	PUNCT
ejpam-4923	364	4	72(1):99–119	72(1):99–119	PROPN
ejpam-4923	364	5	,	,	PUNCT
ejpam-4923	364	6	1993	1993	NUM
ejpam-4923	364	7	.	.	PUNCT
ejpam-4923	365	1	[	[	X
ejpam-4923	365	2	7	7	X
ejpam-4923	365	3	]	]	X
ejpam-4923	365	4	r.	r.	PROPN
ejpam-4923	365	5	howe	howe	PROPN
ejpam-4923	365	6	and	and	CCONJ
ejpam-4923	365	7	e.	e.	PROPN
ejpam-4923	365	8	tan	tan	PROPN
ejpam-4923	365	9	.	.	PUNCT
ejpam-4923	366	1	non	non	ADJ
ejpam-4923	366	2	-	-	ADJ
ejpam-4923	366	3	abelian	abelian	ADJ
ejpam-4923	366	4	harmonic	harmonic	ADJ
ejpam-4923	366	5	analysis	analysis	NOUN
ejpam-4923	366	6	:	:	PUNCT
ejpam-4923	366	7	applications	application	NOUN
ejpam-4923	366	8	of	of	ADP
ejpam-4923	366	9	sl(2,r	sl(2,r	NOUN
ejpam-4923	366	10	)	)	PUNCT
ejpam-4923	366	11	.	.	PUNCT
ejpam-4923	367	1	universitext	universitext	PROPN
ejpam-4923	367	2	.	.	PUNCT
ejpam-4923	367	3	springer	springer	NOUN
ejpam-4923	367	4	-	-	PUNCT
ejpam-4923	367	5	verlag	verlag	PROPN
ejpam-4923	367	6	,	,	PUNCT
ejpam-4923	367	7	new	new	PROPN
ejpam-4923	367	8	york	york	PROPN
ejpam-4923	367	9	,	,	PUNCT
ejpam-4923	367	10	1992	1992	NUM
ejpam-4923	367	11	.	.	PUNCT
ejpam-4923	368	1	references	reference	NOUN
ejpam-4923	368	2	2367	2367	NUM
ejpam-4923	368	3	[	[	X
ejpam-4923	368	4	8	8	NUM
ejpam-4923	368	5	]	]	PUNCT
ejpam-4923	368	6	eberhard	eberhard	NOUN
ejpam-4923	368	7	kaniuth	kaniuth	NOUN
ejpam-4923	368	8	and	and	CCONJ
ejpam-4923	368	9	keith	keith	PROPN
ejpam-4923	368	10	f	f	PROPN
ejpam-4923	368	11	taylor	taylor	PROPN
ejpam-4923	368	12	.	.	PUNCT
ejpam-4923	369	1	induced	induce	VERB
ejpam-4923	369	2	representations	representation	NOUN
ejpam-4923	369	3	of	of	ADP
ejpam-4923	369	4	locally	locally	ADV
ejpam-4923	369	5	compact	compact	ADJ
ejpam-4923	369	6	groups	group	NOUN
ejpam-4923	369	7	,	,	PUNCT
ejpam-4923	369	8	volume	volume	NOUN
ejpam-4923	369	9	197	197	NUM
ejpam-4923	369	10	.	.	PUNCT
ejpam-4923	370	1	cambridge	cambridge	PROPN
ejpam-4923	370	2	university	university	PROPN
ejpam-4923	370	3	press	press	NOUN
ejpam-4923	370	4	,	,	PUNCT
ejpam-4923	370	5	2013	2013	NUM
ejpam-4923	370	6	.	.	PUNCT
ejpam-4923	371	1	[	[	X
ejpam-4923	371	2	9	9	NUM
ejpam-4923	371	3	]	]	X
ejpam-4923	371	4	v.	v.	PROPN
ejpam-4923	371	5	v.	v.	ADP
ejpam-4923	371	6	kisil	kisil	PROPN
ejpam-4923	371	7	.	.	PUNCT
ejpam-4923	372	1	geometry	geometry	NOUN
ejpam-4923	372	2	of	of	ADP
