id	sid	tid	token	lemma	pos
ejpam-5245	1	1	european	european	PROPN
ejpam-5245	1	2	journal	journal	PROPN
ejpam-5245	1	3	of	of	ADP
ejpam-5245	1	4	pure	pure	ADJ
ejpam-5245	1	5	and	and	CCONJ
ejpam-5245	1	6	applied	apply	VERB
ejpam-5245	1	7	mathematics	mathematic	NOUN
ejpam-5245	1	8	vol	vol	NOUN
ejpam-5245	1	9	.	.	PROPN
ejpam-5245	2	1	17	17	NUM
ejpam-5245	2	2	,	,	PUNCT
ejpam-5245	2	3	no	no	INTJ
ejpam-5245	2	4	.	.	NOUN
ejpam-5245	2	5	3	3	NUM
ejpam-5245	2	6	,	,	PUNCT
ejpam-5245	2	7	2024	2024	NUM
ejpam-5245	2	8	,	,	PUNCT
ejpam-5245	2	9	2092	2092	NUM
ejpam-5245	2	10	-	-	SYM
ejpam-5245	2	11	2105	2105	NUM
ejpam-5245	2	12	issn	issn	PROPN
ejpam-5245	2	13	1307	1307	NUM
ejpam-5245	2	14	-	-	SYM
ejpam-5245	2	15	5543	5543	NUM
ejpam-5245	2	16	–	–	PUNCT
ejpam-5245	3	1	ejpam.com	ejpam.com	X
ejpam-5245	3	2	published	publish	VERB
ejpam-5245	3	3	by	by	ADP
ejpam-5245	3	4	new	new	PROPN
ejpam-5245	3	5	york	york	PROPN
ejpam-5245	3	6	business	business	PROPN
ejpam-5245	3	7	global	global	ADJ
ejpam-5245	3	8	decomposition	decomposition	NOUN
ejpam-5245	3	9	of	of	ADP
ejpam-5245	3	10	the	the	DET
ejpam-5245	3	11	unitary	unitary	ADJ
ejpam-5245	3	12	representation	representation	NOUN
ejpam-5245	3	13	of	of	ADP
ejpam-5245	3	14	sl2(r	sl2(r	PROPN
ejpam-5245	3	15	)	)	PUNCT
ejpam-5245	3	16	on	on	ADP
ejpam-5245	3	17	the	the	DET
ejpam-5245	3	18	upper	upper	ADJ
ejpam-5245	3	19	half	half	ADJ
ejpam-5245	3	20	plane	plane	NOUN
ejpam-5245	3	21	into	into	ADP
ejpam-5245	3	22	irreducible	irreducible	ADJ
ejpam-5245	3	23	components	component	NOUN
ejpam-5245	3	24	fatimah	fatimah	PROPN
ejpam-5245	3	25	abdullah	abdullah	PROPN
ejpam-5245	3	26	alabbad	alabbad	PROPN
ejpam-5245	3	27	department	department	PROPN
ejpam-5245	3	28	of	of	ADP
ejpam-5245	3	29	mathematics	mathematics	PROPN
ejpam-5245	3	30	and	and	CCONJ
ejpam-5245	3	31	statistics	statistic	NOUN
ejpam-5245	3	32	,	,	PUNCT
ejpam-5245	3	33	faculty	faculty	NOUN
ejpam-5245	3	34	of	of	ADP
ejpam-5245	3	35	science	science	NOUN
ejpam-5245	3	36	,	,	PUNCT
ejpam-5245	3	37	king	king	NOUN
ejpam-5245	3	38	faisal	faisal	PROPN
ejpam-5245	3	39	university	university	PROPN
ejpam-5245	3	40	,	,	PUNCT
ejpam-5245	3	41	saudi	saudi	PROPN
ejpam-5245	3	42	arabia	arabia	PROPN
ejpam-5245	3	43	abstract	abstract	NOUN
ejpam-5245	3	44	.	.	PUNCT
ejpam-5245	4	1	the	the	DET
ejpam-5245	4	2	main	main	ADJ
ejpam-5245	4	3	purpose	purpose	NOUN
ejpam-5245	4	4	of	of	ADP
ejpam-5245	4	5	this	this	DET
ejpam-5245	4	6	paper	paper	NOUN
ejpam-5245	4	7	is	be	AUX
ejpam-5245	4	8	to	to	PART
ejpam-5245	4	9	find	find	VERB
ejpam-5245	4	10	the	the	DET
ejpam-5245	4	11	inversion	inversion	NOUN
ejpam-5245	4	12	formula	formula	NOUN
ejpam-5245	4	13	for	for	ADP
ejpam-5245	4	14	the	the	DET
ejpam-5245	4	15	covariant	covariant	PROPN
ejpam-5245	4	16	transform	transform	NOUN
ejpam-5245	4	17	wρk	wρk	NOUN
ejpam-5245	4	18	φ0	φ0	PROPN
ejpam-5245	4	19	.	.	PUNCT
ejpam-5245	5	1	this	this	DET
ejpam-5245	5	2	formula	formula	NOUN
ejpam-5245	5	3	is	be	AUX
ejpam-5245	5	4	equivalent	equivalent	ADJ
ejpam-5245	5	5	to	to	ADP
ejpam-5245	5	6	the	the	DET
ejpam-5245	5	7	decomposition	decomposition	NOUN
ejpam-5245	5	8	of	of	ADP
ejpam-5245	5	9	the	the	DET
ejpam-5245	5	10	unitary	unitary	ADJ
ejpam-5245	5	11	representation	representation	NOUN
ejpam-5245	5	12	ρk	ρk	ADP
ejpam-5245	5	13	into	into	ADP
ejpam-5245	5	14	irreducible	irreducible	ADJ
ejpam-5245	5	15	components	component	NOUN
ejpam-5245	5	16	.	.	PUNCT
ejpam-5245	6	1	we	we	PRON
ejpam-5245	6	2	consider	consider	VERB
ejpam-5245	6	3	an	an	DET
ejpam-5245	6	4	eigenvalue	eigenvalue	NOUN
ejpam-5245	6	5	1	1	NUM
ejpam-5245	6	6	+	+	NUM
ejpam-5245	6	7	s2	s2	NOUN
ejpam-5245	6	8	of	of	ADP
ejpam-5245	6	9	the	the	DET
ejpam-5245	6	10	casimir	casimir	NOUN
ejpam-5245	6	11	operator	operator	NOUN
ejpam-5245	6	12	:	:	PUNCT
ejpam-5245	6	13	dρk(c	dρk(c	PROPN
ejpam-5245	6	14	)	)	PUNCT
ejpam-5245	6	15	=	=	SYM
ejpam-5245	6	16	−4v2	−4v2	NUM
ejpam-5245	6	17	(	(	PUNCT
ejpam-5245	6	18	∂2u	∂2u	X
ejpam-5245	6	19	+	+	CCONJ
ejpam-5245	6	20	∂2v	∂2v	NOUN
ejpam-5245	6	21	)	)	PUNCT
ejpam-5245	6	22	,	,	PUNCT
ejpam-5245	6	23	where	where	SCONJ
ejpam-5245	6	24	k	k	PROPN
ejpam-5245	6	25	=	=	NOUN
ejpam-5245	6	26	0	0	PROPN
ejpam-5245	6	27	.	.	PUNCT
ejpam-5245	6	28	to	to	PART
ejpam-5245	6	29	find	find	VERB
ejpam-5245	6	30	the	the	DET
ejpam-5245	6	31	inversion	inversion	NOUN
ejpam-5245	6	32	formula	formula	NOUN
ejpam-5245	6	33	,	,	PUNCT
ejpam-5245	6	34	first	first	ADV
ejpam-5245	6	35	we	we	PRON
ejpam-5245	6	36	study	study	VERB
ejpam-5245	6	37	the	the	DET
ejpam-5245	6	38	representations	representation	NOUN
ejpam-5245	6	39	of	of	ADP
ejpam-5245	6	40	sl2(r	sl2(r	NOUN
ejpam-5245	6	41	)	)	PUNCT
ejpam-5245	6	42	,	,	PUNCT
ejpam-5245	6	43	ρk	ρk	NOUN
ejpam-5245	6	44	and	and	CCONJ
ejpam-5245	6	45	ρτ	ρτ	INTJ
ejpam-5245	6	46	,	,	PUNCT
ejpam-5245	6	47	induced	induce	VERB
ejpam-5245	6	48	from	from	ADP
ejpam-5245	6	49	the	the	DET
ejpam-5245	6	50	complex	complex	ADJ
ejpam-5245	6	51	characters	character	NOUN
ejpam-5245	6	52	of	of	ADP
ejpam-5245	6	53	k	k	PROPN
ejpam-5245	6	54	and	and	CCONJ
ejpam-5245	6	55	n	n	PRON
ejpam-5245	6	56	respectively	respectively	ADV
ejpam-5245	6	57	.	.	PUNCT
ejpam-5245	7	1	then	then	ADV
ejpam-5245	7	2	,	,	PUNCT
ejpam-5245	7	3	we	we	PRON
ejpam-5245	7	4	find	find	VERB
ejpam-5245	7	5	the	the	DET
ejpam-5245	7	6	induced	induced	ADJ
ejpam-5245	7	7	covariant	covariant	NOUN
ejpam-5245	7	8	transform	transform	NOUN
ejpam-5245	7	9	wρk	wρk	NOUN
ejpam-5245	7	10	φ0	φ0	PROPN
ejpam-5245	7	11	withn	withn	PROPN
ejpam-5245	7	12	-eigenvector	-eigenvector	NOUN
ejpam-5245	7	13	to	to	PART
ejpam-5245	7	14	obtain	obtain	VERB
ejpam-5245	7	15	a	a	DET
ejpam-5245	7	16	transform	transform	NOUN
ejpam-5245	7	17	in	in	ADP
ejpam-5245	7	18	the	the	DET
ejpam-5245	7	19	space	space	NOUN
ejpam-5245	7	20	l2(sl2(r)/n	l2(sl2(r)/n	PROPN
ejpam-5245	7	21	)	)	PUNCT
ejpam-5245	7	22	.	.	PUNCT
ejpam-5245	8	1	thereafter	thereafter	ADV
ejpam-5245	8	2	,	,	PUNCT
ejpam-5245	8	3	we	we	PRON
ejpam-5245	8	4	compute	compute	VERB
ejpam-5245	8	5	the	the	DET
ejpam-5245	8	6	contravariant	contravariant	PROPN
ejpam-5245	8	7	transform	transform	NOUN
ejpam-5245	8	8	with	with	ADP
ejpam-5245	8	9	k	k	ADJ
ejpam-5245	8	10	-	-	PUNCT
ejpam-5245	8	11	eigenvector	eigenvector	PROPN
ejpam-5245	8	12	mρτ	mρτ	PROPN
ejpam-5245	8	13	ϕ0	ϕ0	NOUN
ejpam-5245	8	14	:	:	PUNCT
ejpam-5245	8	15	l2(sl2(r)/n	l2(sl2(r)/n	PROPN
ejpam-5245	8	16	)	)	PUNCT
ejpam-5245	8	17	→	→	SYM
ejpam-5245	8	18	l2(sl2(r)/k	l2(sl2(r)/k	NOUN
ejpam-5245	8	19	)	)	PUNCT
ejpam-5245	8	20	.	.	PUNCT
ejpam-5245	9	1	2020	2020	NUM
ejpam-5245	9	2	mathematics	mathematic	NOUN
ejpam-5245	9	3	subject	subject	NOUN
ejpam-5245	9	4	classifications	classification	NOUN
ejpam-5245	9	5	:	:	PUNCT
ejpam-5245	9	6	22d10,22d30,42a38	22d10,22d30,42a38	NUM
ejpam-5245	9	7	key	key	ADJ
ejpam-5245	9	8	words	word	NOUN
ejpam-5245	9	9	and	and	CCONJ
ejpam-5245	9	10	phrases	phrase	NOUN
ejpam-5245	9	11	:	:	PUNCT
ejpam-5245	9	12	unitary	unitary	ADJ
ejpam-5245	9	13	representation	representation	NOUN
ejpam-5245	9	14	,	,	PUNCT
ejpam-5245	9	15	sl2(r	sl2(r	PROPN
ejpam-5245	9	16	)	)	PUNCT
ejpam-5245	9	17	group	group	NOUN
ejpam-5245	9	18	,	,	PUNCT
ejpam-5245	9	19	covariant	covariant	PROPN
ejpam-5245	9	20	transform	transform	NOUN
ejpam-5245	9	21	,	,	PUNCT
ejpam-5245	9	22	inversion	inversion	NOUN
ejpam-5245	9	23	formula	formula	NOUN
ejpam-5245	9	24	1	1	NUM
ejpam-5245	9	25	.	.	PUNCT
ejpam-5245	10	1	introduction	introduction	NOUN
ejpam-5245	10	2	integral	integral	ADJ
ejpam-5245	10	3	transforms	transform	NOUN
ejpam-5245	10	4	establishes	establish	VERB
ejpam-5245	10	5	a	a	DET
ejpam-5245	10	6	correspondence	correspondence	NOUN
ejpam-5245	10	7	between	between	ADP
ejpam-5245	10	8	functions	function	NOUN
ejpam-5245	10	9	on	on	ADP
ejpam-5245	10	10	a	a	DET
ejpam-5245	10	11	manifold	manifold	ADJ
ejpam-5245	10	12	x	x	PUNCT
ejpam-5245	10	13	and	and	CCONJ
ejpam-5245	10	14	functions	function	NOUN
ejpam-5245	10	15	on	on	ADP
ejpam-5245	10	16	some	some	DET
ejpam-5245	10	17	manifold	manifold	ADJ
ejpam-5245	10	18	m	m	NOUN
ejpam-5245	10	19	of	of	ADP
ejpam-5245	10	20	submanifolds	submanifold	NOUN
ejpam-5245	10	21	of	of	ADP
ejpam-5245	10	22	x.	x.	NOUN
ejpam-5245	10	23	the	the	DET
ejpam-5245	10	24	main	main	ADJ
ejpam-5245	10	25	problems	problem	NOUN
ejpam-5245	10	26	are	be	AUX
ejpam-5245	10	27	in	in	ADP
ejpam-5245	10	28	the	the	DET
ejpam-5245	10	29	description	description	NOUN
ejpam-5245	10	30	of	of	ADP
ejpam-5245	10	31	the	the	DET
ejpam-5245	10	32	images	image	NOUN
ejpam-5245	10	33	and	and	CCONJ
ejpam-5245	10	34	kernels	kernel	NOUN
ejpam-5245	10	35	of	of	ADP
ejpam-5245	10	36	these	these	DET
ejpam-5245	10	37	transforms	transform	VERB
ejpam-5245	10	38	and	and	CCONJ
ejpam-5245	10	39	in	in	ADP
ejpam-5245	10	40	the	the	DET
ejpam-5245	10	41	construction	construction	NOUN
ejpam-5245	10	42	of	of	ADP
ejpam-5245	10	43	explicit	explicit	ADJ
ejpam-5245	10	44	inversion	inversion	NOUN
ejpam-5245	10	45	formulas	formula	NOUN
ejpam-5245	10	46	recovering	recover	VERB
ejpam-5245	10	47	the	the	DET
ejpam-5245	10	48	original	original	ADJ
ejpam-5245	10	49	objects	object	NOUN
ejpam-5245	10	50	from	from	ADP
ejpam-5245	10	51	their	their	PRON
ejpam-5245	10	52	images	image	NOUN
ejpam-5245	10	53	.	.	PUNCT
ejpam-5245	11	1	the	the	DET
ejpam-5245	11	2	first	first	ADJ
ejpam-5245	11	3	book	book	NOUN
ejpam-5245	11	4	devoted	devote	VERB
ejpam-5245	11	5	to	to	ADP
ejpam-5245	11	6	this	this	DET
ejpam-5245	11	7	area	area	NOUN
ejpam-5245	11	8	was	be	AUX
ejpam-5245	11	9	by	by	ADP
ejpam-5245	11	10	i.	i.	PROPN
ejpam-5245	11	11	m.	m.	PROPN
ejpam-5245	11	12	gelfand	gelfand	PROPN
ejpam-5245	11	13	,	,	PUNCT
ejpam-5245	11	14	m.	m.	NOUN
ejpam-5245	11	15	i.	i.	PROPN
ejpam-5245	11	16	graev	graev	PROPN
ejpam-5245	11	17	and	and	CCONJ
ejpam-5245	11	18	n.	n.	PROPN
ejpam-5245	11	19	ya	ya	PROPN
ejpam-5245	11	20	.	.	PROPN
ejpam-5245	12	1	vilenkin	vilenkin	PROPN
ejpam-5245	13	1	[	[	X
ejpam-5245	13	2	4	4	NUM
ejpam-5245	13	3	]	]	PUNCT
ejpam-5245	13	4	.	.	PUNCT
ejpam-5245	14	1	from	from	ADP
ejpam-5245	14	2	the	the	DET
ejpam-5245	14	3	1940s	1940	NOUN
ejpam-5245	14	4	,	,	PUNCT
ejpam-5245	14	5	one	one	NUM
ejpam-5245	14	6	of	of	ADP
ejpam-5245	14	7	the	the	DET
ejpam-5245	14	8	main	main	ADJ
ejpam-5245	14	9	problems	problem	NOUN
ejpam-5245	14	10	in	in	ADP
ejpam-5245	14	11	mathematics	mathematic	NOUN
ejpam-5245	14	12	was	be	AUX
ejpam-5245	14	13	to	to	PART
ejpam-5245	14	14	develop	develop	VERB
ejpam-5245	14	15	an	an	DET
ejpam-5245	14	16	analog	analog	NOUN
ejpam-5245	14	17	of	of	ADP
ejpam-5245	14	18	the	the	DET
ejpam-5245	14	19	fourier	fourier	NOUN
ejpam-5245	14	20	transform	transform	NOUN
ejpam-5245	14	21	for	for	ADP
ejpam-5245	14	22	noncommutative	noncommutative	ADJ
ejpam-5245	14	23	lie	lie	NOUN