ejpam-4923	372	3	möbius	möbius	PROPN
ejpam-4923	372	4	transformations	transformation	NOUN
ejpam-4923	372	5	.	.	PUNCT
ejpam-4923	373	1	imperial	imperial	ADJ
ejpam-4923	373	2	college	college	PROPN
ejpam-4923	373	3	press	press	PROPN
ejpam-4923	373	4	,	,	PUNCT
ejpam-4923	373	5	london	london	PROPN
ejpam-4923	373	6	,	,	PUNCT
ejpam-4923	373	7	2012	2012	NUM
ejpam-4923	373	8	.	.	PUNCT
ejpam-4923	374	1	elliptic	elliptic	ADJ
ejpam-4923	374	2	,	,	PUNCT
ejpam-4923	374	3	parabolic	parabolic	ADJ
ejpam-4923	374	4	and	and	CCONJ
ejpam-4923	374	5	hyperbolic	hyperbolic	ADJ
ejpam-4923	374	6	actions	action	NOUN
ejpam-4923	374	7	of	of	ADP
ejpam-4923	374	8	sl2(r	sl2(r	PROPN
ejpam-4923	374	9	)	)	PUNCT
ejpam-4923	374	10	,	,	PUNCT
ejpam-4923	374	11	with	with	ADP
ejpam-4923	374	12	1	1	NUM
ejpam-4923	374	13	dvd	dvd	PROPN
ejpam-4923	374	14	-	-	PUNCT
ejpam-4923	374	15	rom	rom	NOUN
ejpam-4923	374	16	.	.	PUNCT
ejpam-4923	375	1	[	[	X
ejpam-4923	375	2	10	10	NUM
ejpam-4923	375	3	]	]	X
ejpam-4923	375	4	vladimir	vladimir	PROPN
ejpam-4923	375	5	v.	v.	ADP
ejpam-4923	375	6	kisil	kisil	PROPN
ejpam-4923	375	7	.	.	PUNCT
ejpam-4923	376	1	analysis	analysis	NOUN
ejpam-4923	376	2	inr1,1	inr1,1	ADV
ejpam-4923	376	3	or	or	CCONJ
ejpam-4923	376	4	the	the	DET
ejpam-4923	376	5	principal	principal	ADJ
ejpam-4923	376	6	function	function	NOUN
ejpam-4923	376	7	theory	theory	NOUN
ejpam-4923	376	8	.	.	PUNCT
ejpam-4923	377	1	complex	complex	ADJ
ejpam-4923	377	2	variables	variable	NOUN
ejpam-4923	377	3	theory	theory	NOUN
ejpam-4923	377	4	appl	appl	PROPN
ejpam-4923	377	5	.	.	PROPN
ejpam-4923	377	6	,	,	PUNCT
ejpam-4923	378	1	40(2):93–118	40(2):93–118	PROPN
ejpam-4923	378	2	,	,	PUNCT
ejpam-4923	378	3	1999	1999	NUM
ejpam-4923	378	4	.	.	PUNCT
ejpam-4923	379	1	funct	funct	ADJ
ejpam-4923	379	2	-	-	PUNCT
ejpam-4923	379	3	an/9712003	an/9712003	NOUN
ejpam-4923	379	4	.	.	PUNCT
ejpam-4923	380	1	[	[	X
ejpam-4923	380	2	11	11	NUM
ejpam-4923	380	3	]	]	X
ejpam-4923	380	4	vladimir	vladimir	PROPN
ejpam-4923	380	5	v	v	NOUN
ejpam-4923	380	6	kisil	kisil	PROPN
ejpam-4923	380	7	.	.	PUNCT
ejpam-4923	381	1	induced	induce	VERB
ejpam-4923	381	2	representations	representation	NOUN
ejpam-4923	381	3	and	and	CCONJ
ejpam-4923	381	4	hypercomplex	hypercomplex	NOUN
ejpam-4923	381	5	numbers	number	NOUN
ejpam-4923	381	6	.	.	PUNCT
ejpam-4923	382	1	advances	advance	NOUN