ejpam-5245	14	24	group	group	NOUN
ejpam-5245	14	25	.	.	PUNCT
ejpam-5245	15	1	for	for	ADP
ejpam-5245	15	2	the	the	DET
ejpam-5245	15	3	group	group	NOUN
ejpam-5245	15	4	sl2(c	sl2(c	NOUN
ejpam-5245	15	5	)	)	PUNCT
ejpam-5245	15	6	,	,	PUNCT
ejpam-5245	15	7	i.	i.	PROPN
ejpam-5245	15	8	m.	m.	PROPN
ejpam-5245	15	9	gelfand	gelfand	PROPN
ejpam-5245	15	10	and	and	CCONJ
ejpam-5245	15	11	m.	m.	PROPN
ejpam-5245	15	12	a.	a.	PROPN
ejpam-5245	15	13	naimark	naimark	PROPN
ejpam-5245	15	14	constructed	construct	VERB
ejpam-5245	15	15	a	a	DET
ejpam-5245	15	16	theory	theory	NOUN
ejpam-5245	15	17	in	in	ADP
ejpam-5245	15	18	which	which	PRON
ejpam-5245	15	19	the	the	DET
ejpam-5245	15	20	role	role	NOUN
ejpam-5245	15	21	of	of	ADP
ejpam-5245	15	22	exponential	exponential	ADJ
ejpam-5245	15	23	functions	function	NOUN
ejpam-5245	15	24	was	be	AUX
ejpam-5245	15	25	played	play	VERB
ejpam-5245	15	26	by	by	ADP
ejpam-5245	15	27	irreducible	irreducible	ADJ
ejpam-5245	15	28	infinite	infinite	ADJ
ejpam-5245	15	29	-	-	PUNCT
ejpam-5245	15	30	dimensional	dimensional	ADJ
ejpam-5245	15	31	unitary	unitary	ADJ
ejpam-5245	15	32	representations	representation	NOUN
ejpam-5245	15	33	of	of	ADP
ejpam-5245	15	34	the	the	DET
ejpam-5245	15	35	sl2(c	sl2(c	NOUN
ejpam-5245	15	36	)	)	PUNCT
ejpam-5245	15	37	group	group	NOUN
ejpam-5245	15	38	.	.	PUNCT
ejpam-5245	16	1	obtaining	obtain	VERB
ejpam-5245	16	2	analogs	analog	NOUN
ejpam-5245	16	3	of	of	ADP
ejpam-5245	16	4	the	the	DET
ejpam-5245	16	5	inversion	inversion	NOUN
ejpam-5245	16	6	formula	formula	NOUN
ejpam-5245	16	7	and	and	CCONJ
ejpam-5245	16	8	the	the	DET
ejpam-5245	16	9	plancherel	plancherel	NOUN
ejpam-5245	16	10	formula	formula	NOUN
ejpam-5245	16	11	for	for	ADP
ejpam-5245	16	12	the	the	DET
ejpam-5245	16	13	fourier	fourier	NOUN
ejpam-5245	16	14	transform	transform	NOUN
ejpam-5245	16	15	was	be	AUX
ejpam-5245	16	16	doi	doi	ADJ
ejpam-5245	16	17	:	:	PUNCT
ejpam-5245	16	18	https://doi.org/10.29020/nybg.ejpam.v17i3.5245	https://doi.org/10.29020/nybg.ejpam.v17i3.5245	PROPN
ejpam-5245	16	19	email	email	NOUN
ejpam-5245	16	20	address	address	NOUN
ejpam-5245	16	21	:	:	PUNCT
ejpam-5245	16	22	falabbad@kfu.edu.sa	falabbad@kfu.edu.sa	PROPN
ejpam-5245	16	23	(	(	PUNCT
ejpam-5245	16	24	f.	f.	PROPN
ejpam-5245	16	25	a.	a.	PROPN
ejpam-5245	16	26	alabbad	alabbad	PROPN
ejpam-5245	16	27	)	)	PUNCT
ejpam-5245	16	28	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5245	16	29	2092	2092	NUM
ejpam-5245	17	1	©	©	ADP
ejpam-5245	17	2	2024	2024	NUM
ejpam-5245	17	3	ejpam	ejpam	NOUN
ejpam-5245	17	4	all	all	DET
ejpam-5245	17	5	rights	right	NOUN
ejpam-5245	17	6	reserved	reserve	VERB
ejpam-5245	17	7	.	.	PUNCT
ejpam-5245	18	1	f.	f.	PROPN
ejpam-5245	18	2	a.	a.	PROPN
ejpam-5245	18	3	alabbad	alabbad	PROPN
ejpam-5245	18	4	/	/	SYM
ejpam-5245	18	5	eur	eur	PROPN
ejpam-5245	18	6	.	.	PUNCT
ejpam-5245	19	1	j.	j.	PROPN
ejpam-5245	19	2	pure	pure	PROPN
ejpam-5245	19	3	appl	appl	PROPN
ejpam-5245	19	4	.	.	PROPN
ejpam-5245	19	5	math	math	PROPN
ejpam-5245	19	6	,	,	PUNCT
ejpam-5245	19	7	17	17	NUM
ejpam-5245	19	8	(	(	PUNCT
ejpam-5245	19	9	3	3	NUM
ejpam-5245	19	10	)	)	PUNCT
ejpam-5245	19	11	(	(	PUNCT
ejpam-5245	19	12	2024	2024	NUM
ejpam-5245	19	13	)	)	PUNCT
ejpam-5245	19	14	,	,	PUNCT
ejpam-5245	19	15	2092	2092	NUM
ejpam-5245	19	16	-	-	SYM
ejpam-5245	19	17	2105	2105	NUM
ejpam-5245	19	18	2093	2093	NUM
ejpam-5245	19	19	the	the	DET
ejpam-5245	19	20	most	most	ADV
ejpam-5245	19	21	important	important	ADJ
ejpam-5245	19	22	result	result	NOUN
ejpam-5245	19	23	of	of	ADP
ejpam-5245	19	24	this	this	DET
ejpam-5245	19	25	theory	theory	NOUN
ejpam-5245	19	26	.	.	PUNCT
ejpam-5245	20	1	our	our	PRON
ejpam-5245	20	2	contribution	contribution	NOUN
ejpam-5245	20	3	is	be	AUX
ejpam-5245	20	4	to	to	PART
ejpam-5245	20	5	use	use	VERB
ejpam-5245	20	6	a	a	DET
ejpam-5245	20	7	new	new	ADJ
ejpam-5245	20	8	method	method	NOUN
ejpam-5245	20	9	starting	start	VERB
ejpam-5245	20	10	with	with	ADP
ejpam-5245	20	11	the	the	DET
ejpam-5245	20	12	covariant	covariant	PROPN
ejpam-5245	20	13	transform	transform	NOUN
ejpam-5245	20	14	to	to	PART
ejpam-5245	20	15	obtain	obtain	VERB
ejpam-5245	20	16	the	the	DET
ejpam-5245	20	17	inversion	inversion	NOUN
ejpam-5245	20	18	formula	formula	NOUN
ejpam-5245	20	19	.	.	PUNCT
ejpam-5245	21	1	action	action	NOUN
ejpam-5245	21	2	of	of	ADP
ejpam-5245	21	3	sl2(r	sl2(r	PROPN
ejpam-5245	21	4	)	)	PUNCT
ejpam-5245	21	5	by	by	ADP
ejpam-5245	21	6	linear	linear	ADJ
ejpam-5245	21	7	-	-	PUNCT
ejpam-5245	21	8	fractional	fractional	ADJ
ejpam-5245	21	9	transformation	transformation	NOUN
ejpam-5245	21	10	on	on	ADP
ejpam-5245	21	11	complex	complex	ADJ
ejpam-5245	21	12	numbers	number	NOUN
ejpam-5245	21	13	produces	produce	VERB
ejpam-5245	21	14	isometrical	isometrical	ADJ
ejpam-5245	21	15	motions	motion	NOUN
ejpam-5245	21	16	of	of	ADP
ejpam-5245	21	17	the	the	DET
ejpam-5245	21	18	lobachevsky	lobachevsky	ADJ
ejpam-5245	21	19	geometry	geometry	NOUN
ejpam-5245	21	20	.	.	PUNCT
ejpam-5245	22	1	it	it	PRON
ejpam-5245	22	2	is	be	AUX
ejpam-5245	22	3	less	less	ADV
ejpam-5245	22	4	known	known	ADJ
ejpam-5245	22	5	that	that	SCONJ
ejpam-5245	22	6	there	there	PRON
ejpam-5245	22	7	are	be	VERB
ejpam-5245	22	8	related	related	ADJ
ejpam-5245	22	9	actions	action	NOUN
ejpam-5245	22	10	of	of	ADP
ejpam-5245	22	11	sl2(r	sl2(r	PROPN
ejpam-5245	22	12	)	)	PUNCT
ejpam-5245	22	13	on	on	ADP
ejpam-5245	22	14	dual	dual	ADJ
ejpam-5245	22	15	and	and	CCONJ
ejpam-5245	22	16	double	double	ADJ
ejpam-5245	22	17	numbers	number	NOUN
ejpam-5245	22	18	which	which	PRON
ejpam-5245	22	19	have	have	VERB
ejpam-5245	22	20	the	the	DET
ejpam-5245	22	21	form	form	NOUN
ejpam-5245	22	22	z	z	NOUN
ejpam-5245	22	23	=	=	SYM
ejpam-5245	22	24	x+	x+	PROPN
ejpam-5245	22	25	ιy	ιy	INTJ
ejpam-5245	22	26	,	,	PUNCT
ejpam-5245	22	27	ι2	ι2	PROPN
ejpam-5245	22	28	=	=	SYM
ejpam-5245	22	29	0	0	NUM
ejpam-5245	22	30	or	or	CCONJ
ejpam-5245	22	31	ι2	ι2	VERB
ejpam-5245	22	32	=	=	SYM
ejpam-5245	22	33	1	1	NUM
ejpam-5245	22	34	,	,	PUNCT
ejpam-5245	22	35	correspondingly	correspondingly	ADV
ejpam-5245	22	36	.	.	PUNCT
ejpam-5245	23	1	we	we	PRON
ejpam-5245	23	2	write	write	VERB
ejpam-5245	23	3	ε	ε	PROPN
ejpam-5245	23	4	and	and	CCONJ
ejpam-5245	23	5	j	j	PROPN
ejpam-5245	23	6	instead	instead	ADV
ejpam-5245	23	7	of	of	ADP
ejpam-5245	23	8	ι	ι	PROPN
ejpam-5245	23	9	within	within	ADP
ejpam-5245	23	10	dual	dual	ADJ
ejpam-5245	23	11	and	and	CCONJ
ejpam-5245	23	12	double	double	ADJ
ejpam-5245	23	13	numbers	number	NOUN
ejpam-5245	23	14	,	,	PUNCT
ejpam-5245	23	15	respectively	respectively	ADV
ejpam-5245	23	16	.	.	PUNCT
ejpam-5245	24	1	three	three	NUM
ejpam-5245	24	2	possible	possible	ADJ
ejpam-5245	24	3	values	value	NOUN
ejpam-5245	24	4	−1	−1	NOUN
ejpam-5245	24	5	,	,	PUNCT
ejpam-5245	24	6	0	0	NUM
ejpam-5245	24	7	and	and	CCONJ
ejpam-5245	24	8	1	1	NUM
ejpam-5245	24	9	of	of	ADP
ejpam-5245	24	10	σ	σ	NOUN
ejpam-5245	24	11	:	:	PUNCT
ejpam-5245	25	1	=	=	SYM
ejpam-5245	25	2	ι2	ι2	PROPN
ejpam-5245	25	3	will	will	AUX
ejpam-5245	25	4	be	be	AUX
ejpam-5245	25	5	referred	refer	VERB
ejpam-5245	25	6	to	to	ADP
ejpam-5245	25	7	elliptic	elliptic	ADJ
ejpam-5245	25	8	,	,	PUNCT
ejpam-5245	25	9	parabolic	parabolic	ADJ
ejpam-5245	25	10	and	and	CCONJ
ejpam-5245	25	11	hyperbolic	hyperbolic	ADJ
ejpam-5245	25	12	cases	case	NOUN
ejpam-5245	25	13	,	,	PUNCT
ejpam-5245	25	14	respectively	respectively	ADV
ejpam-5245	25	15	.	.	PUNCT
ejpam-5245	26	1	a	a	DET
ejpam-5245	26	2	generic	generic	ADJ
ejpam-5245	26	3	cycle	cycle	NOUN
ejpam-5245	26	4	[	[	X
ejpam-5245	26	5	9	9	NUM
ejpam-5245	26	6	]	]	PUNCT
ejpam-5245	26	7	,	,	PUNCT
ejpam-5245	26	8	§	§	PROPN
ejpam-5245	26	9	4.2	4.2	NUM
ejpam-5245	26	10	is	be	AUX
ejpam-5245	26	11	the	the	DET
ejpam-5245	26	12	set	set	NOUN
ejpam-5245	26	13	of	of	ADP
ejpam-5245	26	14	points	point	NOUN
ejpam-5245	26	15	(	(	PUNCT
ejpam-5245	26	16	u	u	NOUN
ejpam-5245	26	17	,	,	PUNCT
ejpam-5245	26	18	v	v	NOUN
ejpam-5245	26	19	)	)	PUNCT
ejpam-5245	26	20	∈	∈	PROPN
ejpam-5245	26	21	r2	r2	NOUN
ejpam-5245	26	22	defined	define	VERB
ejpam-5245	26	23	for	for	ADP
ejpam-5245	26	24	all	all	DET
ejpam-5245	26	25	values	value	NOUN
ejpam-5245	26	26	of	of	ADP
ejpam-5245	26	27	σ	σ	NOUN
ejpam-5245	26	28	by	by	ADP
ejpam-5245	26	29	the	the	DET
ejpam-5245	26	30	equation	equation	NOUN
ejpam-5245	26	31	k(u2	k(u2	PROPN
ejpam-5245	26	32	−	−	PROPN
ejpam-5245	26	33	σv2)−	σv2)−	ADJ
ejpam-5245	26	34	2lu−	2lu−	NUM
ejpam-5245	26	35	2nv	2nv	ADJ
ejpam-5245	26	36	+	+	NOUN
ejpam-5245	26	37	m	m	NOUN
ejpam-5245	26	38	=	=	ADJ
ejpam-5245	26	39	0	0	NUM
ejpam-5245	26	40	.	.	PUNCT
ejpam-5245	27	1	(	(	PUNCT
ejpam-5245	27	2	1	1	X
ejpam-5245	27	3	)	)	PUNCT
ejpam-5245	27	4	this	this	DET
ejpam-5245	27	5	equation	equation	NOUN
ejpam-5245	27	6	is	be	AUX
ejpam-5245	27	7	represented	represent	VERB
ejpam-5245	27	8	by	by	ADP
ejpam-5245	27	9	a	a	DET
ejpam-5245	27	10	point	point	NOUN
ejpam-5245	27	11	(	(	PUNCT
ejpam-5245	27	12	k	k	X
ejpam-5245	27	13	,	,	PUNCT
ejpam-5245	27	14	l	l	NOUN
ejpam-5245	27	15	,	,	PUNCT
ejpam-5245	27	16	n	n	CCONJ
ejpam-5245	27	17	,	,	PUNCT
ejpam-5245	27	18	m	m	NOUN
ejpam-5245	27	19	)	)	PUNCT
ejpam-5245	27	20	from	from	ADP
ejpam-5245	27	21	a	a	DET
ejpam-5245	27	22	projective	projective	ADJ
ejpam-5245	27	23	space	space	NOUN
ejpam-5245	27	24	p3	p3	PROPN
ejpam-5245	27	25	,	,	PUNCT
ejpam-5245	27	26	since	since	SCONJ
ejpam-5245	27	27	for	for	ADP
ejpam-5245	27	28	a	a	DET
ejpam-5245	27	29	scaling	scale	VERB
ejpam-5245	27	30	factor	factor	NOUN
ejpam-5245	27	31	λ	λ	PROPN
ejpam-5245	27	32	̸=	̸=	PROPN
ejpam-5245	27	33	0	0	NUM
ejpam-5245	27	34	,	,	PUNCT
ejpam-5245	27	35	the	the	DET
ejpam-5245	27	36	point	point	NOUN
ejpam-5245	27	37	(	(	PUNCT
ejpam-5245	27	38	λk	λk	INTJ
ejpam-5245	27	39	,	,	PUNCT
ejpam-5245	27	40	λl	λl	PROPN
ejpam-5245	27	41	,	,	PUNCT
ejpam-5245	27	42	λn	λn	NOUN
ejpam-5245	27	43	,	,	PUNCT
ejpam-5245	27	44	λm	λm	NOUN
ejpam-5245	27	45	)	)	PUNCT
ejpam-5245	27	46	defines	define	VERB
ejpam-5245	27	47	an	an	DET
ejpam-5245	27	48	equation	equation	NOUN
ejpam-5245	27	49	equivalent	equivalent	ADJ
ejpam-5245	27	50	to	to	ADP
ejpam-5245	27	51	(	(	PUNCT
ejpam-5245	27	52	1	1	NUM
ejpam-5245	27	53	)	)	PUNCT
ejpam-5245	27	54	.	.	PUNCT
ejpam-5245	28	1	we	we	PRON
ejpam-5245	28	2	call	call	VERB
ejpam-5245	28	3	p3	p3	PROPN
ejpam-5245	28	4	the	the	DET
ejpam-5245	28	5	cycle	cycle	NOUN
ejpam-5245	28	6	space	space	NOUN
ejpam-5245	28	7	and	and	CCONJ
ejpam-5245	28	8	refer	refer	VERB
ejpam-5245	28	9	to	to	ADP
ejpam-5245	28	10	the	the	DET
ejpam-5245	28	11	initial	initial	ADJ
ejpam-5245	28	12	r2	r2	NOUN
ejpam-5245	28	13	as	as	ADP
ejpam-5245	28	14	the	the	DET
ejpam-5245	28	15	point	point	NOUN
ejpam-5245	28	16	space	space	NOUN
ejpam-5245	28	17	.	.	PUNCT
ejpam-5245	29	1	in	in	ADP
ejpam-5245	29	2	order	order	NOUN