ejpam-4923	382	2	in	in	ADP
ejpam-4923	382	3	applied	apply	VERB
ejpam-4923	382	4	clifford	clifford	PROPN
ejpam-4923	382	5	algebras	algebras	PROPN
ejpam-4923	382	6	,	,	PUNCT
ejpam-4923	382	7	23(2):417–440	23(2):417–440	PROPN
ejpam-4923	382	8	,	,	PUNCT
ejpam-4923	382	9	2013	2013	NUM
ejpam-4923	382	10	.	.	PUNCT
ejpam-4923	383	1	[	[	X
ejpam-4923	383	2	12	12	NUM
ejpam-4923	383	3	]	]	X
ejpam-4923	383	4	vladimir	vladimir	PROPN
ejpam-4923	383	5	v.	v.	ADP
ejpam-4923	383	6	kisil	kisil	PROPN
ejpam-4923	383	7	.	.	PUNCT
ejpam-4923	384	1	uncertainty	uncertainty	NOUN
ejpam-4923	384	2	and	and	CCONJ
ejpam-4923	384	3	analyticity	analyticity	NOUN
ejpam-4923	384	4	.	.	PUNCT
ejpam-4923	385	1	arxiv	arxiv	PROPN
ejpam-4923	385	2	:	:	PUNCT
ejpam-4923	385	3	mathematical	mathematical	ADJ
ejpam-4923	385	4	physics	physics	NOUN
ejpam-4923	385	5	,	,	PUNCT
ejpam-4923	385	6	pages	page	NOUN
ejpam-4923	385	7	583–590	583–590	NUM
ejpam-4923	385	8	,	,	PUNCT
ejpam-4923	385	9	2013	2013	NUM
ejpam-4923	385	10	.	.	PUNCT
ejpam-4923	386	1	[	[	X
ejpam-4923	386	2	13	13	NUM
ejpam-4923	386	3	]	]	PUNCT
ejpam-4923	386	4	s.	s.	PROPN
ejpam-4923	386	5	lang	lang	PROPN
ejpam-4923	386	6	.	.	PUNCT
ejpam-4923	387	1	sl2(r	sl2(r	PROPN
ejpam-4923	387	2	)	)	PUNCT
ejpam-4923	388	1	,	,	PUNCT
ejpam-4923	388	2	volume	volume	NOUN
ejpam-4923	388	3	105	105	NUM
ejpam-4923	388	4	of	of	ADP
ejpam-4923	388	5	graduate	graduate	ADJ
ejpam-4923	388	6	texts	text	NOUN
ejpam-4923	388	7	in	in	ADP
ejpam-4923	388	8	mathematics	mathematic	NOUN
ejpam-4923	388	9	,	,	PUNCT
ejpam-4923	388	10	1985	1985	NUM
ejpam-4923	388	11	.	.	PUNCT
ejpam-4923	389	1	[	[	X
ejpam-4923	389	2	14	14	NUM
ejpam-4923	389	3	]	]	X
ejpam-4923	389	4	g.	g.	PROPN
ejpam-4923	389	5	w.	w.	PROPN
ejpam-4923	389	6	mackey	mackey	PROPN
ejpam-4923	389	7	.	.	PUNCT
ejpam-4923	390	1	induced	induce	VERB
ejpam-4923	390	2	representations	representation	NOUN
ejpam-4923	390	3	of	of	ADP
ejpam-4923	390	4	locally	locally	ADV
ejpam-4923	390	5	compact	compact	ADJ
ejpam-4923	390	6	groups	group	NOUN
ejpam-4923	390	7	.	.	PUNCT
ejpam-4923	391	1	annals	annal	NOUN
ejpam-4923	391	2	of	of	ADP
ejpam-4923	391	3	mathematics	mathematic	NOUN
ejpam-4923	391	4	,	,	PUNCT
ejpam-4923	391	5	55(1):101–139	55(1):101–139	NUM
ejpam-4923	391	6	,	,	PUNCT
ejpam-4923	391	7	1952	1952	NUM
ejpam-4923	391	8	.	.	PUNCT
ejpam-4923	392	1	[	[	X