ejpam-5245	29	3	to	to	PART
ejpam-5245	29	4	obtain	obtain	VERB
ejpam-5245	29	5	a	a	DET
ejpam-5245	29	6	connection	connection	NOUN
ejpam-5245	29	7	with	with	ADP
ejpam-5245	29	8	the	the	DET
ejpam-5245	29	9	möbius	möbius	PROPN
ejpam-5245	29	10	action	action	NOUN
ejpam-5245	29	11	,	,	PUNCT
ejpam-5245	29	12	we	we	PRON
ejpam-5245	29	13	arrange	arrange	VERB
ejpam-5245	29	14	numbers	number	NOUN
ejpam-5245	29	15	(	(	PUNCT
ejpam-5245	29	16	k	k	X
ejpam-5245	29	17	,	,	PUNCT
ejpam-5245	29	18	l	l	NOUN
ejpam-5245	29	19	,	,	PUNCT
ejpam-5245	29	20	n	n	CCONJ
ejpam-5245	29	21	,	,	PUNCT
ejpam-5245	29	22	m	m	NOUN
ejpam-5245	29	23	)	)	PUNCT
ejpam-5245	29	24	into	into	ADP
ejpam-5245	29	25	the	the	DET
ejpam-5245	29	26	matrix	matrix	NOUN
ejpam-5245	29	27	[	[	X
ejpam-5245	29	28	9	9	NUM
ejpam-5245	29	29	]	]	PUNCT
ejpam-5245	29	30	,	,	PUNCT
ejpam-5245	29	31	definition	definition	NOUN
ejpam-5245	29	32	4.11	4.11	NUM
ejpam-5245	29	33	cσ̆	cσ̆	NOUN
ejpam-5245	29	34	=	=	PUNCT
ejpam-5245	29	35	(	(	PUNCT
ejpam-5245	29	36	l	l	NOUN
ejpam-5245	29	37	+	+	CCONJ
ejpam-5245	29	38	ῐn	ῐn	X
ejpam-5245	29	39	−m	−m	INTJ
ejpam-5245	29	40	k	k	PROPN
ejpam-5245	29	41	−l	−l	PROPN
ejpam-5245	29	42	+	+	CCONJ
ejpam-5245	29	43	ῐn	ῐn	NUM
ejpam-5245	29	44	)	)	PUNCT
ejpam-5245	29	45	.	.	PUNCT
ejpam-5245	30	1	(	(	PUNCT
ejpam-5245	30	2	2	2	X
ejpam-5245	30	3	)	)	PUNCT
ejpam-5245	30	4	the	the	DET
ejpam-5245	30	5	values	value	NOUN
ejpam-5245	30	6	of	of	ADP
ejpam-5245	30	7	σ̆	σ̆	NOUN
ejpam-5245	30	8	:	:	PUNCT
ejpam-5245	30	9	=	=	SYM
ejpam-5245	30	10	ῐ2	ῐ2	PUNCT
ejpam-5245	30	11	are	be	AUX
ejpam-5245	30	12	−1	−1	ADJ
ejpam-5245	30	13	,	,	PUNCT
ejpam-5245	30	14	0	0	NUM
ejpam-5245	30	15	or	or	CCONJ
ejpam-5245	30	16	1	1	NUM
ejpam-5245	30	17	may	may	AUX
ejpam-5245	30	18	be	be	AUX
ejpam-5245	30	19	chosen	choose	VERB
ejpam-5245	30	20	to	to	PART
ejpam-5245	30	21	be	be	AUX
ejpam-5245	30	22	independent	independent	ADJ
ejpam-5245	30	23	of	of	ADP
ejpam-5245	30	24	the	the	DET
ejpam-5245	30	25	values	value	NOUN
ejpam-5245	30	26	of	of	ADP
ejpam-5245	30	27	σ	σ	PROPN
ejpam-5245	30	28	.	.	PUNCT
ejpam-5245	30	29	theorem	theorem	PROPN
ejpam-5245	30	30	1	1	NUM
ejpam-5245	30	31	.	.	PUNCT
ejpam-5245	31	1	[	[	X
ejpam-5245	31	2	9	9	NUM
ejpam-5245	31	3	]	]	PUNCT
ejpam-5245	31	4	,	,	PUNCT
ejpam-5245	31	5	theorem	theorem	VERB
ejpam-5245	31	6	4.13	4.13	NUM
ejpam-5245	31	7	let	let	VERB
ejpam-5245	31	8	a	a	DET
ejpam-5245	31	9	matrix	matrix	NOUN
ejpam-5245	31	10	g=	g=	NOUN
ejpam-5245	31	11	(	(	PUNCT
ejpam-5245	31	12	a	a	DET
ejpam-5245	31	13	b	b	NOUN
ejpam-5245	31	14	c	c	PROPN
ejpam-5245	31	15	d	d	NOUN
ejpam-5245	31	16	)	)	PUNCT
ejpam-5245	31	17	∈	∈	PROPN
ejpam-5245	31	18	sl2(r	sl2(r	PROPN
ejpam-5245	31	19	)	)	PUNCT
ejpam-5245	31	20	defines	define	VERB
ejpam-5245	31	21	a	a	DET
ejpam-5245	31	22	möbius	möbius	PROPN
ejpam-5245	31	23	transformation	transformation	NOUN
ejpam-5245	31	24	g	g	NOUN
ejpam-5245	31	25	:	:	PUNCT
ejpam-5245	31	26	(	(	PUNCT
ejpam-5245	31	27	u+	u+	NUM
ejpam-5245	31	28	ιv	ιv	NOUN
ejpam-5245	31	29	)	)	PUNCT
ejpam-5245	31	30	→	→	SYM
ejpam-5245	32	1	a(u+	a(u+	NOUN
ejpam-5245	32	2	ιv	ιv	NOUN
ejpam-5245	32	3	)	)	PUNCT
ejpam-5245	32	4	+	+	NUM
ejpam-5245	32	5	b	b	NOUN
ejpam-5245	32	6	c(u+	c(u+	NOUN
ejpam-5245	32	7	ιv	ιv	NOUN
ejpam-5245	32	8	)	)	PUNCT
ejpam-5245	33	1	+	+	NUM
ejpam-5245	34	1	d	d	NOUN
ejpam-5245	34	2	.	.	PUNCT
ejpam-5245	35	1	(	(	PUNCT
ejpam-5245	35	2	3	3	X
ejpam-5245	35	3	)	)	PUNCT
ejpam-5245	35	4	then	then	ADV
ejpam-5245	35	5	the	the	DET
ejpam-5245	35	6	image	image	NOUN
ejpam-5245	35	7	c̃σ̆	c̃σ̆	NOUN
ejpam-5245	35	8	of	of	ADP
ejpam-5245	35	9	a	a	DET
ejpam-5245	35	10	cycle	cycle	NOUN
ejpam-5245	35	11	cσ̆	cσ̆	VERB
ejpam-5245	35	12	under	under	ADP
ejpam-5245	35	13	transformation	transformation	NOUN
ejpam-5245	35	14	with	with	ADP
ejpam-5245	35	15	g	g	PROPN
ejpam-5245	35	16	∈	∈	PROPN
ejpam-5245	35	17	sl2(r	sl2(r	PROPN
ejpam-5245	35	18	)	)	PUNCT
ejpam-5245	35	19	is	be	AUX
ejpam-5245	35	20	given	give	VERB
ejpam-5245	35	21	by	by	ADP
ejpam-5245	35	22	similarity	similarity	NOUN
ejpam-5245	35	23	of	of	ADP
ejpam-5245	35	24	the	the	DET
ejpam-5245	35	25	matrix	matrix	NOUN
ejpam-5245	35	26	(	(	PUNCT
ejpam-5245	35	27	2	2	NUM
ejpam-5245	35	28	):	):	PUNCT
ejpam-5245	35	29	c̃σ̆	c̃σ̆	NOUN
ejpam-5245	35	30	=	=	SYM
ejpam-5245	35	31	gcσ̆g	gcσ̆g	PROPN
ejpam-5245	35	32	−1	−1	NOUN
ejpam-5245	35	33	.	.	PUNCT
ejpam-5245	36	1	(	(	PUNCT
ejpam-5245	36	2	4	4	X
ejpam-5245	36	3	)	)	PUNCT
ejpam-5245	36	4	definition	definition	NOUN
ejpam-5245	36	5	1	1	NUM
ejpam-5245	36	6	.	.	PUNCT
ejpam-5245	37	1	[	[	X
ejpam-5245	37	2	9	9	NUM
ejpam-5245	37	3	]	]	PUNCT
ejpam-5245	37	4	,	,	PUNCT
ejpam-5245	37	5	definition	definition	NOUN
ejpam-5245	37	6	5.11	5.11	NUM
ejpam-5245	37	7	for	for	ADP
ejpam-5245	37	8	two	two	NUM
ejpam-5245	37	9	cycles	cycle	NOUN
ejpam-5245	37	10	c	c	NOUN
ejpam-5245	37	11	and	and	CCONJ
ejpam-5245	37	12	c1	c1	PROPN
ejpam-5245	37	13	,	,	PUNCT
ejpam-5245	37	14	define	define	VERB
ejpam-5245	37	15	the	the	DET
ejpam-5245	37	16	cycles	cycle	NOUN
ejpam-5245	37	17	product	product	NOUN
ejpam-5245	37	18	by	by	ADP
ejpam-5245	37	19	:	:	PUNCT
ejpam-5245	37	20	⟨c	⟨c	NUM
ejpam-5245	37	21	,	,	PUNCT
ejpam-5245	37	22	c1⟩	c1⟩	PART
ejpam-5245	37	23	=	=	NOUN
ejpam-5245	37	24	−	−	NOUN
ejpam-5245	37	25	tr(cc̄1	tr(cc̄1	NOUN
ejpam-5245	37	26	)	)	PUNCT
ejpam-5245	37	27	,	,	PUNCT
ejpam-5245	37	28	(	(	PUNCT
ejpam-5245	37	29	5	5	X
ejpam-5245	37	30	)	)	PUNCT
ejpam-5245	37	31	where	where	SCONJ
ejpam-5245	37	32	tr	tr	PRON
ejpam-5245	37	33	denotes	denote	VERB
ejpam-5245	37	34	the	the	DET
ejpam-5245	37	35	trace	trace	NOUN
ejpam-5245	37	36	of	of	ADP
ejpam-5245	37	37	a	a	DET
ejpam-5245	37	38	matrix	matrix	NOUN
ejpam-5245	37	39	.	.	PUNCT
ejpam-5245	38	1	we	we	PRON
ejpam-5245	38	2	can	can	AUX
ejpam-5245	38	3	find	find	VERB
ejpam-5245	38	4	the	the	DET
ejpam-5245	38	5	explicit	explicit	ADJ
ejpam-5245	38	6	expression	expression	NOUN
ejpam-5245	38	7	of	of	ADP
ejpam-5245	38	8	the	the	DET
ejpam-5245	38	9	cycle	cycle	NOUN
ejpam-5245	38	10	product	product	NOUN
ejpam-5245	38	11	(	(	PUNCT
ejpam-5245	38	12	5	5	NUM
ejpam-5245	38	13	)	)	PUNCT
ejpam-5245	38	14	with	with	ADP
ejpam-5245	38	15	σ	σ	PROPN
ejpam-5245	38	16	=	=	SYM
ejpam-5245	38	17	−1	−1	NOUN
ejpam-5245	38	18	,	,	PUNCT
ejpam-5245	38	19	0	0	NUM
ejpam-5245	38	20	and	and	CCONJ
ejpam-5245	38	21	1	1	NUM
ejpam-5245	38	22	:	:	PUNCT
ejpam-5245	38	23	⟨c	⟨c	NUM
ejpam-5245	38	24	,	,	PUNCT
ejpam-5245	38	25	c1⟩	c1⟩	PART
ejpam-5245	39	1	=	=	PUNCT
ejpam-5245	39	2	km1	km1	NOUN
ejpam-5245	40	1	+	+	CCONJ
ejpam-5245	40	2	k1m−	k1m−	NOUN
ejpam-5245	40	3	2ll1	2ll1	NUM
ejpam-5245	40	4	+	+	CCONJ
ejpam-5245	40	5	2σnn1	2σnn1	NUM
ejpam-5245	40	6	,	,	PUNCT
ejpam-5245	40	7	(	(	PUNCT
ejpam-5245	40	8	6	6	NUM
ejpam-5245	40	9	)	)	PUNCT
ejpam-5245	40	10	where	where	SCONJ
ejpam-5245	40	11	c	c	NOUN
ejpam-5245	40	12	=	=	SYM
ejpam-5245	40	13	(	(	PUNCT
ejpam-5245	40	14	k	k	X
ejpam-5245	40	15	,	,	PUNCT
ejpam-5245	40	16	l	l	NOUN
ejpam-5245	40	17	,	,	PUNCT
ejpam-5245	40	18	n	n	CCONJ
ejpam-5245	40	19	,	,	PUNCT
ejpam-5245	40	20	m	m	NOUN
ejpam-5245	40	21	)	)	PUNCT
ejpam-5245	40	22	and	and	CCONJ
ejpam-5245	40	23	c1	c1	PROPN
ejpam-5245	40	24	=	=	SYM
ejpam-5245	40	25	(	(	PUNCT
ejpam-5245	40	26	k1	k1	PROPN
ejpam-5245	40	27	,	,	PUNCT
ejpam-5245	40	28	l1	l1	PROPN
ejpam-5245	40	29	,	,	PUNCT
ejpam-5245	40	30	n1,m1	n1,m1	PROPN
ejpam-5245	40	31	)	)	PUNCT
ejpam-5245	40	32	.	.	PUNCT
ejpam-5245	41	1	f.	f.	PROPN
ejpam-5245	41	2	a.	a.	PROPN
ejpam-5245	41	3	alabbad	alabbad	PROPN
ejpam-5245	41	4	/	/	SYM
ejpam-5245	41	5	eur	eur	PROPN
ejpam-5245	41	6	.	.	PUNCT
ejpam-5245	42	1	j.	j.	PROPN
ejpam-5245	42	2	pure	pure	PROPN
ejpam-5245	42	3	appl	appl	PROPN
ejpam-5245	42	4	.	.	PROPN
ejpam-5245	42	5	math	math	PROPN
ejpam-5245	42	6	,	,	PUNCT
ejpam-5245	42	7	17	17	NUM
ejpam-5245	42	8	(	(	PUNCT
ejpam-5245	42	9	3	3	NUM
ejpam-5245	42	10	)	)	PUNCT
ejpam-5245	42	11	(	(	PUNCT
ejpam-5245	42	12	2024	2024	NUM
ejpam-5245	42	13	)	)	PUNCT
ejpam-5245	42	14	,	,	PUNCT
ejpam-5245	42	15	2092	2092	NUM
ejpam-5245	42	16	-	-	SYM
ejpam-5245	42	17	2105	2105	NUM
ejpam-5245	42	18	2094	2094	NUM
ejpam-5245	42	19	definition	definition	NOUN
ejpam-5245	42	20	2	2	NUM
ejpam-5245	42	21	.	.	PUNCT
ejpam-5245	43	1	[	[	X
ejpam-5245	43	2	3	3	NUM
ejpam-5245	43	3	]	]	PUNCT
ejpam-5245	43	4	,	,	PUNCT
ejpam-5245	43	5	chap	chap	NOUN
ejpam-5245	43	6	.	.	PUNCT
ejpam-5245	44	1	3	3	NUM
ejpam-5245	44	2	,	,	PUNCT
ejpam-5245	44	3	§	§	PROPN
ejpam-5245	44	4	1.2	1.2	NUM
ejpam-5245	44	5	on	on	ADP
ejpam-5245	44	6	the	the	DET
ejpam-5245	44	7	hyperbolic	hyperbolic	ADJ
ejpam-5245	44	8	plane	plane	NOUN
ejpam-5245	44	9	one	one	NOUN
ejpam-5245	44	10	can	can	AUX
ejpam-5245	44	11	define	define	VERB
ejpam-5245	44	12	circles	circle	NOUN
ejpam-5245	44	13	of	of	ADP
ejpam-5245	44	14	infinitely	infinitely	ADV
ejpam-5245	44	15	large	large	ADJ
ejpam-5245	44	16	radius	radius	NOUN
ejpam-5245	44	17	(	(	PUNCT
ejpam-5245	44	18	horocycles	horocycle	NOUN
ejpam-5245	44	19	)	)	PUNCT
ejpam-5245	44	20	,	,	PUNCT
ejpam-5245	44	21	which	which	PRON
ejpam-5245	44	22	are	be	AUX
ejpam-5245	44	23	the	the	DET
ejpam-5245	44	24	limits	limit	NOUN
ejpam-5245	44	25	of	of	ADP
ejpam-5245	44	26	non	non	ADJ
ejpam-5245	44	27	-	-	ADJ
ejpam-5245	44	28	euclidean	euclidean	ADJ
ejpam-5245	44	29	circles	circle	NOUN
ejpam-5245	44	30	as	as	ADP
ejpam-5245	44	31	the	the	DET
ejpam-5245	44	32	center	center	NOUN
ejpam-5245	44	33	and	and	CCONJ
ejpam-5245	44	34	the	the	DET
ejpam-5245	44	35	radius	radius	NOUN
ejpam-5245	44	36	of	of	ADP
ejpam-5245	44	37	these	these	DET
ejpam-5245	44	38	circles	circle	NOUN
ejpam-5245	44	39	consistently	consistently	ADV
ejpam-5245	44	40	tend	tend	VERB
ejpam-5245	44	41	to	to	PART
ejpam-5245	44	42	infinity	infinity	VERB
ejpam-5245	44	43	.	.	PUNCT
ejpam-5245	45	1	in	in	ADP
ejpam-5245	45	2	the	the	DET
ejpam-5245	45	3	lobachevsky	lobachevsky	ADJ
ejpam-5245	45	4	model	model	NOUN
ejpam-5245	45	5	,	,	PUNCT
ejpam-5245	45	6	the	the	DET
ejpam-5245	45	7	horocycles	horocycle	NOUN
ejpam-5245	45	8	are	be	AUX
ejpam-5245	45	9	represented	represent	VERB
ejpam-5245	45	10	either	either	CCONJ
ejpam-5245	45	11	as	as	SCONJ
ejpam-5245	45	12	euclidean	euclidean	ADJ
ejpam-5245	45	13	circles	circle	NOUN
ejpam-5245	45	14	tangent	tangent	VERB
ejpam-5245	45	15	to	to	ADP
ejpam-5245	45	16	the	the	DET
ejpam-5245	45	17	real	real	ADJ
ejpam-5245	45	18	axis	axis	NOUN
ejpam-5245	45	19	or	or	CCONJ
ejpam-5245	45	20	as	as	SCONJ
ejpam-5245	45	21	lines	line	NOUN
ejpam-5245	45	22	parallel	parallel	ADJ
ejpam-5245	45	23	to	to	ADP
ejpam-5245	45	24	the	the	DET
ejpam-5245	45	25	real	real	ADJ
ejpam-5245	45	26	axis	axis	NOUN
ejpam-5245	45	27	.	.	PUNCT
ejpam-5245	46	1	the	the	DET
ejpam-5245	46	2	horizontal	horizontal	ADJ
ejpam-5245	46	3	line	line	NOUN
ejpam-5245	46	4	v−1	v−1	PROPN
ejpam-5245	46	5	=	=	SYM
ejpam-5245	46	6	0	0	PUNCT
ejpam-5245	46	7	as	as	SCONJ
ejpam-5245	46	8	a	a	DET
ejpam-5245	46	9	cycle	cycle	NOUN
ejpam-5245	46	10	is	be	AUX
ejpam-5245	46	11	represented	represent	VERB
ejpam-5245	46	12	by	by	ADP
ejpam-5245	46	13	the	the	DET
ejpam-5245	46	14	matrix	matrix	NOUN
ejpam-5245	46	15	(	(	PUNCT
ejpam-5245	46	16	−	−	PROPN
ejpam-5245	46	17	i	i	PRON
ejpam-5245	46	18	2	2	NUM
ejpam-5245	46	19	−1	−1	NOUN
ejpam-5245	46	20	0	0	NUM
ejpam-5245	47	1	−	−	NOUN
ejpam-5245	48	1	i	i	PRON
ejpam-5245	48	2	2	2	NUM
ejpam-5245	48	3	)	)	PUNCT
ejpam-5245	48	4	.	.	PUNCT
ejpam-5245	49	1	this	this	DET
ejpam-5245	49	2	line	line	NOUN
ejpam-5245	49	3	is	be	AUX
ejpam-5245	49	4	invariant	invariant	ADJ
ejpam-5245	49	5	under	under	ADP
ejpam-5245	49	6	the	the	DET
ejpam-5245	49	7	subgroup	subgroup	NOUN
ejpam-5245	49	8	n	n	NOUN
ejpam-5245	49	9	=	=	PUNCT
ejpam-5245	49	10	(	(	PUNCT
ejpam-5245	49	11	1	1	NUM
ejpam-5245	49	12	n	n	NOUN
ejpam-5245	49	13	0	0	NUM
ejpam-5245	49	14	1	1	NUM
ejpam-5245	49	15	)	)	PUNCT
ejpam-5245	49	16	,	,	PUNCT
ejpam-5245	49	17	that	that	ADV
ejpam-5245	49	18	is	is	ADV
ejpam-5245	49	19	(	(	PUNCT
ejpam-5245	49	20	1	1	NUM
ejpam-5245	49	21	n	n	NOUN
ejpam-5245	49	22	0	0	NUM
ejpam-5245	49	23	1	1	NUM
ejpam-5245	49	24	)	)	PUNCT
ejpam-5245	49	25	(	(	PUNCT
ejpam-5245	49	26	−	−	PROPN
ejpam-5245	49	27	i	i	PRON
ejpam-5245	49	28	2	2	NUM
ejpam-5245	49	29	−1	−1	NOUN
ejpam-5245	49	30	0	0	NUM
ejpam-5245	50	1	−	−	NOUN
ejpam-5245	51	1	i	i	PRON
ejpam-5245	51	2	2	2	NUM
ejpam-5245	51	3	)	)	PUNCT
ejpam-5245	51	4	(	(	PUNCT
ejpam-5245	51	5	1	1	NUM
ejpam-5245	51	6	−n	−n	NOUN
ejpam-5245	51	7	0	0	NUM
ejpam-5245	51	8	1	1	NUM
ejpam-5245	51	9	)	)	PUNCT
ejpam-5245	51	10	=	=	SYM
ejpam-5245	52	1	(	(	PUNCT
ejpam-5245	52	2	−	−	PUNCT
ejpam-5245	52	3	i	i	PRON
ejpam-5245	52	4	2	2	NUM
ejpam-5245	52	5	−1	−1	NOUN
ejpam-5245	52	6	0	0	NUM
ejpam-5245	53	1	−	−	NOUN
ejpam-5245	54	1	i	i	PRON
ejpam-5245	54	2	2	2	NUM
ejpam-5245	54	3	)	)	PUNCT
ejpam-5245	54	4	.	.	PUNCT
ejpam-5245	55	1	thus	thus	ADV
ejpam-5245	55	2	all	all	DET
ejpam-5245	55	3	horocycles	horocycle	NOUN
ejpam-5245	55	4	obtained	obtain	VERB
ejpam-5245	55	5	by	by	ADP
ejpam-5245	55	6	sl2(r	sl2(r	PROPN
ejpam-5245	55	7	)	)	PUNCT
ejpam-5245	55	8	action	action	NOUN
ejpam-5245	55	9	are	be	AUX
ejpam-5245	55	10	parametrized	parametrize	VERB
ejpam-5245	55	11	by	by	ADP
ejpam-5245	55	12	points	point	NOUN
ejpam-5245	55	13	of	of	ADP
ejpam-5245	55	14	the	the	DET
ejpam-5245	55	15	homogeneous	homogeneous	ADJ
ejpam-5245	55	16	space	space	NOUN
ejpam-5245	55	17	sl2(r)/n	sl2(r)/n	NOUN
ejpam-5245	55	18	.	.	PUNCT
ejpam-5245	56	1	the	the	DET
ejpam-5245	56	2	image	image	NOUN
ejpam-5245	56	3	of	of	ADP
ejpam-5245	56	4	v	v	NOUN
ejpam-5245	56	5	−	−	PROPN
ejpam-5245	56	6	1	1	NUM
ejpam-5245	56	7	=	=	SYM
ejpam-5245	56	8	0	0	NUM
ejpam-5245	56	9	under	under	ADP
ejpam-5245	56	10	the	the	DET
ejpam-5245	56	11	lower	low	ADJ
ejpam-5245	56	12	triangular	triangular	NOUN
ejpam-5245	56	13	matrix	matrix	NOUN
ejpam-5245	56	14	(	(	PUNCT
ejpam-5245	56	15	ξ1	ξ1	NOUN
ejpam-5245	56	16	0	0	NUM
ejpam-5245	56	17	ξ2	ξ2	NOUN
ejpam-5245	56	18	1	1	NUM
ejpam-5245	56	19	ξ1	ξ1	NOUN
ejpam-5245	56	20	)	)	PUNCT
ejpam-5245	56	21	∈	∈	PROPN
ejpam-5245	56	22	sl2(r	sl2(r	PROPN
ejpam-5245	56	23	)	)	PUNCT
ejpam-5245	56	24	is	be	AUX
ejpam-5245	56	25	(	(	PUNCT
ejpam-5245	56	26	ξ1	ξ1	NOUN
ejpam-5245	56	27	0	0	NUM
ejpam-5245	56	28	ξ2	ξ2	NOUN
ejpam-5245	56	29	1	1	NUM
ejpam-5245	56	30	ξ1	ξ1	NOUN
ejpam-5245	56	31	)	)	PUNCT
ejpam-5245	56	32	(	(	PUNCT
ejpam-5245	56	33	−	−	PUNCT
ejpam-5245	56	34	i	i	PRON
ejpam-5245	56	35	2	2	NUM
ejpam-5245	56	36	−1	−1	NOUN
ejpam-5245	56	37	0	0	NUM
ejpam-5245	56	38	−	−	NOUN
ejpam-5245	57	1	i	i	PRON
ejpam-5245	57	2	2	2	NUM
ejpam-5245	57	3	)	)	PUNCT
ejpam-5245	57	4	(	(	PUNCT
ejpam-5245	57	5	1	1	NUM
ejpam-5245	57	6	ξ1	ξ1	NOUN
ejpam-5245	57	7	0	0	NUM
ejpam-5245	57	8	−ξ2	−ξ2	NOUN
ejpam-5245	57	9	ξ1	ξ1	NOUN
ejpam-5245	57	10	)	)	PUNCT
ejpam-5245	57	11	=	=	PUNCT
ejpam-5245	58	1	(	(	PUNCT
ejpam-5245	58	2	ξ1ξ2	ξ1ξ2	X
ejpam-5245	58	3	−	−	NOUN
ejpam-5245	58	4	i	i	NOUN
ejpam-5245	58	5	2	2	NUM
ejpam-5245	58	6	−ξ21	−ξ21	PRON
ejpam-5245	58	7	ξ22	ξ22	NOUN
ejpam-5245	58	8	−ξ1ξ2	−ξ1ξ2	ADP
ejpam-5245	58	9	−	−	PROPN
ejpam-5245	58	10	i	i	PRON
ejpam-5245	58	11	2	2	NUM
ejpam-5245	58	12	,	,	PUNCT
ejpam-5245	58	13	)	)	PUNCT
ejpam-5245	58	14	(	(	PUNCT
ejpam-5245	58	15	7	7	X
ejpam-5245	58	16	)	)	PUNCT
ejpam-5245	58	17	that	that	PRON
ejpam-5245	58	18	is	be	AUX
ejpam-5245	58	19	,	,	PUNCT
ejpam-5245	58	20	cycle	cycle	NOUN
ejpam-5245	58	21	(	(	PUNCT
ejpam-5245	58	22	ξ22	ξ22	NUM
ejpam-5245	58	23	,	,	PUNCT
ejpam-5245	58	24	ξ1ξ2	ξ1ξ2	X
ejpam-5245	58	25	,	,	PUNCT
ejpam-5245	58	26	1	1	NUM
ejpam-5245	58	27	2	2	NUM
ejpam-5245	58	28	,	,	PUNCT
ejpam-5245	58	29	ξ	ξ	PROPN
ejpam-5245	58	30	2	2	NUM
ejpam-5245	58	31	1	1	NUM
ejpam-5245	58	32	)	)	PUNCT
ejpam-5245	58	33	with	with	ADP
ejpam-5245	58	34	the	the	DET
ejpam-5245	58	35	equation	equation	NOUN
ejpam-5245	58	36	ξ22u	ξ22u	ADP
ejpam-5245	58	37	2	2	NUM
ejpam-5245	58	38	+	+	NUM
ejpam-5245	58	39	ξ22v	ξ22v	X
ejpam-5245	58	40	2	2	NUM
ejpam-5245	58	41	−	−	PROPN
ejpam-5245	58	42	2ξ1ξ2u−	2ξ1ξ2u−	NUM
ejpam-5245	58	43	v	v	NOUN
ejpam-5245	58	44	+	+	CCONJ
ejpam-5245	58	45	ξ21	ξ21	NOUN
ejpam-5245	58	46	=	=	SYM
ejpam-5245	58	47	0	0	NUM
ejpam-5245	58	48	⇔	⇔	X
ejpam-5245	58	49	(	(	PUNCT
ejpam-5245	58	50	ξ22u	ξ22u	PROPN
ejpam-5245	58	51	2	2	NUM
ejpam-5245	58	52	−	−	NOUN
ejpam-5245	58	53	2ξ1ξ2u+	2ξ1ξ2u+	NOUN
ejpam-5245	58	54	ξ21	ξ21	NOUN
ejpam-5245	58	55	)	)	PUNCT
ejpam-5245	58	56	+	+	CCONJ
ejpam-5245	58	57	ξ22v	ξ22v	X
ejpam-5245	58	58	2	2	NUM
ejpam-5245	58	59	=	=	SYM
ejpam-5245	58	60	v	v	X
ejpam-5245	58	61	⇔	⇔	X
ejpam-5245	58	62	(	(	PUNCT
ejpam-5245	58	63	ξ2u−	ξ2u−	PROPN
ejpam-5245	58	64	ξ1	ξ1	PROPN
ejpam-5245	58	65	)	)	PUNCT
ejpam-5245	58	66	2	2	NUM
ejpam-5245	58	67	+	+	CCONJ
ejpam-5245	58	68	(	(	PUNCT
ejpam-5245	58	69	ξ2v	ξ2v	NOUN
ejpam-5245	58	70	)	)	PUNCT
ejpam-5245	58	71	2	2	NUM
ejpam-5245	58	72	=	=	SYM
ejpam-5245	58	73	v	v	ADP
ejpam-5245	58	74	⇔	⇔	PROPN
ejpam-5245	58	75	|(ξ2u−	|(ξ2u−	PROPN
ejpam-5245	58	76	ξ1	ξ1	NOUN
ejpam-5245	58	77	)	)	PUNCT
ejpam-5245	59	1	+	+	CCONJ
ejpam-5245	59	2	iξ2v|2	iξ2v|2	NOUN
ejpam-5245	59	3	=	=	SYM
ejpam-5245	59	4	v	v	ADP
ejpam-5245	59	5	⇔	⇔	X
ejpam-5245	59	6	|ξ2(u+	|ξ2(u+	NOUN
ejpam-5245	59	7	iv)−	iv)−	X
ejpam-5245	59	8	ξ1|2	ξ1|2	PROPN
ejpam-5245	59	9	=	=	SYM
ejpam-5245	59	10	v	v	ADP
ejpam-5245	59	11	⇔	⇔	PROPN
ejpam-5245	59	12	|ξ2z	|ξ2z	PROPN
ejpam-5245	59	13	−	−	NOUN
ejpam-5245	59	14	ξ1|2	ξ1|2	PROPN
ejpam-5245	59	15	=	=	SYM
ejpam-5245	59	16	v	v	NOUN
ejpam-5245	59	17	,	,	PUNCT
ejpam-5245	59	18	z	z	NOUN
ejpam-5245	59	19	=	=	SYM
ejpam-5245	59	20	u+	u+	NOUN
ejpam-5245	59	21	iv	iv	NUM
ejpam-5245	59	22	,	,	PUNCT
ejpam-5245	59	23	(	(	PUNCT
ejpam-5245	59	24	ξ1	ξ1	NOUN
ejpam-5245	59	25	,	,	PUNCT
ejpam-5245	59	26	ξ2	ξ2	ADJ
ejpam-5245	59	27	)	)	PUNCT
ejpam-5245	59	28	∈	∈	PROPN
ejpam-5245	59	29	r2	r2	PROPN
ejpam-5245	59	30	\	\	PROPN
ejpam-5245	59	31	{	{	PUNCT
ejpam-5245	59	32	0	0	NUM
ejpam-5245	59	33	}	}	PUNCT
ejpam-5245	59	34	.	.	PUNCT
ejpam-5245	60	1	(	(	PUNCT
ejpam-5245	60	2	8)	8)	NUM
ejpam-5245	60	3	therefore	therefore	ADV
ejpam-5245	60	4	,	,	PUNCT
ejpam-5245	60	5	the	the	DET
ejpam-5245	60	6	point	point	NOUN
ejpam-5245	60	7	(	(	PUNCT
ejpam-5245	60	8	ξ1	ξ1	NOUN
ejpam-5245	60	9	,	,	PUNCT
ejpam-5245	60	10	ξ2	ξ2	NOUN
ejpam-5245	60	11	)	)	PUNCT
ejpam-5245	60	12	of	of	ADP
ejpam-5245	60	13	the	the	DET
ejpam-5245	60	14	parabolic	parabolic	PROPN
ejpam-5245	60	15	upper	upper	ADJ
ejpam-5245	60	16	half	half	NOUN
ejpam-5245	60	17	plane	plane	NOUN
ejpam-5245	60	18	sl2(r)/n	sl2(r)/n	NOUN
ejpam-5245	60	19	parametrizes	parametrize	VERB
ejpam-5245	60	20	the	the	DET
ejpam-5245	60	21	space	space	NOUN
ejpam-5245	60	22	of	of	ADP
ejpam-5245	60	23	horocycles	horocycle	NOUN
ejpam-5245	60	24	.	.	PUNCT
ejpam-5245	61	1	denote	denote	VERB
ejpam-5245	61	2	by	by	ADP
ejpam-5245	61	3	h(ξ	h(ξ	NOUN
ejpam-5245	61	4	)	)	PUNCT
ejpam-5245	61	5	=	=	SYM
ejpam-5245	61	6	h(ξ1	h(ξ1	ADJ
ejpam-5245	61	7	,	,	PUNCT
ejpam-5245	61	8	ξ2	ξ2	NOUN
ejpam-5245	61	9	)	)	PUNCT
ejpam-5245	61	10	the	the	DET
ejpam-5245	61	11	horocycle	horocycle	NOUN
ejpam-5245	61	12	given	give	VERB
ejpam-5245	61	13	by	by	ADP
ejpam-5245	61	14	(	(	PUNCT
ejpam-5245	61	15	8)	8)	NUM
ejpam-5245	61	16	.	.	PUNCT
ejpam-5245	62	1	every	every	DET
ejpam-5245	62	2	horocycle	horocycle	NOUN
ejpam-5245	62	3	has	have	VERB
ejpam-5245	62	4	a	a	DET
ejpam-5245	62	5	unique	unique	ADJ
ejpam-5245	62	6	common	common	ADJ
ejpam-5245	62	7	point	point	NOUN
ejpam-5245	62	8	with	with	ADP
ejpam-5245	62	9	the	the	DET
ejpam-5245	62	10	real	real	ADJ
ejpam-5245	62	11	axis	axis	NOUN
ejpam-5245	62	12	,	,	PUNCT
ejpam-5245	62	13	which	which	PRON
ejpam-5245	62	14	is	be	AUX
ejpam-5245	62	15	called	call	VERB
ejpam-5245	62	16	the	the	DET
ejpam-5245	62	17	center	center	NOUN
ejpam-5245	62	18	of	of	ADP
ejpam-5245	62	19	the	the	DET
ejpam-5245	62	20	horocycle	horocycle	NOUN
ejpam-5245	62	21	.	.	PUNCT
ejpam-5245	63	1	horocycles	horocycle	NOUN
ejpam-5245	63	2	with	with	ADP
ejpam-5245	63	3	common	common	ADJ
ejpam-5245	63	4	center	center	NOUN
ejpam-5245	63	5	are	be	AUX
ejpam-5245	63	6	said	say	VERB
ejpam-5245	63	7	to	to	PART
ejpam-5245	63	8	be	be	AUX
ejpam-5245	63	9	parallel	parallel	VERB
ejpam-5245	63	10	.	.	PUNCT
ejpam-5245	64	1	note	note	VERB
ejpam-5245	64	2	that	that	SCONJ
ejpam-5245	64	3	a	a	DET
ejpam-5245	64	4	horocycle	horocycle	NOUN
ejpam-5245	64	5	h(ξ1	h(ξ1	NOUN
ejpam-5245	64	6	,	,	PUNCT
ejpam-5245	64	7	ξ2	ξ2	NOUN
ejpam-5245	64	8	)	)	PUNCT
ejpam-5245	64	9	is	be	AUX
ejpam-5245	64	10	tangent	tangent	ADJ
ejpam-5245	64	11	to	to	ADP
ejpam-5245	64	12	the	the	DET
ejpam-5245	64	13	real	real	ADJ
ejpam-5245	64	14	axis	axis	NOUN
ejpam-5245	64	15	at	at	ADP
ejpam-5245	64	16	the	the	DET
ejpam-5245	64	17	point	point	NOUN
ejpam-5245	64	18	ξ1	ξ1	NOUN
ejpam-5245	64	19	ξ2	ξ2	NOUN
ejpam-5245	64	20	,	,	PUNCT
ejpam-5245	64	21	hence	hence	ADV
ejpam-5245	64	22	every	every	DET
ejpam-5245	64	23	parallel	parallel	ADJ
ejpam-5245	64	24	horocycle	horocycle	NOUN
ejpam-5245	64	25	is	be	AUX
ejpam-5245	64	26	of	of	ADP
ejpam-5245	64	27	the	the	DET
ejpam-5245	64	28	form	form	NOUN
ejpam-5245	64	29	{	{	PUNCT
ejpam-5245	64	30	h(λξ1	h(λξ1	PROPN
ejpam-5245	64	31	,	,	PUNCT
ejpam-5245	64	32	λξ2	λξ2	PROPN
ejpam-5245	64	33	)	)	PUNCT
ejpam-5245	64	34	:	:	PUNCT
ejpam-5245	65	1	0	0	PUNCT
ejpam-5245	65	2	<	<	X
ejpam-5245	65	3	λ	λ	X
ejpam-5245	65	4	<	<	X
ejpam-5245	65	5	∞	∞	NUM
ejpam-5245	65	6	}	}	PUNCT
ejpam-5245	65	7	for	for	ADP
ejpam-5245	65	8	some	some	DET
ejpam-5245	65	9	chosen	choose	VERB
ejpam-5245	65	10	(	(	PUNCT
ejpam-5245	65	11	ξ1	ξ1	NOUN
ejpam-5245	65	12	,	,	PUNCT
ejpam-5245	65	13	ξ2	ξ2	NOUN