ejpam-4923	392	2	15	15	NUM
ejpam-4923	392	3	]	]	X
ejpam-4923	392	4	w.	w.	PROPN
ejpam-4923	392	5	t.	t.	PROPN
ejpam-4923	392	6	ross	ross	PROPN
ejpam-4923	392	7	.	.	PUNCT
ejpam-4923	393	1	the	the	DET
ejpam-4923	393	2	classical	classical	ADJ
ejpam-4923	393	3	dirichlet	dirichlet	NOUN
ejpam-4923	393	4	space	space	NOUN
ejpam-4923	393	5	.	.	PUNCT
ejpam-4923	394	1	recent	recent	ADJ
ejpam-4923	394	2	advances	advance	NOUN
ejpam-4923	394	3	in	in	ADP
ejpam-4923	394	4	operator	operator	NOUN
ejpam-4923	394	5	-	-	PUNCT
ejpam-4923	394	6	related	relate	VERB
ejpam-4923	394	7	function	function	NOUN
ejpam-4923	394	8	theory	theory	NOUN
ejpam-4923	394	9	,	,	PUNCT
ejpam-4923	394	10	171	171	NUM
ejpam-4923	394	11	-	-	SYM
ejpam-4923	394	12	197	197	NUM
ejpam-4923	394	13	,	,	PUNCT
ejpam-4923	394	14	contemp	contemp	NOUN
ejpam-4923	394	15	.	.	PUNCT
ejpam-4923	395	1	math	math	NOUN
ejpam-4923	395	2	.	.	PUNCT
ejpam-4923	395	3	,	,	PUNCT
ejpam-4923	395	4	393	393	NUM
ejpam-4923	395	5	,	,	PUNCT
ejpam-4923	396	1	amer	amer	PROPN
ejpam-4923	396	2	.	.	PROPN
ejpam-4923	396	3	math	math	PROPN
ejpam-4923	396	4	.	.	PUNCT
ejpam-4923	397	1	soc	soc	PROPN
ejpam-4923	397	2	.	.	PUNCT
ejpam-4923	397	3	,	,	PUNCT
ejpam-4923	397	4	providence	providence	NOUN
ejpam-4923	397	5	,	,	PUNCT
ejpam-4923	397	6	ri	ri	PROPN
ejpam-4923	397	7	.	.	PROPN
ejpam-4923	397	8	,	,	PUNCT
ejpam-4923	397	9	2006	2006	NUM
ejpam-4923	397	10	.	.	PUNCT
ejpam-4923	398	1	[	[	X
ejpam-4923	398	2	16	16	NUM
ejpam-4923	398	3	]	]	X
ejpam-4923	398	4	n.	n.	PROPN
ejpam-4923	398	5	l.	l.	PROPN
ejpam-4923	398	6	vasilevski	vasilevski	PROPN
ejpam-4923	398	7	.	.	PUNCT
ejpam-4923	399	1	on	on	ADP
ejpam-4923	399	2	the	the	DET
ejpam-4923	399	3	structure	structure	NOUN
ejpam-4923	399	4	of	of	ADP
ejpam-4923	399	5	bergman	bergman	PROPN
ejpam-4923	399	6	and	and	CCONJ
ejpam-4923	399	7	poly	poly	ADJ
ejpam-4923	399	8	-	-	PUNCT
ejpam-4923	399	9	bergman	bergman	NOUN
ejpam-4923	399	10	spaces	space	VERB
ejpam-4923	399	11	.	.	PUNCT
ejpam-4923	400	1	integral	integral	ADJ
ejpam-4923	400	2	equations	equation	NOUN
ejpam-4923	400	3	and	and	CCONJ
ejpam-4923	400	4	operator	operator	NOUN
ejpam-4923	400	5	theory	theory	NOUN
ejpam-4923	400	6	,	,	PUNCT
ejpam-4923	400	7	33:471–488	33:471–488	PROPN
ejpam-4923	400	8	,	,	PUNCT
ejpam-4923	400	9	12	12	NUM
ejpam-4923	400	10	1999	1999	NUM
ejpam-4923	400	11	.	.	PUNCT