ejpam-5245	65	14	)	)	PUNCT
ejpam-5245	66	1	[	[	X
ejpam-5245	66	2	3	3	NUM
ejpam-5245	66	3	]	]	PUNCT
ejpam-5245	66	4	,	,	PUNCT
ejpam-5245	66	5	chap	chap	NOUN
ejpam-5245	66	6	.	.	PUNCT
ejpam-5245	67	1	3	3	NUM
ejpam-5245	67	2	,	,	PUNCT
ejpam-5245	67	3	§	§	PROPN
ejpam-5245	67	4	1.2	1.2	NUM
ejpam-5245	67	5	.	.	PUNCT
ejpam-5245	68	1	now	now	ADV
ejpam-5245	68	2	,	,	PUNCT
ejpam-5245	68	3	in	in	ADP
ejpam-5245	68	4	order	order	NOUN
ejpam-5245	68	5	to	to	PART
ejpam-5245	68	6	find	find	VERB
ejpam-5245	68	7	the	the	DET
ejpam-5245	68	8	invariant	invariant	ADJ
ejpam-5245	68	9	distance	distance	NOUN
ejpam-5245	68	10	of	of	ADP
ejpam-5245	68	11	a	a	DET
ejpam-5245	68	12	point	point	NOUN
ejpam-5245	68	13	z	z	NOUN
ejpam-5245	68	14	in	in	ADP
ejpam-5245	68	15	the	the	DET
ejpam-5245	68	16	upper	upper	ADJ
ejpam-5245	68	17	half	half	ADJ
ejpam-5245	68	18	plane	plane	NOUN
ejpam-5245	68	19	to	to	ADP
ejpam-5245	68	20	the	the	DET
ejpam-5245	68	21	horocycle	horocycle	NOUN
ejpam-5245	68	22	h(ξ	h(ξ	PROPN
ejpam-5245	68	23	)	)	PUNCT
ejpam-5245	68	24	,	,	PUNCT
ejpam-5245	68	25	first	first	ADV
ejpam-5245	68	26	we	we	PRON
ejpam-5245	68	27	calculate	calculate	VERB
ejpam-5245	68	28	the	the	DET
ejpam-5245	68	29	distance	distance	NOUN
ejpam-5245	68	30	from	from	ADP
ejpam-5245	68	31	a	a	DET
ejpam-5245	68	32	point	point	NOUN
ejpam-5245	68	33	z1	z1	NOUN
ejpam-5245	68	34	=	=	SYM
ejpam-5245	68	35	(	(	PUNCT
ejpam-5245	68	36	u	u	NOUN
ejpam-5245	68	37	,	,	PUNCT
ejpam-5245	68	38	v	v	NOUN
ejpam-5245	68	39	)	)	PUNCT
ejpam-5245	68	40	∈	∈	PROPN
ejpam-5245	68	41	h(λξ1	h(λξ1	PROPN
ejpam-5245	68	42	,	,	PUNCT
ejpam-5245	68	43	λξ2	λξ2	PROPN
ejpam-5245	68	44	)	)	PUNCT
ejpam-5245	68	45	to	to	ADP
ejpam-5245	68	46	a	a	DET
ejpam-5245	68	47	horocycle	horocycle	NOUN
ejpam-5245	68	48	h(ξ1	h(ξ1	NOUN
ejpam-5245	68	49	,	,	PUNCT
ejpam-5245	68	50	ξ2	ξ2	NOUN
ejpam-5245	68	51	)	)	PUNCT
ejpam-5245	68	52	.	.	PUNCT
ejpam-5245	69	1	the	the	DET
ejpam-5245	69	2	point	point	NOUN
ejpam-5245	69	3	z2	z2	PROPN
ejpam-5245	69	4	=	=	SYM
ejpam-5245	69	5	(	(	PUNCT
ejpam-5245	69	6	u	u	NOUN
ejpam-5245	69	7	,	,	PUNCT
ejpam-5245	69	8	λ−2v	λ−2v	PROPN
ejpam-5245	69	9	)	)	PUNCT
ejpam-5245	69	10	is	be	AUX
ejpam-5245	69	11	in	in	ADP
ejpam-5245	69	12	the	the	DET
ejpam-5245	69	13	horocycle	horocycle	NOUN
ejpam-5245	69	14	h(ξ1	h(ξ1	PROPN
ejpam-5245	69	15	,	,	PUNCT
ejpam-5245	69	16	ξ2	ξ2	ADJ
ejpam-5245	69	17	):	):	PUNCT
ejpam-5245	69	18	|λξ2z	|λξ2z	PROPN
ejpam-5245	69	19	−	−	NOUN
ejpam-5245	69	20	λξ1|2	λξ1|2	ADJ
ejpam-5245	69	21	=	=	X
ejpam-5245	69	22	v	v	ADJ
ejpam-5245	69	23	⇒	⇒	NOUN
ejpam-5245	69	24	|ξ2z	|ξ2z	NUM
ejpam-5245	70	1	−	−	NOUN
ejpam-5245	70	2	ξ1|2	ξ1|2	PROPN
ejpam-5245	70	3	=	=	SYM
ejpam-5245	70	4	λ−2v	λ−2v	PROPN
ejpam-5245	70	5	.	.	PUNCT
ejpam-5245	70	6	f.	f.	PROPN
ejpam-5245	70	7	a.	a.	PROPN
ejpam-5245	70	8	alabbad	alabbad	PROPN
ejpam-5245	70	9	/	/	SYM
ejpam-5245	70	10	eur	eur	PROPN
ejpam-5245	70	11	.	.	PUNCT
ejpam-5245	71	1	j.	j.	PROPN
ejpam-5245	71	2	pure	pure	PROPN
ejpam-5245	71	3	appl	appl	PROPN
ejpam-5245	71	4	.	.	PROPN
ejpam-5245	71	5	math	math	PROPN
ejpam-5245	71	6	,	,	PUNCT
ejpam-5245	71	7	17	17	NUM
ejpam-5245	71	8	(	(	PUNCT
ejpam-5245	71	9	3	3	NUM
ejpam-5245	71	10	)	)	PUNCT
ejpam-5245	71	11	(	(	PUNCT
ejpam-5245	71	12	2024	2024	NUM
ejpam-5245	71	13	)	)	PUNCT
ejpam-5245	71	14	,	,	PUNCT
ejpam-5245	71	15	2092	2092	NUM
ejpam-5245	71	16	-	-	SYM
ejpam-5245	71	17	2105	2105	NUM
ejpam-5245	71	18	2095	2095	NUM
ejpam-5245	71	19	note	note	NOUN
ejpam-5245	71	20	that	that	SCONJ
ejpam-5245	71	21	the	the	DET
ejpam-5245	71	22	points	point	NOUN
ejpam-5245	71	23	z1	z1	NOUN
ejpam-5245	71	24	and	and	CCONJ
ejpam-5245	71	25	z2	z2	NOUN
ejpam-5245	71	26	are	be	AUX
ejpam-5245	71	27	on	on	ADP
ejpam-5245	71	28	the	the	DET
ejpam-5245	71	29	same	same	ADJ
ejpam-5245	71	30	vertical	vertical	ADJ
ejpam-5245	71	31	line	line	NOUN
ejpam-5245	71	32	,	,	PUNCT
ejpam-5245	71	33	thus	thus	ADV
ejpam-5245	71	34	the	the	DET
ejpam-5245	71	35	distance	distance	NOUN
ejpam-5245	71	36	between	between	ADP
ejpam-5245	71	37	them	they	PRON
ejpam-5245	71	38	is	be	AUX
ejpam-5245	71	39	∣∣∣∣∫	∣∣∣∣∫	DET
ejpam-5245	71	40	v	v	NUM
ejpam-5245	71	41	vλ−2	vλ−2	PROPN
ejpam-5245	71	42	1	1	NUM
ejpam-5245	71	43	y	y	PROPN
ejpam-5245	71	44	dy	dy	NOUN
ejpam-5245	71	45	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5245	71	46	=	=	SYM
ejpam-5245	71	47	∣∣log	∣∣log	PROPN
ejpam-5245	71	48	v	v	NOUN
ejpam-5245	71	49	−	−	NOUN
ejpam-5245	71	50	log	log	NOUN
ejpam-5245	71	51	vλ−2	vλ−2	PROPN
ejpam-5245	71	52	∣∣	∣∣	X
ejpam-5245	71	53	=	=	SYM
ejpam-5245	71	54	2	2	NUM
ejpam-5245	71	55	|log	|log	X
ejpam-5245	71	56	λ|	λ|	PROPN
ejpam-5245	71	57	.	.	PUNCT
ejpam-5245	72	1	(	(	PUNCT
ejpam-5245	72	2	9	9	NUM
ejpam-5245	72	3	)	)	PUNCT
ejpam-5245	72	4	thus	thus	ADV
ejpam-5245	72	5	,	,	PUNCT
ejpam-5245	72	6	all	all	DET
ejpam-5245	72	7	points	point	NOUN
ejpam-5245	72	8	of	of	ADP
ejpam-5245	72	9	the	the	DET
ejpam-5245	72	10	horocycle	horocycle	NOUN
ejpam-5245	72	11	h(λξ1	h(λξ1	PROPN
ejpam-5245	72	12	,	,	PUNCT
ejpam-5245	72	13	λξ2	λξ2	PROPN
ejpam-5245	72	14	)	)	PUNCT
ejpam-5245	72	15	are	be	AUX
ejpam-5245	72	16	placed	place	VERB
ejpam-5245	72	17	at	at	ADP
ejpam-5245	72	18	the	the	DET
ejpam-5245	72	19	same	same	ADJ
ejpam-5245	72	20	distance	distance	NOUN
ejpam-5245	72	21	2	2	NUM
ejpam-5245	72	22	|log	|log	NOUN
ejpam-5245	72	23	λ|	λ|	PROPN
ejpam-5245	72	24	from	from	ADP
ejpam-5245	72	25	the	the	DET
ejpam-5245	72	26	parallel	parallel	ADJ
ejpam-5245	72	27	horocycle	horocycle	NOUN
ejpam-5245	72	28	h(ξ1	h(ξ1	PROPN
ejpam-5245	72	29	,	,	PUNCT
ejpam-5245	72	30	ξ2	ξ2	NOUN
ejpam-5245	72	31	)	)	PUNCT
ejpam-5245	72	32	.	.	PUNCT
ejpam-5245	73	1	then	then	ADV
ejpam-5245	73	2	,	,	PUNCT
ejpam-5245	73	3	the	the	DET
ejpam-5245	73	4	signed	sign	VERB
ejpam-5245	73	5	distance	distance	NOUN
ejpam-5245	73	6	from	from	ADP
ejpam-5245	73	7	a	a	DET
ejpam-5245	73	8	point	point	NOUN
ejpam-5245	73	9	z	z	NOUN
ejpam-5245	73	10	∈	∈	PROPN
ejpam-5245	73	11	h(λξ	h(λξ	NOUN
ejpam-5245	73	12	)	)	PUNCT
ejpam-5245	73	13	to	to	ADP
ejpam-5245	73	14	a	a	DET
ejpam-5245	73	15	horocycle	horocycle	NOUN
ejpam-5245	73	16	h(ξ	h(ξ	PROPN
ejpam-5245	73	17	)	)	PUNCT
ejpam-5245	73	18	is	be	AUX
ejpam-5245	73	19	ϱ(z	ϱ(z	NOUN
ejpam-5245	73	20	;	;	PUNCT
ejpam-5245	73	21	ξ	ξ	X
ejpam-5245	73	22	)	)	PUNCT
ejpam-5245	73	23	=	=	SYM
ejpam-5245	74	1	−2	−2	NOUN
ejpam-5245	74	2	log	log	NOUN
ejpam-5245	74	3	λ	λ	X
ejpam-5245	74	4	=	=	NOUN
ejpam-5245	74	5	log	log	PROPN
ejpam-5245	74	6	(	(	PUNCT
ejpam-5245	74	7	v−1|ξ2z	v−1|ξ2z	NOUN
ejpam-5245	74	8	−	−	PROPN
ejpam-5245	74	9	ξ1|2	ξ1|2	PROPN
ejpam-5245	74	10	)	)	PUNCT
ejpam-5245	74	11	,	,	PUNCT
ejpam-5245	74	12	(	(	PUNCT
ejpam-5245	74	13	10	10	NUM
ejpam-5245	74	14	)	)	PUNCT
ejpam-5245	74	15	because	because	SCONJ
ejpam-5245	74	16	λ−2	λ−2	PROPN
ejpam-5245	74	17	=	=	PUNCT
ejpam-5245	74	18	v−1|ξ2z	v−1|ξ2z	NOUN
ejpam-5245	74	19	−	−	PROPN
ejpam-5245	74	20	ξ1|2	ξ1|2	PROPN
ejpam-5245	74	21	.	.	PROPN
ejpam-5245	74	22	2	2	NUM
ejpam-5245	74	23	.	.	NUM
ejpam-5245	74	24	induced	induce	VERB
ejpam-5245	74	25	representations	representation	NOUN
ejpam-5245	74	26	of	of	ADP
ejpam-5245	74	27	the	the	DET
ejpam-5245	74	28	group	group	NOUN
ejpam-5245	74	29	sl2(r	sl2(r	PROPN
ejpam-5245	74	30	)	)	PUNCT
ejpam-5245	74	31	(	(	PUNCT
ejpam-5245	74	32	i	i	NOUN
ejpam-5245	74	33	)	)	PUNCT
ejpam-5245	74	34	for	for	ADP
ejpam-5245	74	35	the	the	DET
ejpam-5245	74	36	subgroupk	subgroupk	NOUN
ejpam-5245	74	37	=	=	PRON
ejpam-5245	74	38	{	{	PUNCT
ejpam-5245	74	39	(	(	PUNCT
ejpam-5245	74	40	cos	cos	PROPN
ejpam-5245	74	41	t	t	PROPN
ejpam-5245	74	42	sin	sin	NOUN
ejpam-5245	74	43	t	t	PROPN
ejpam-5245	74	44	−	−	PROPN
ejpam-5245	74	45	sin	sin	PROPN
ejpam-5245	74	46	t	t	PROPN
ejpam-5245	74	47	cos	cos	PROPN
ejpam-5245	74	48	t	t	PROPN
ejpam-5245	74	49	)	)	PUNCT
ejpam-5245	74	50	:	:	PUNCT
ejpam-5245	75	1	t	t	PROPN
ejpam-5245	75	2	∈	∈	PROPN
ejpam-5245	75	3	r	r	NOUN
ejpam-5245	75	4	}	}	PUNCT
ejpam-5245	75	5	,	,	PUNCT
ejpam-5245	75	6	the	the	DET
ejpam-5245	75	7	homogeneous	homogeneous	ADJ
ejpam-5245	75	8	space	space	NOUN
ejpam-5245	75	9	sl2(r)/k	sl2(r)/k	NOUN
ejpam-5245	75	10	are	be	AUX
ejpam-5245	75	11	parametrised	parametrise	VERB
ejpam-5245	75	12	by	by	ADP
ejpam-5245	75	13	points	point	NOUN
ejpam-5245	75	14	of	of	ADP
ejpam-5245	75	15	the	the	DET
ejpam-5245	75	16	upper	upper	ADJ
ejpam-5245	75	17	half	half	ADJ
ejpam-5245	75	18	-	-	PUNCT
ejpam-5245	75	19	plane	plane	NOUN
ejpam-5245	75	20	h+	h+	NOUN
ejpam-5245	75	21	.	.	PUNCT
ejpam-5245	76	1	the	the	DET
ejpam-5245	76	2	respective	respective	ADJ
ejpam-5245	76	3	maps	map	NOUN
ejpam-5245	76	4	are	be	AUX
ejpam-5245	76	5	:	:	PUNCT
ejpam-5245	76	6	p	p	X
ejpam-5245	76	7	(	(	PUNCT
ejpam-5245	76	8	a	a	DET
ejpam-5245	76	9	b	b	NOUN
ejpam-5245	76	10	c	c	NOUN
ejpam-5245	76	11	d	d	NOUN
ejpam-5245	76	12	)	)	PUNCT
ejpam-5245	77	1	=	=	SYM
ejpam-5245	77	2	(	(	PUNCT
ejpam-5245	77	3	bd+	bd+	PROPN
ejpam-5245	77	4	ac	ac	PROPN
ejpam-5245	77	5	c2	c2	PROPN
ejpam-5245	77	6	+	+	CCONJ
ejpam-5245	77	7	d2	d2	PROPN
ejpam-5245	77	8	,	,	PUNCT
ejpam-5245	77	9	1	1	NUM
ejpam-5245	77	10	c2	c2	PROPN
ejpam-5245	77	11	+	+	CCONJ
ejpam-5245	77	12	d2	d2	PROPN
ejpam-5245	77	13	)	)	PUNCT
ejpam-5245	77	14	,	,	PUNCT
ejpam-5245	77	15	s(u	s(u	PROPN
ejpam-5245	77	16	,	,	PUNCT
ejpam-5245	77	17	v	v	NOUN
ejpam-5245	77	18	)	)	PUNCT
ejpam-5245	77	19	=	=	SYM
ejpam-5245	77	20	1√	1√	NUM
ejpam-5245	77	21	v	v	ADP
ejpam-5245	77	22	(	(	PUNCT
ejpam-5245	77	23	v	v	NUM
ejpam-5245	77	24	u	u	NOUN
ejpam-5245	77	25	0	0	NUM
ejpam-5245	77	26	1	1	NUM
ejpam-5245	77	27	)	)	PUNCT
ejpam-5245	77	28	,	,	PUNCT
ejpam-5245	77	29	r	r	NOUN
ejpam-5245	77	30	(	(	PUNCT
ejpam-5245	77	31	a	a	DET
ejpam-5245	77	32	b	b	NOUN
ejpam-5245	77	33	c	c	NOUN
ejpam-5245	77	34	d	d	NOUN
ejpam-5245	77	35	)	)	PUNCT
ejpam-5245	77	36	=	=	SYM
ejpam-5245	77	37	1√	1√	PROPN
ejpam-5245	77	38	c2	c2	PROPN
ejpam-5245	77	39	+	+	CCONJ
ejpam-5245	77	40	d2	d2	PROPN
ejpam-5245	77	41	(	(	PUNCT
ejpam-5245	77	42	d	d	NOUN
ejpam-5245	77	43	−c	−c	NOUN
ejpam-5245	77	44	c	c	PROPN
ejpam-5245	77	45	d	d	NOUN
ejpam-5245	77	46	)	)	PUNCT
ejpam-5245	77	47	.	.	PUNCT
ejpam-5245	78	1	(	(	PUNCT
ejpam-5245	78	2	11	11	NUM
ejpam-5245	78	3	)	)	PUNCT
ejpam-5245	78	4	the	the	DET
ejpam-5245	78	5	decomposition	decomposition	NOUN
ejpam-5245	78	6	defined	define	VERB
ejpam-5245	78	7	by	by	ADP
ejpam-5245	78	8	the	the	DET
ejpam-5245	78	9	formula	formula	NOUN
ejpam-5245	78	10	g	g	PROPN
ejpam-5245	78	11	=	=	SYM
ejpam-5245	78	12	s(p(g))r(g	s(p(g))r(g	NOUN
ejpam-5245	78	13	)	)	PUNCT
ejpam-5245	78	14	takes	take	VERB
ejpam-5245	78	15	the	the	DET
ejpam-5245	78	16	form	form	NOUN
ejpam-5245	78	17	:(	:(	PUNCT
ejpam-5245	78	18	a	a	DET
ejpam-5245	78	19	b	b	NOUN
ejpam-5245	78	20	c	c	NOUN
ejpam-5245	78	21	d	d	NOUN
ejpam-5245	78	22	)	)	PUNCT
ejpam-5245	79	1	=	=	SYM
ejpam-5245	79	2	1	1	NUM
ejpam-5245	79	3	c2	c2	PROPN
ejpam-5245	79	4	+	+	CCONJ
ejpam-5245	79	5	d2	d2	PROPN
ejpam-5245	79	6	(	(	PUNCT
ejpam-5245	79	7	1	1	NUM
ejpam-5245	79	8	bd+	bd+	NOUN
ejpam-5245	79	9	ac	ac	PROPN
ejpam-5245	79	10	0	0	PROPN
ejpam-5245	80	1	c2	c2	PROPN
ejpam-5245	80	2	+	+	CCONJ
ejpam-5245	80	3	d2	d2	PROPN
ejpam-5245	80	4	)	)	PUNCT
ejpam-5245	80	5	(	(	PUNCT
ejpam-5245	80	6	d	d	NOUN
ejpam-5245	80	7	−c	−c	NOUN
ejpam-5245	80	8	c	c	PROPN
ejpam-5245	80	9	d	d	NOUN
ejpam-5245	80	10	)	)	PUNCT
ejpam-5245	80	11	.	.	PUNCT
ejpam-5245	81	1	(	(	PUNCT
ejpam-5245	81	2	12	12	NUM
ejpam-5245	81	3	)	)	PUNCT
ejpam-5245	81	4	the	the	DET
ejpam-5245	81	5	sl2(r)-action	sl2(r)-action	NOUN
ejpam-5245	81	6	defined	define	VERB
ejpam-5245	81	7	by	by	ADP
ejpam-5245	81	8	the	the	DET
ejpam-5245	81	9	formula	formula	NOUN
ejpam-5245	81	10	g	g	NOUN
ejpam-5245	81	11	·	·	PUNCT
ejpam-5245	81	12	x	x	SYM
ejpam-5245	82	1	=	=	PUNCT
ejpam-5245	82	2	p(g	p(g	PROPN
ejpam-5245	82	3	∗	∗	X
ejpam-5245	82	4	s(x	s(x	PROPN
ejpam-5245	82	5	)	)	PUNCT
ejpam-5245	82	6	)	)	PUNCT
ejpam-5245	82	7	takes	take	VERB
ejpam-5245	82	8	the	the	DET
ejpam-5245	82	9	form	form	NOUN
ejpam-5245	82	10	:(	:(	PUNCT
ejpam-5245	82	11	a	a	DET
ejpam-5245	82	12	b	b	NOUN
ejpam-5245	82	13	c	c	NOUN
ejpam-5245	82	14	d	d	PROPN
ejpam-5245	82	15	)	)	PUNCT
ejpam-5245	82	16	:	:	PUNCT
ejpam-5245	82	17	(	(	PUNCT
ejpam-5245	82	18	u	u	NOUN
ejpam-5245	82	19	,	,	PUNCT
ejpam-5245	82	20	v	v	NOUN
ejpam-5245	82	21	)	)	PUNCT
ejpam-5245	82	22	7→	7→	NUM
ejpam-5245	82	23	(	(	PUNCT
ejpam-5245	82	24	(	(	PUNCT
ejpam-5245	82	25	au+	au+	PROPN
ejpam-5245	82	26	b)(cu+	b)(cu+	NOUN
ejpam-5245	82	27	d	d	NOUN
ejpam-5245	82	28	)	)	PUNCT
ejpam-5245	82	29	+	+	NUM
ejpam-5245	82	30	cav2	cav2	NOUN
ejpam-5245	82	31	(	(	PUNCT
ejpam-5245	82	32	cu+	cu+	NOUN
ejpam-5245	82	33	d)2	d)2	PROPN
ejpam-5245	82	34	+	+	CCONJ
ejpam-5245	83	1	(	(	PUNCT
ejpam-5245	83	2	cv)2	cv)2	PROPN
ejpam-5245	83	3	,	,	PUNCT
ejpam-5245	83	4	v	v	PROPN
ejpam-5245	83	5	(	(	PUNCT
ejpam-5245	83	6	cu+	cu+	NOUN
ejpam-5245	83	7	d)2	d)2	PROPN
ejpam-5245	83	8	+	+	CCONJ
ejpam-5245	83	9	(	(	PUNCT
ejpam-5245	83	10	cv)2	cv)2	PROPN
ejpam-5245	83	11	)	)	PUNCT
ejpam-5245	83	12	.	.	PUNCT
ejpam-5245	84	1	(	(	PUNCT
ejpam-5245	84	2	13	13	NUM
ejpam-5245	84	3	)	)	PUNCT
ejpam-5245	84	4	this	this	DET
ejpam-5245	84	5	map	map	NOUN
ejpam-5245	84	6	preserves	preserve	VERB
ejpam-5245	84	7	the	the	DET
ejpam-5245	84	8	upper	upper	ADJ
ejpam-5245	84	9	half	half	ADJ
ejpam-5245	84	10	plane	plane	NOUN
ejpam-5245	84	11	v	v	ADP
ejpam-5245	84	12	>	>	X
ejpam-5245	84	13	0	0	NUM
ejpam-5245	84	14	.	.	PUNCT
ejpam-5245	85	1	we	we	PRON
ejpam-5245	85	2	can	can	AUX
ejpam-5245	85	3	simplify	simplify	VERB
ejpam-5245	85	4	this	this	DET
ejpam-5245	85	5	map	map	NOUN
ejpam-5245	85	6	as	as	ADP
ejpam-5245	85	7	a	a	DET
ejpam-5245	85	8	linear	linear	ADJ
ejpam-5245	85	9	-	-	PUNCT
ejpam-5245	85	10	fractional	fractional	ADJ
ejpam-5245	85	11	transformation	transformation	NOUN
ejpam-5245	85	12	with	with	ADP
ejpam-5245	85	13	the	the	DET
ejpam-5245	85	14	complex	complex	ADJ
ejpam-5245	85	15	number	number	NOUN
ejpam-5245	85	16	unit	unit	NOUN
ejpam-5245	85	17	i2	i2	PROPN
ejpam-5245	85	18	=	=	PROPN
ejpam-5245	85	19	−1	−1	PROPN
ejpam-5245	85	20	:(	:(	PUNCT
ejpam-5245	85	21	a	a	DET
ejpam-5245	85	22	b	b	NOUN
ejpam-5245	85	23	c	c	NOUN
ejpam-5245	85	24	d	d	PROPN
ejpam-5245	85	25	)	)	PUNCT
ejpam-5245	85	26	:	:	PUNCT
ejpam-5245	86	1	w	w	X
ejpam-5245	86	2	7→	7→	NUM
ejpam-5245	86	3	aw	aw	INTJ
ejpam-5245	87	1	+	+	NUM
ejpam-5245	87	2	b	b	X
ejpam-5245	87	3	cw	cw	NOUN
ejpam-5245	87	4	+	+	CCONJ
ejpam-5245	87	5	d	d	NOUN
ejpam-5245	87	6	,	,	PUNCT
ejpam-5245	87	7	wherew	wherew	NOUN
ejpam-5245	87	8	=	=	SYM
ejpam-5245	87	9	u+	u+	NUM
ejpam-5245	87	10	iv	iv	NUM
ejpam-5245	87	11	.	.	PUNCT
ejpam-5245	88	1	(	(	PUNCT
ejpam-5245	88	2	14	14	NUM
ejpam-5245	88	3	)	)	PUNCT
ejpam-5245	88	4	f.	f.	NOUN
ejpam-5245	88	5	a.	a.	PROPN
ejpam-5245	88	6	alabbad	alabbad	PROPN
ejpam-5245	88	7	/	/	SYM
ejpam-5245	88	8	eur	eur	PROPN
ejpam-5245	88	9	.	.	PUNCT
ejpam-5245	89	1	j.	j.	PROPN
ejpam-5245	89	2	pure	pure	PROPN
ejpam-5245	89	3	appl	appl	PROPN
ejpam-5245	89	4	.	.	PROPN
ejpam-5245	89	5	math	math	PROPN
ejpam-5245	89	6	,	,	PUNCT
ejpam-5245	89	7	17	17	NUM
ejpam-5245	89	8	(	(	PUNCT
ejpam-5245	89	9	3	3	NUM
ejpam-5245	89	10	)	)	PUNCT
ejpam-5245	89	11	(	(	PUNCT
ejpam-5245	89	12	2024	2024	NUM
ejpam-5245	89	13	)	)	PUNCT
ejpam-5245	89	14	,	,	PUNCT
ejpam-5245	89	15	2092	2092	NUM
ejpam-5245	89	16	-	-	SYM
ejpam-5245	89	17	2105	2105	NUM
ejpam-5245	89	18	2096	2096	NUM
ejpam-5245	89	19	the	the	DET
ejpam-5245	89	20	left	leave	VERB
ejpam-5245	89	21	invariant	invariant	ADJ
ejpam-5245	89	22	measure	measure	NOUN
ejpam-5245	89	23	on	on	ADP
ejpam-5245	89	24	the	the	DET
ejpam-5245	89	25	upper	upper	ADJ
ejpam-5245	89	26	half	half	ADJ
ejpam-5245	89	27	plane	plane	NOUN
ejpam-5245	89	28	h+	h+	PUNCT
ejpam-5245	89	29	is	be	AUX
ejpam-5245	89	30	equal	equal	ADJ
ejpam-5245	89	31	to	to	ADP
ejpam-5245	89	32	dµ(w	dµ(w	PUNCT
ejpam-5245	89	33	)	)	PUNCT
ejpam-5245	90	1	=	=	PUNCT
ejpam-5245	90	2	dudv	dudv	ADP
ejpam-5245	90	3	v2	v2	PROPN
ejpam-5245	90	4	,	,	PUNCT
ejpam-5245	90	5	w	w	NOUN
ejpam-5245	90	6	=	=	SYM
ejpam-5245	90	7	u+	u+	NUM
ejpam-5245	90	8	iv	iv	NUM
ejpam-5245	90	9	.	.	PUNCT
ejpam-5245	91	1	(	(	PUNCT
ejpam-5245	91	2	15	15	NUM
ejpam-5245	91	3	)	)	PUNCT
ejpam-5245	91	4	the	the	DET
ejpam-5245	91	5	character	character	NOUN
ejpam-5245	91	6	χk	χk	PROPN
ejpam-5245	91	7	(	(	PUNCT
ejpam-5245	91	8	cos	cos	PROPN
ejpam-5245	91	9	t	t	PROPN
ejpam-5245	91	10	sin	sin	NOUN
ejpam-5245	91	11	t	t	PROPN
ejpam-5245	91	12	−	−	PROPN
ejpam-5245	91	13	sin	sin	PROPN
ejpam-5245	91	14	t	t	PROPN
ejpam-5245	91	15	cos	cos	PROPN
ejpam-5245	91	16	t	t	PROPN
ejpam-5245	91	17	)	)	PUNCT
ejpam-5245	92	1	=	=	SYM
ejpam-5245	92	2	e−ikt	e−ikt	PROPN
ejpam-5245	92	3	,	,	PUNCT
ejpam-5245	92	4	k	k	PROPN
ejpam-5245	92	5	∈	∈	PROPN
ejpam-5245	92	6	z	z	PROPN
ejpam-5245	92	7	of	of	ADP
ejpam-5245	92	8	k	k	PROPN
ejpam-5245	92	9	,	,	PUNCT
ejpam-5245	92	10	induces	induce	VERB
ejpam-5245	92	11	a	a	DET
ejpam-5245	92	12	linear	linear	ADJ
ejpam-5245	92	13	representation	representation	NOUN
ejpam-5245	92	14	ρk	ρk	ADP
ejpam-5245	92	15	on	on	ADP
ejpam-5245	92	16	the	the	DET
ejpam-5245	92	17	space	space	NOUN
ejpam-5245	92	18	of	of	ADP
ejpam-5245	92	19	square	square	ADJ
ejpam-5245	92	20	integrable	integrable	ADJ
ejpam-5245	92	21	functions	function	NOUN
ejpam-5245	92	22	,	,	PUNCT
ejpam-5245	92	23	which	which	PRON
ejpam-5245	92	24	is	be	AUX
ejpam-5245	92	25	given	give	VERB
ejpam-5245	92	26	by	by	ADP
ejpam-5245	92	27	the	the	DET
ejpam-5245	92	28	formula	formula	NOUN
ejpam-5245	92	29	:	:	PUNCT
ejpam-5245	93	1	[	[	X
ejpam-5245	93	2	ρk(g)f	ρk(g)f	X
ejpam-5245	93	3	]	]	X
ejpam-5245	93	4	(	(	PUNCT
ejpam-5245	93	5	w	w	NOUN
ejpam-5245	93	6	)	)	PUNCT
ejpam-5245	93	7	=	=	PRON
ejpam-5245	93	8	χτ	χτ	PROPN
ejpam-5245	93	9	(	(	PUNCT
ejpam-5245	93	10	r(g−1	r(g−1	X
ejpam-5245	93	11	∗	∗	NOUN
ejpam-5245	93	12	s(w)))f(g−1	s(w)))f(g−1	NOUN
ejpam-5245	93	13	·	·	PUNCT
ejpam-5245	93	14	w	w	X
ejpam-5245	93	15	)	)	PUNCT
ejpam-5245	93	16	,	,	PUNCT
ejpam-5245	93	17	(	(	PUNCT
ejpam-5245	93	18	16	16	NUM
ejpam-5245	93	19	)	)	PUNCT
ejpam-5245	93	20	where	where	SCONJ
ejpam-5245	93	21	g	g	PROPN
ejpam-5245	93	22	∈	∈	PROPN
ejpam-5245	93	23	sl2(r	sl2(r	PROPN
ejpam-5245	93	24	)	)	PUNCT
ejpam-5245	93	25	and	and	CCONJ
ejpam-5245	93	26	w	w	PROPN
ejpam-5245	93	27	∈	∈	PROPN
ejpam-5245	93	28	sl2(r)/k	sl2(r)/k	NOUN
ejpam-5245	93	29	.	.	PUNCT
ejpam-5245	94	1	by	by	ADP
ejpam-5245	94	2	simple	simple	ADJ
ejpam-5245	94	3	calculation	calculation	NOUN
ejpam-5245	94	4	we	we	PRON
ejpam-5245	94	5	obtain	obtain	VERB
ejpam-5245	94	6	[	[	X
ejpam-5245	94	7	7	7	NUM
ejpam-5245	94	8	]	]	PUNCT
ejpam-5245	94	9	,	,	PUNCT
ejpam-5245	94	10	§	§	PROPN
ejpam-5245	94	11	8	8	NUM
ejpam-5245	94	12	:	:	PUNCT
ejpam-5245	95	1	[	[	X
ejpam-5245	95	2	ρk(g)f	ρk(g)f	X
ejpam-5245	95	3	]	]	X
ejpam-5245	95	4	(	(	PUNCT
ejpam-5245	95	5	w	w	NOUN
ejpam-5245	95	6	)	)	PUNCT
ejpam-5245	95	7	=	=	NOUN
ejpam-5245	95	8	|a−	|a−	NOUN
ejpam-5245	95	9	cw|k	cw|k	NOUN
ejpam-5245	95	10	(	(	PUNCT
ejpam-5245	95	11	a−	a−	PROPN
ejpam-5245	95	12	cw)k	cw)k	PROPN
ejpam-5245	95	13	f	f	PROPN
ejpam-5245	95	14	(	(	PUNCT
ejpam-5245	95	15	dw	dw	PROPN
ejpam-5245	95	16	−	−	PROPN
ejpam-5245	95	17	b	b	PROPN
ejpam-5245	95	18	a−	a−	PROPN
ejpam-5245	95	19	cw	cw	NOUN
ejpam-5245	95	20	)	)	PUNCT
ejpam-5245	95	21	,	,	PUNCT
ejpam-5245	95	22	wherew	wherew	NOUN
ejpam-5245	95	23	=	=	SYM
ejpam-5245	95	24	u+	u+	NUM
ejpam-5245	95	25	iv	iv	NUM
ejpam-5245	95	26	.	.	PUNCT
ejpam-5245	95	27	(	(	PUNCT
ejpam-5245	95	28	17	17	NUM
ejpam-5245	95	29	)	)	PUNCT
ejpam-5245	95	30	we	we	PRON
ejpam-5245	95	31	consider	consider	VERB
ejpam-5245	95	32	the	the	DET
ejpam-5245	95	33	basis	basis	NOUN
ejpam-5245	95	34	in	in	ADP
ejpam-5245	95	35	the	the	DET
ejpam-5245	95	36	lie	lie	NOUN
ejpam-5245	95	37	algebra	algebra	PROPN
ejpam-5245	95	38	sl2(r	sl2(r	PROPN
ejpam-5245	95	39	)	)	PUNCT
ejpam-5245	95	40	:	:	PUNCT
ejpam-5245	95	41	a	a	DET
ejpam-5245	95	42	=	=	NOUN
ejpam-5245	95	43	1	1	NUM
ejpam-5245	95	44	2	2	NUM
ejpam-5245	95	45	(	(	PUNCT
ejpam-5245	95	46	−1	−1	NOUN
ejpam-5245	95	47	0	0	SYM
ejpam-5245	95	48	0	0	NUM
ejpam-5245	95	49	1	1	NUM
ejpam-5245	95	50	)	)	PUNCT
ejpam-5245	95	51	,	,	PUNCT
ejpam-5245	95	52	b	b	X
ejpam-5245	95	53	=	=	SYM
ejpam-5245	95	54	1	1	NUM
ejpam-5245	95	55	2	2	NUM
ejpam-5245	95	56	(	(	PUNCT
ejpam-5245	95	57	0	0	NUM
ejpam-5245	95	58	1	1	NUM
ejpam-5245	95	59	1	1	NUM
ejpam-5245	95	60	0	0	NUM
ejpam-5245	95	61	)	)	PUNCT
ejpam-5245	95	62	,	,	PUNCT
ejpam-5245	95	63	z	z	NOUN
ejpam-5245	95	64	=	=	PUNCT
ejpam-5245	95	65	(	(	PUNCT
ejpam-5245	95	66	0	0	NUM
ejpam-5245	95	67	1	1	NUM
ejpam-5245	95	68	−1	−1	NOUN
ejpam-5245	95	69	0	0	NUM
ejpam-5245	95	70	)	)	PUNCT
ejpam-5245	95	71	.	.	PUNCT
ejpam-5245	96	1	(	(	PUNCT
ejpam-5245	96	2	18	18	NUM
ejpam-5245	96	3	)	)	PUNCT
ejpam-5245	96	4	they	they	PRON
ejpam-5245	96	5	generate	generate	VERB
ejpam-5245	96	6	one	one	NUM
ejpam-5245	96	7	-	-	PUNCT
ejpam-5245	96	8	parameter	parameter	NOUN
ejpam-5245	96	9	subgroup	subgroup	NOUN
ejpam-5245	96	10	of	of	ADP
ejpam-5245	96	11	sl2(r	sl2(r	PROPN
ejpam-5245	96	12	):	):	PUNCT
ejpam-5245	97	1	eta	eta	PROPN
ejpam-5245	97	2	=	=	PRON
ejpam-5245	97	3	(	(	PUNCT
ejpam-5245	97	4	e−	e−	X
ejpam-5245	97	5	t	t	PROPN
ejpam-5245	97	6	2	2	NUM
ejpam-5245	97	7	0	0	NUM
ejpam-5245	97	8	0	0	NUM
ejpam-5245	97	9	e	e	NOUN
ejpam-5245	97	10	t	t	PROPN
ejpam-5245	97	11	2	2	NUM
ejpam-5245	97	12	)	)	PUNCT
ejpam-5245	97	13	,	,	PUNCT
ejpam-5245	97	14	etb	etb	PROPN
ejpam-5245	97	15	=	=	PUNCT
ejpam-5245	97	16	(	(	PUNCT
ejpam-5245	97	17	cosh	cosh	PROPN
ejpam-5245	97	18	t	t	PROPN
ejpam-5245	97	19	2	2	NUM
ejpam-5245	97	20	sinh	sinh	NOUN
ejpam-5245	97	21	t	t	PROPN
ejpam-5245	97	22	2	2	NUM
ejpam-5245	97	23	sinh	sinh	NOUN
ejpam-5245	97	24	t	t	PROPN
ejpam-5245	97	25	2	2	NUM
ejpam-5245	97	26	cosh	cosh	NOUN
ejpam-5245	97	27	t	t	PROPN
ejpam-5245	97	28	2	2	NUM
ejpam-5245	97	29	)	)	PUNCT
ejpam-5245	97	30	,	,	PUNCT
ejpam-5245	97	31	etz	etz	PROPN
ejpam-5245	97	32	=	=	SYM
ejpam-5245	97	33	(	(	PUNCT
ejpam-5245	97	34	cos	cos	PROPN
ejpam-5245	97	35	t	t	PROPN
ejpam-5245	97	36	sin	sin	NOUN
ejpam-5245	97	37	t	t	PROPN
ejpam-5245	97	38	−	−	PROPN
ejpam-5245	97	39	sin	sin	PROPN
ejpam-5245	97	40	t	t	PROPN
ejpam-5245	97	41	cos	cos	PROPN
ejpam-5245	97	42	t	t	PROPN
ejpam-5245	97	43	)	)	PUNCT
ejpam-5245	97	44	.	.	PUNCT
ejpam-5245	98	1	the	the	DET
ejpam-5245	98	2	derived	derive	VERB
ejpam-5245	98	3	representations	representation	NOUN
ejpam-5245	98	4	are	be	AUX
ejpam-5245	98	5	:	:	PUNCT
ejpam-5245	98	6	dρak	dρak	ADJ
ejpam-5245	98	7	=	=	NOUN
ejpam-5245	98	8	w∂w	w∂w	VERB
ejpam-5245	98	9	+	+	CCONJ
ejpam-5245	99	1	w̄∂w̄	w̄∂w̄	PROPN
ejpam-5245	99	2	(	(	PUNCT
ejpam-5245	99	3	19	19	NUM
ejpam-5245	99	4	)	)	PUNCT
ejpam-5245	99	5	=	=	NOUN
ejpam-5245	99	6	u∂u	u∂u	NOUN
ejpam-5245	99	7	+	+	CCONJ
ejpam-5245	99	8	v∂v	v∂v	NOUN
ejpam-5245	99	9	,	,	PUNCT
ejpam-5245	99	10	(	(	PUNCT
ejpam-5245	99	11	20	20	X
ejpam-5245	99	12	)	)	PUNCT
ejpam-5245	99	13	dρbk	dρbk	NOUN
ejpam-5245	99	14	=	=	SYM
ejpam-5245	99	15	1	1	NUM
ejpam-5245	99	16	4	4	NUM
ejpam-5245	99	17	k(w	k(w	PROPN
ejpam-5245	99	18	−	−	PROPN
ejpam-5245	99	19	w̄	w̄	NOUN
ejpam-5245	99	20	)	)	PUNCT
ejpam-5245	99	21	·	·	PUNCT
ejpam-5245	100	1	i	i	PRON
ejpam-5245	100	2	−	−	NUM
ejpam-5245	101	1	1	1	NUM
ejpam-5245	101	2	2	2	NUM
ejpam-5245	101	3	(	(	PUNCT
ejpam-5245	101	4	1−	1−	NUM
ejpam-5245	101	5	w2)∂w	w2)∂w	NOUN
ejpam-5245	101	6	−	−	PROPN
ejpam-5245	101	7	1	1	NUM
ejpam-5245	101	8	2	2	NUM
ejpam-5245	101	9	(	(	PUNCT
ejpam-5245	101	10	1−	1−	NUM
ejpam-5245	101	11	w̄2)∂w̄	w̄2)∂w̄	X
ejpam-5245	101	12	(	(	PUNCT
ejpam-5245	101	13	21	21	NUM
ejpam-5245	101	14	)	)	PUNCT
ejpam-5245	101	15	=	=	SYM
ejpam-5245	101	16	1	1	NUM
ejpam-5245	101	17	2	2	NUM
ejpam-5245	101	18	kvi	kvi	NOUN
ejpam-5245	101	19	·	·	PUNCT
ejpam-5245	102	1	i	i	PRON
ejpam-5245	102	2	−	−	NUM
ejpam-5245	102	3	1	1	NUM
ejpam-5245	102	4	2	2	NUM
ejpam-5245	102	5	(	(	PUNCT
ejpam-5245	102	6	1−	1−	NUM
ejpam-5245	102	7	u2	u2	NOUN
ejpam-5245	102	8	+	+	CCONJ
ejpam-5245	102	9	v2)∂u	v2)∂u	NOUN
ejpam-5245	102	10	+	+	CCONJ
ejpam-5245	102	11	uv∂v	uv∂v	ADJ
ejpam-5245	102	12	,	,	PUNCT
ejpam-5245	102	13	(	(	PUNCT
ejpam-5245	102	14	22	22	NUM
ejpam-5245	102	15	)	)	PUNCT
ejpam-5245	102	16	dρzk	dρzk	NOUN
ejpam-5245	102	17	=	=	SYM
ejpam-5245	102	18	−1	−1	NOUN
ejpam-5245	102	19	2	2	NUM
ejpam-5245	102	20	k(w	k(w	PROPN
ejpam-5245	102	21	−	−	PROPN
ejpam-5245	102	22	w̄	w̄	NOUN
ejpam-5245	102	23	)	)	PUNCT
ejpam-5245	102	24	·	·	PUNCT
ejpam-5245	103	1	i	i	PRON
ejpam-5245	103	2	−	−	PROPN
ejpam-5245	104	1	(	(	PUNCT
ejpam-5245	104	2	1	1	NUM
ejpam-5245	104	3	+	+	NUM
ejpam-5245	104	4	w2)∂w	w2)∂w	NOUN
ejpam-5245	104	5	−	−	PROPN
ejpam-5245	104	6	(	(	PUNCT
ejpam-5245	104	7	1	1	NUM
ejpam-5245	104	8	+	+	NUM
ejpam-5245	104	9	w̄2)∂w̄	w̄2)∂w̄	X
ejpam-5245	104	10	(	(	PUNCT
ejpam-5245	104	11	23	23	NUM
ejpam-5245	104	12	)	)	PUNCT
ejpam-5245	104	13	=	=	SYM
ejpam-5245	105	1	−ikv	−ikv	NOUN
ejpam-5245	105	2	·	·	PUNCT
ejpam-5245	106	1	i	i	PRON
ejpam-5245	106	2	−	−	PROPN
ejpam-5245	107	1	(	(	PUNCT
ejpam-5245	107	2	1	1	NUM
ejpam-5245	107	3	+	+	CCONJ
ejpam-5245	107	4	u2	u2	PROPN
ejpam-5245	107	5	−	−	PROPN
ejpam-5245	107	6	v2)∂u	v2)∂u	NOUN
ejpam-5245	107	7	−	−	PROPN
ejpam-5245	107	8	2uv∂v	2uv∂v	NUM
ejpam-5245	107	9	,	,	PUNCT
ejpam-5245	107	10	(	(	PUNCT
ejpam-5245	107	11	24	24	NUM
ejpam-5245	107	12	)	)	PUNCT
ejpam-5245	107	13	where	where	SCONJ
ejpam-5245	107	14	w	w	NOUN
ejpam-5245	107	15	=	=	SYM
ejpam-5245	107	16	u+	u+	NUM
ejpam-5245	107	17	iv	iv	NUM
ejpam-5245	107	18	,	,	PUNCT
ejpam-5245	107	19	∂w	∂w	PROPN
ejpam-5245	107	20	=	=	SYM
ejpam-5245	107	21	1	1	NUM
ejpam-5245	107	22	2(∂u	2(∂u	ADJ
ejpam-5245	107	23	−	−	PROPN
ejpam-5245	107	24	i∂v	i∂v	NOUN
ejpam-5245	107	25	)	)	PUNCT
ejpam-5245	107	26	and	and	CCONJ
ejpam-5245	107	27	∂w̄	∂w̄	PROPN
ejpam-5245	107	28	=	=	SYM
ejpam-5245	107	29	1	1	NUM
ejpam-5245	107	30	2(∂u	2(∂u	NOUN
ejpam-5245	107	31	+	+	CCONJ
ejpam-5245	107	32	i∂v	i∂v	NOUN
ejpam-5245	107	33	)	)	PUNCT
ejpam-5245	107	34	.	.	PUNCT
ejpam-5245	108	1	the	the	DET
ejpam-5245	108	2	casimir	casimir	NOUN
ejpam-5245	108	3	operator	operator	NOUN
ejpam-5245	108	4	is	be	AUX
ejpam-5245	108	5	:	:	PUNCT
ejpam-5245	108	6	dρk(c	dρk(c	PROPN
ejpam-5245	108	7	)	)	PUNCT
ejpam-5245	108	8	=	=	PRON
ejpam-5245	109	1	dρz	dρz	ADV
ejpam-5245	109	2	2−4a2−4b2	2−4a2−4b2	NUM
ejpam-5245	109	3	τ	τ	X
ejpam-5245	109	4	=	=	SYM
ejpam-5245	109	5	4ikv∂u	4ikv∂u	NUM
ejpam-5245	110	1	−	−	NUM
ejpam-5245	110	2	4v2(∂2u	4v2(∂2u	NUM
ejpam-5245	110	3	+	+	NUM
ejpam-5245	110	4	∂2v	∂2v	NOUN
ejpam-5245	110	5	)	)	PUNCT
ejpam-5245	110	6	.	.	PUNCT
ejpam-5245	111	1	(	(	PUNCT
ejpam-5245	111	2	25	25	NUM
ejpam-5245	111	3	)	)	PUNCT
ejpam-5245	111	4	f.	f.	PROPN
ejpam-5245	111	5	a.	a.	PROPN
ejpam-5245	111	6	alabbad	alabbad	PROPN
ejpam-5245	111	7	/	/	SYM
ejpam-5245	111	8	eur	eur	PROPN
ejpam-5245	111	9	.	.	PUNCT
ejpam-5245	112	1	j.	j.	PROPN
ejpam-5245	112	2	pure	pure	PROPN
ejpam-5245	112	3	appl	appl	PROPN
ejpam-5245	112	4	.	.	PROPN
ejpam-5245	112	5	math	math	PROPN
ejpam-5245	112	6	,	,	PUNCT
ejpam-5245	112	7	17	17	NUM
ejpam-5245	112	8	(	(	PUNCT
ejpam-5245	112	9	3	3	NUM
ejpam-5245	112	10	)	)	PUNCT
ejpam-5245	112	11	(	(	PUNCT
ejpam-5245	112	12	2024	2024	NUM
ejpam-5245	112	13	)	)	PUNCT
ejpam-5245	112	14	,	,	PUNCT
ejpam-5245	112	15	2092	2092	NUM
ejpam-5245	112	16	-	-	SYM
ejpam-5245	112	17	2105	2105	NUM
ejpam-5245	112	18	2097	2097	NUM
ejpam-5245	112	19	(	(	PUNCT
ejpam-5245	112	20	ii	ii	NOUN
ejpam-5245	112	21	)	)	PUNCT
ejpam-5245	112	22	for	for	ADP
ejpam-5245	112	23	the	the	DET
ejpam-5245	112	24	subgroup	subgroup	NOUN
ejpam-5245	112	25	n	n	NOUN
ejpam-5245	112	26	′	′	NUM
ejpam-5245	113	1	=	=	PUNCT
ejpam-5245	114	1	{	{	PUNCT
ejpam-5245	115	1	(	(	PUNCT
ejpam-5245	115	2	1	1	NUM
ejpam-5245	115	3	0	0	NUM
ejpam-5245	115	4	n	n	PRON
ejpam-5245	115	5	1	1	NUM
ejpam-5245	115	6	)	)	PUNCT
ejpam-5245	115	7	:	:	PUNCT
ejpam-5245	116	1	n	n	X
ejpam-5245	116	2	∈	∈	NOUN
ejpam-5245	116	3	r	r	NOUN
ejpam-5245	116	4	}	}	PUNCT
ejpam-5245	116	5	,	,	PUNCT
ejpam-5245	116	6	the	the	DET
ejpam-5245	116	7	homogeneous	homogeneous	ADJ
ejpam-5245	116	8	space	space	NOUN
ejpam-5245	116	9	sl2(r	sl2(r	PROPN
ejpam-5245	116	10	)	)	PUNCT
ejpam-5245	116	11	/n	/n	PUNCT
ejpam-5245	117	1	′	′	NOUN
ejpam-5245	117	2	can	can	AUX
ejpam-5245	117	3	be	be	AUX
ejpam-5245	117	4	identified	identify	VERB
ejpam-5245	117	5	with	with	ADP
ejpam-5245	117	6	the	the	DET
ejpam-5245	117	7	upper	upper	ADJ
ejpam-5245	117	8	half	half	ADJ
ejpam-5245	117	9	plane	plane	NOUN
ejpam-5245	117	10	.	.	PUNCT
ejpam-5245	118	1	the	the	DET
ejpam-5245	118	2	respective	respective	ADJ
ejpam-5245	118	3	maps	map	NOUN
ejpam-5245	118	4	are	be	AUX
ejpam-5245	118	5	:	:	PUNCT
ejpam-5245	118	6	p	p	X
ejpam-5245	118	7	(	(	PUNCT
ejpam-5245	118	8	a	a	DET
ejpam-5245	118	9	b	b	NOUN
ejpam-5245	118	10	c	c	NOUN
ejpam-5245	118	11	d	d	NOUN
ejpam-5245	118	12	)	)	PUNCT
ejpam-5245	118	13	=	=	PRON
ejpam-5245	118	14	(	(	PUNCT
ejpam-5245	118	15	b	b	X
ejpam-5245	118	16	d	d	PROPN
ejpam-5245	118	17	,	,	PUNCT
ejpam-5245	118	18	1	1	NUM
ejpam-5245	118	19	d2	d2	PROPN
ejpam-5245	118	20	)	)	PUNCT
ejpam-5245	118	21	,	,	PUNCT
ejpam-5245	119	1	s(u	s(u	PROPN
ejpam-5245	119	2	,	,	PUNCT
ejpam-5245	119	3	v	v	NOUN
ejpam-5245	119	4	)	)	PUNCT
ejpam-5245	119	5	=	=	SYM
ejpam-5245	119	6	1√	1√	NUM
ejpam-5245	119	7	v	v	ADP
ejpam-5245	119	8	(	(	PUNCT
ejpam-5245	119	9	v	v	NUM
ejpam-5245	119	10	u	u	NOUN
ejpam-5245	119	11	0	0	NUM
ejpam-5245	119	12	1	1	NUM
ejpam-5245	119	13	)	)	PUNCT
ejpam-5245	119	14	,	,	PUNCT
ejpam-5245	120	1	r	r	NOUN
ejpam-5245	120	2	(	(	PUNCT
ejpam-5245	120	3	a	a	DET
ejpam-5245	120	4	b	b	NOUN
ejpam-5245	120	5	c	c	NOUN
ejpam-5245	120	6	d	d	NOUN
ejpam-5245	120	7	)	)	PUNCT
ejpam-5245	120	8	=	=	PUNCT
ejpam-5245	120	9	(	(	PUNCT
ejpam-5245	120	10	1	1	NUM
ejpam-5245	120	11	0	0	NUM
ejpam-5245	120	12	c	c	NOUN
ejpam-5245	120	13	d	d	NOUN
ejpam-5245	120	14	1	1	NUM
ejpam-5245	120	15	)	)	PUNCT
ejpam-5245	120	16	.	.	PUNCT
ejpam-5245	121	1	(	(	PUNCT
ejpam-5245	121	2	26	26	NUM
ejpam-5245	121	3	)	)	PUNCT
ejpam-5245	121	4	the	the	DET
ejpam-5245	121	5	maps	map	NOUN
ejpam-5245	121	6	p	p	NOUN
ejpam-5245	121	7	and	and	CCONJ
ejpam-5245	121	8	s	s	VERB
ejpam-5245	121	9	produce	produce	VERB
ejpam-5245	121	10	the	the	DET
ejpam-5245	121	11	following	follow	VERB
ejpam-5245	121	12	decomposition	decomposition	NOUN
ejpam-5245	121	13	g	g	NOUN
ejpam-5245	121	14	=	=	SYM
ejpam-5245	121	15	s(p(g))r(g	s(p(g))r(g	PROPN
ejpam-5245	121	16	):	):	PUNCT
ejpam-5245	121	17	(	(	PUNCT
ejpam-5245	121	18	a	a	DET
ejpam-5245	121	19	b	b	NOUN
ejpam-5245	121	20	c	c	NOUN
ejpam-5245	121	21	d	d	NOUN
ejpam-5245	121	22	)	)	PUNCT
ejpam-5245	121	23	=	=	SYM
ejpam-5245	121	24	1	1	NUM
ejpam-5245	121	25	d2	d2	PROPN
ejpam-5245	121	26	(	(	PUNCT
ejpam-5245	121	27	1	1	NUM
ejpam-5245	121	28	bd	bd	PROPN
ejpam-5245	121	29	0	0	NUM
ejpam-5245	121	30	d2	d2	PROPN
ejpam-5245	121	31	)	)	PUNCT
ejpam-5245	121	32	(	(	PUNCT
ejpam-5245	121	33	d	d	NOUN
ejpam-5245	121	34	0	0	PUNCT
ejpam-5245	121	35	c	c	NOUN
ejpam-5245	121	36	d	d	NOUN
ejpam-5245	121	37	)	)	PUNCT
ejpam-5245	121	38	,	,	PUNCT
ejpam-5245	121	39	where	where	SCONJ
ejpam-5245	121	40	d	d	PROPN
ejpam-5245	121	41	̸=	̸=	PROPN
ejpam-5245	121	42	0	0	NUM
ejpam-5245	121	43	.	.	PUNCT
ejpam-5245	122	1	(	(	PUNCT
ejpam-5245	122	2	27	27	NUM
ejpam-5245	122	3	)	)	PUNCT
ejpam-5245	122	4	the	the	DET
ejpam-5245	122	5	action	action	NOUN
ejpam-5245	122	6	of	of	ADP
ejpam-5245	122	7	sl2(r	sl2(r	PROPN
ejpam-5245	122	8	)	)	PUNCT
ejpam-5245	122	9	on	on	ADP
ejpam-5245	122	10	sl2(r	sl2(r	PROPN
ejpam-5245	122	11	)	)	PUNCT
ejpam-5245	123	1	/ń	/ń	PUNCT
ejpam-5245	123	2	defined	define	VERB
ejpam-5245	123	3	by	by	ADP
ejpam-5245	123	4	the	the	DET
ejpam-5245	123	5	formula	formula	NOUN
ejpam-5245	123	6	g	g	NOUN
ejpam-5245	123	7	·	·	PUNCT
ejpam-5245	123	8	x	x	SYM
ejpam-5245	124	1	=	=	PUNCT
ejpam-5245	124	2	p(g	p(g	PROPN
ejpam-5245	124	3	∗	∗	X
ejpam-5245	124	4	s(x	s(x	PROPN
ejpam-5245	124	5	)	)	PUNCT
ejpam-5245	124	6	)	)	PUNCT
ejpam-5245	124	7	takes	take	VERB
ejpam-5245	124	8	the	the	DET
ejpam-5245	124	9	form	form	NOUN
ejpam-5245	124	10	:	:	PUNCT
ejpam-5245	124	11	(	(	PUNCT
ejpam-5245	124	12	a	a	DET
ejpam-5245	124	13	b	b	NOUN
ejpam-5245	124	14	c	c	NOUN
ejpam-5245	124	15	d	d	PROPN
ejpam-5245	124	16	)	)	PUNCT
ejpam-5245	124	17	:	:	PUNCT
ejpam-5245	124	18	(	(	PUNCT
ejpam-5245	124	19	u	u	NOUN
ejpam-5245	124	20	,	,	PUNCT
ejpam-5245	124	21	v	v	NOUN
ejpam-5245	124	22	)	)	PUNCT
ejpam-5245	124	23	7→	7→	PROPN
ejpam-5245	124	24	(	(	PUNCT
ejpam-5245	124	25	au+	au+	PROPN
ejpam-5245	124	26	b	b	PROPN
ejpam-5245	124	27	cu+	cu+	PROPN
ejpam-5245	124	28	d	d	PROPN
ejpam-5245	124	29	,	,	PUNCT
ejpam-5245	124	30	v	v	PROPN
ejpam-5245	124	31	(	(	PUNCT
ejpam-5245	124	32	cu+	cu+	NOUN
ejpam-5245	124	33	d)2	d)2	PROPN
ejpam-5245	124	34	)	)	PUNCT
ejpam-5245	124	35	.	.	PUNCT
ejpam-5245	125	1	(	(	PUNCT
ejpam-5245	125	2	28	28	NUM
ejpam-5245	125	3	)	)	PUNCT
ejpam-5245	125	4	it	it	PRON
ejpam-5245	125	5	preserves	preserve	VERB
ejpam-5245	125	6	the	the	DET
ejpam-5245	125	7	upper	upper	ADJ
ejpam-5245	125	8	half	half	ADJ
ejpam-5245	125	9	plane	plane	NOUN
ejpam-5245	125	10	v	v	ADP
ejpam-5245	125	11	>	>	X
ejpam-5245	125	12	0	0	NUM
ejpam-5245	125	13	.	.	PUNCT
ejpam-5245	126	1	we	we	PRON
ejpam-5245	126	2	can	can	AUX
ejpam-5245	126	3	rewrite	rewrite	VERB
ejpam-5245	126	4	this	this	DET
ejpam-5245	126	5	map	map	NOUN
ejpam-5245	126	6	as	as	ADP
ejpam-5245	126	7	a	a	DET
ejpam-5245	126	8	linear	linear	ADJ
ejpam-5245	126	9	-	-	PUNCT
ejpam-5245	126	10	fractional	fractional	ADJ
ejpam-5245	126	11	transformation	transformation	NOUN
ejpam-5245	126	12	with	with	ADP
ejpam-5245	126	13	the	the	DET
ejpam-5245	126	14	dual	dual	ADJ
ejpam-5245	126	15	number	number	NOUN
ejpam-5245	126	16	unit	unit	NOUN
ejpam-5245	126	17	ε2	ε2	NOUN
ejpam-5245	126	18	=	=	PROPN
ejpam-5245	126	19	0	0	NUM
ejpam-5245	126	20	:(	:(	PUNCT
ejpam-5245	126	21	a	a	DET
ejpam-5245	126	22	b	b	NOUN
ejpam-5245	126	23	c	c	NOUN
ejpam-5245	126	24	d	d	PROPN
ejpam-5245	126	25	)	)	PUNCT
ejpam-5245	126	26	:	:	PUNCT
ejpam-5245	127	1	w	w	X
ejpam-5245	127	2	7→	7→	NUM
ejpam-5245	127	3	aw	aw	INTJ
ejpam-5245	128	1	+	+	NUM
ejpam-5245	128	2	b	b	X
ejpam-5245	128	3	cw	cw	NOUN
ejpam-5245	128	4	+	+	CCONJ
ejpam-5245	128	5	d	d	NOUN
ejpam-5245	128	6	,	,	PUNCT
ejpam-5245	128	7	wherew	wherew	NOUN
ejpam-5245	128	8	=	=	SYM
ejpam-5245	128	9	u+	u+	NOUN
ejpam-5245	128	10	εv	εv	NOUN
ejpam-5245	128	11	.	.	PUNCT
ejpam-5245	129	1	(	(	PUNCT
ejpam-5245	129	2	29	29	NUM
ejpam-5245	129	3	)	)	PUNCT
ejpam-5245	129	4	the	the	DET
ejpam-5245	129	5	complex	complex	ADJ
ejpam-5245	129	6	character	character	NOUN
ejpam-5245	129	7	χτ	χτ	VERB
ejpam-5245	129	8	of	of	ADP
ejpam-5245	129	9	n	n	PROPN
ejpam-5245	129	10	′	′	NUM
ejpam-5245	129	11	is	be	AUX
ejpam-5245	129	12	:	:	PUNCT
ejpam-5245	129	13	χτ	χτ	PROPN
ejpam-5245	129	14	(	(	PUNCT
ejpam-5245	129	15	1	1	NUM
ejpam-5245	129	16	0	0	NUM
ejpam-5245	129	17	n	n	NUM
ejpam-5245	129	18	1	1	NUM
ejpam-5245	129	19	)	)	PUNCT
ejpam-5245	129	20	=	=	SYM
ejpam-5245	129	21	e−2πiτn	e−2πiτn	NOUN
ejpam-5245	129	22	,	,	PUNCT
ejpam-5245	129	23	where	where	SCONJ
ejpam-5245	129	24	τ	τ	PROPN
ejpam-5245	129	25	∈	∈	PROPN
ejpam-5245	129	26	r.	r.	NOUN
ejpam-5245	129	27	this	this	DET
ejpam-5245	129	28	character	character	NOUN
ejpam-5245	129	29	induces	induce	VERB
ejpam-5245	129	30	a	a	DET
ejpam-5245	129	31	linear	linear	ADJ
ejpam-5245	129	32	representation	representation	NOUN
ejpam-5245	129	33	ρτ	ρτ	NOUN
ejpam-5245	129	34	on	on	ADP
ejpam-5245	129	35	the	the	DET
ejpam-5245	129	36	space	space	NOUN
ejpam-5245	129	37	of	of	ADP
ejpam-5245	129	38	square	square	ADJ
ejpam-5245	129	39	integrable	integrable	ADJ
ejpam-5245	129	40	functions	function	NOUN
ejpam-5245	129	41	,	,	PUNCT
ejpam-5245	129	42	which	which	PRON
ejpam-5245	129	43	is	be	AUX
ejpam-5245	129	44	given	give	VERB
ejpam-5245	129	45	by	by	ADP
ejpam-5245	129	46	the	the	DET
ejpam-5245	129	47	formula	formula	NOUN
ejpam-5245	129	48	:	:	PUNCT
ejpam-5245	130	1	[	[	X
ejpam-5245	130	2	ρτ	ρτ	X
ejpam-5245	130	3	(	(	PUNCT
ejpam-5245	130	4	g)f	g)f	X
ejpam-5245	130	5	]	]	PUNCT
ejpam-5245	130	6	(	(	PUNCT
ejpam-5245	130	7	w	w	NOUN
ejpam-5245	130	8	)	)	PUNCT
ejpam-5245	130	9	=	=	PRON
ejpam-5245	130	10	χτ	χτ	PROPN
ejpam-5245	130	11	(	(	PUNCT
ejpam-5245	130	12	r(g−1	r(g−1	X
ejpam-5245	130	13	∗	∗	NOUN
ejpam-5245	130	14	s(w)))f(g−1	s(w)))f(g−1	NOUN
ejpam-5245	130	15	·	·	PUNCT
ejpam-5245	130	16	w	w	X
ejpam-5245	130	17	)	)	PUNCT
ejpam-5245	130	18	,	,	PUNCT
ejpam-5245	130	19	(	(	PUNCT
ejpam-5245	130	20	30	30	NUM
ejpam-5245	130	21	)	)	PUNCT
ejpam-5245	130	22	where	where	SCONJ
ejpam-5245	130	23	g	g	PROPN
ejpam-5245	130	24	∈	∈	PROPN
ejpam-5245	130	25	sl2(r	sl2(r	PROPN
ejpam-5245	130	26	)	)	PUNCT
ejpam-5245	130	27	and	and	CCONJ
ejpam-5245	130	28	w	w	PROPN
ejpam-5245	130	29	∈	∈	PROPN
ejpam-5245	130	30	sl2(r)/ń	sl2(r)/ń	PROPN
ejpam-5245	130	31	.	.	PUNCT
ejpam-5245	131	1	a	a	DET
ejpam-5245	131	2	direct	direct	ADJ
ejpam-5245	131	3	calculation	calculation	NOUN
ejpam-5245	131	4	shows	show	VERB
ejpam-5245	131	5	that	that	SCONJ
ejpam-5245	131	6	[	[	X
ejpam-5245	131	7	7	7	NUM
ejpam-5245	131	8	]	]	PUNCT
ejpam-5245	131	9	,	,	PUNCT
ejpam-5245	131	10	§	§	PROPN
ejpam-5245	131	11	8	8	NUM
ejpam-5245	131	12	:	:	PUNCT
ejpam-5245	131	13	[	[	X
ejpam-5245	131	14	ρτ	ρτ	X
ejpam-5245	131	15	(	(	PUNCT
ejpam-5245	131	16	g)f	g)f	X
ejpam-5245	131	17	]	]	PUNCT
ejpam-5245	131	18	(	(	PUNCT
ejpam-5245	131	19	w	w	NOUN
ejpam-5245	131	20	)	)	PUNCT
ejpam-5245	131	21	=	=	NOUN
ejpam-5245	131	22	exp	exp	NOUN
ejpam-5245	131	23	(	(	PUNCT
ejpam-5245	131	24	−2πi	−2πi	ADP
ejpam-5245	131	25	τcv	τcv	VERB
ejpam-5245	131	26	a−	a−	PROPN
ejpam-5245	131	27	cu	cu	PROPN
ejpam-5245	131	28	)	)	PUNCT
ejpam-5245	132	1	f	f	PROPN
ejpam-5245	132	2	(	(	PUNCT
ejpam-5245	132	3	dw	dw	NOUN
ejpam-5245	132	4	−	−	PROPN
ejpam-5245	132	5	b	b	PROPN
ejpam-5245	132	6	a−	a−	PROPN
ejpam-5245	132	7	cw	cw	NOUN
ejpam-5245	132	8	)	)	PUNCT
ejpam-5245	132	9	,	,	PUNCT
ejpam-5245	132	10	(	(	PUNCT
ejpam-5245	132	11	31	31	NUM
ejpam-5245	132	12	)	)	PUNCT
ejpam-5245	132	13	where	where	SCONJ
ejpam-5245	132	14	w	w	NOUN
ejpam-5245	132	15	=	=	PUNCT
ejpam-5245	132	16	u+	u+	NOUN
ejpam-5245	132	17	εv	εv	NOUN
ejpam-5245	132	18	and	and	CCONJ
ejpam-5245	132	19	f	f	PROPN
ejpam-5245	132	20	∈	∈	PROPN
ejpam-5245	132	21	l2(h+	l2(h+	PROPN
ejpam-5245	132	22	,	,	PUNCT
ejpam-5245	132	23	dµ	dµ	PROPN
ejpam-5245	132	24	)	)	PUNCT
ejpam-5245	132	25	.	.	PUNCT
ejpam-5245	133	1	this	this	DET
ejpam-5245	133	2	representation	representation	NOUN
ejpam-5245	133	3	is	be	AUX
ejpam-5245	133	4	unitary	unitary	ADJ
ejpam-5245	133	5	on	on	ADP
ejpam-5245	133	6	the	the	DET
ejpam-5245	133	7	space	space	NOUN
ejpam-5245	133	8	of	of	ADP
ejpam-5245	133	9	functions	function	NOUN
ejpam-5245	133	10	on	on	ADP
ejpam-5245	133	11	the	the	DET
ejpam-5245	133	12	upper	upper	ADJ
ejpam-5245	133	13	half	half	ADJ
ejpam-5245	133	14	plane	plane	NOUN
ejpam-5245	133	15	of	of	ADP
ejpam-5245	133	16	f.	f.	PROPN
ejpam-5245	133	17	a.	a.	PROPN
ejpam-5245	133	18	alabbad	alabbad	PROPN
ejpam-5245	133	19	/	/	SYM
ejpam-5245	133	20	eur	eur	PROPN
ejpam-5245	133	21	.	.	PUNCT
ejpam-5245	134	1	j.	j.	PROPN
ejpam-5245	134	2	pure	pure	PROPN
ejpam-5245	134	3	appl	appl	PROPN
ejpam-5245	134	4	.	.	PROPN
ejpam-5245	134	5	math	math	PROPN
ejpam-5245	134	6	,	,	PUNCT
ejpam-5245	134	7	17	17	NUM
ejpam-5245	134	8	(	(	PUNCT
ejpam-5245	134	9	3	3	NUM
ejpam-5245	134	10	)	)	PUNCT
ejpam-5245	134	11	(	(	PUNCT
ejpam-5245	134	12	2024	2024	NUM
ejpam-5245	134	13	)	)	PUNCT
ejpam-5245	134	14	,	,	PUNCT
ejpam-5245	134	15	2092	2092	NUM
ejpam-5245	134	16	-	-	SYM
ejpam-5245	134	17	2105	2105	NUM
ejpam-5245	134	18	2098	2098	NUM
ejpam-5245	134	19	dual	dual	ADJ
ejpam-5245	134	20	numbers	number	NOUN
ejpam-5245	134	21	.	.	PUNCT
ejpam-5245	135	1	the	the	DET
ejpam-5245	135	2	derived	derive	VERB
ejpam-5245	135	3	representations	representation	NOUN
ejpam-5245	135	4	of	of	ADP
ejpam-5245	135	5	the	the	DET
ejpam-5245	135	6	elements	element	NOUN
ejpam-5245	135	7	a	a	DET
ejpam-5245	135	8	,	,	PUNCT
ejpam-5245	135	9	b	b	NOUN
ejpam-5245	135	10	and	and	CCONJ
ejpam-5245	135	11	z	z	PROPN
ejpam-5245	135	12	(	(	PUNCT
ejpam-5245	135	13	18	18	NUM
ejpam-5245	135	14	)	)	PUNCT
ejpam-5245	135	15	of	of	ADP
ejpam-5245	135	16	sl2(r	sl2(r	PROPN
ejpam-5245	135	17	)	)	PUNCT
ejpam-5245	135	18	are	be	AUX
ejpam-5245	135	19	:	:	PUNCT
ejpam-5245	135	20	dρaτ	dρaτ	NOUN
ejpam-5245	135	21	=	=	NOUN
ejpam-5245	135	22	w∂w	w∂w	VERB
ejpam-5245	135	23	+	+	CCONJ
ejpam-5245	135	24	w̄∂w̄	w̄∂w̄	X
ejpam-5245	135	25	(	(	PUNCT
ejpam-5245	135	26	32	32	NUM
ejpam-5245	135	27	)	)	PUNCT
ejpam-5245	135	28	=	=	NOUN
ejpam-5245	135	29	u∂u	u∂u	NOUN
ejpam-5245	135	30	+	+	CCONJ
ejpam-5245	135	31	v∂v	v∂v	NOUN
ejpam-5245	135	32	,	,	PUNCT
ejpam-5245	135	33	(	(	PUNCT
ejpam-5245	135	34	33	33	NUM
ejpam-5245	135	35	)	)	PUNCT
ejpam-5245	135	36	dρbτ	dρbτ	NOUN
ejpam-5245	135	37	=	=	SYM
ejpam-5245	135	38	−πivτ	−πivτ	ADV
ejpam-5245	135	39	·	·	PUNCT
ejpam-5245	136	1	i	i	PRON
ejpam-5245	136	2	−	−	NUM
ejpam-5245	136	3	1	1	NUM
ejpam-5245	136	4	2	2	NUM
ejpam-5245	136	5	(	(	PUNCT
ejpam-5245	136	6	1−	1−	NUM
ejpam-5245	136	7	w2)∂w	w2)∂w	NOUN
ejpam-5245	136	8	−	−	PROPN
ejpam-5245	136	9	1	1	NUM
ejpam-5245	136	10	2	2	NUM
ejpam-5245	136	11	(	(	PUNCT
ejpam-5245	136	12	1−	1−	NUM
ejpam-5245	136	13	w̄2)∂w̄	w̄2)∂w̄	X
ejpam-5245	137	1	(	(	PUNCT
ejpam-5245	137	2	34	34	NUM
ejpam-5245	137	3	)	)	PUNCT
ejpam-5245	137	4	=	=	PUNCT
ejpam-5245	138	1	−πivτ	−πivτ	ADV
ejpam-5245	138	2	·	·	PUNCT
ejpam-5245	139	1	i	i	PRON
ejpam-5245	139	2	−	−	NUM
ejpam-5245	140	1	1	1	NUM
ejpam-5245	140	2	2	2	NUM
ejpam-5245	140	3	(	(	PUNCT
ejpam-5245	140	4	1−	1−	NUM
ejpam-5245	140	5	u2)∂u	u2)∂u	NOUN
ejpam-5245	140	6	+	+	CCONJ
ejpam-5245	141	1	uv∂v	uv∂v	ADJ
ejpam-5245	141	2	,	,	PUNCT
ejpam-5245	141	3	(	(	PUNCT
ejpam-5245	141	4	35	35	NUM
ejpam-5245	141	5	)	)	PUNCT
ejpam-5245	141	6	dρzτ	dρzτ	NOUN
ejpam-5245	142	1	=	=	PUNCT
ejpam-5245	142	2	2πivτ	2πivτ	NUM
ejpam-5245	142	3	·	·	PUNCT
ejpam-5245	143	1	i	i	PRON
ejpam-5245	143	2	−	−	PROPN
ejpam-5245	143	3	(	(	PUNCT
ejpam-5245	143	4	1	1	NUM
ejpam-5245	143	5	+	+	NUM
ejpam-5245	143	6	w2)∂w	w2)∂w	NOUN
ejpam-5245	143	7	−	−	PROPN
ejpam-5245	143	8	(	(	PUNCT
ejpam-5245	143	9	1	1	NUM
ejpam-5245	143	10	+	+	NUM
ejpam-5245	143	11	w̄2)∂w̄	w̄2)∂w̄	X
ejpam-5245	143	12	(	(	PUNCT
ejpam-5245	143	13	36	36	NUM
ejpam-5245	143	14	)	)	PUNCT
ejpam-5245	143	15	=	=	NOUN
ejpam-5245	144	1	2πivτ	2πivτ	NUM
ejpam-5245	144	2	·	·	PUNCT
ejpam-5245	145	1	i	i	PRON
ejpam-5245	145	2	−	−	PROPN
ejpam-5245	145	3	(	(	PUNCT
ejpam-5245	145	4	1	1	NUM
ejpam-5245	145	5	+	+	CCONJ
ejpam-5245	145	6	u2)∂u	u2)∂u	ADJ
ejpam-5245	145	7	−	−	PROPN
ejpam-5245	145	8	2uv∂v	2uv∂v	NUM
ejpam-5245	145	9	,	,	PUNCT
ejpam-5245	145	10	(	(	PUNCT
ejpam-5245	145	11	37	37	NUM
ejpam-5245	145	12	)	)	PUNCT
ejpam-5245	145	13	where	where	SCONJ
ejpam-5245	145	14	w	w	NOUN
ejpam-5245	145	15	=	=	PUNCT
ejpam-5245	145	16	u+	u+	NUM
ejpam-5245	145	17	εv	εv	NOUN
ejpam-5245	145	18	,	,	PUNCT
ejpam-5245	145	19	∂w	∂w	PROPN
ejpam-5245	145	20	=	=	SYM
ejpam-5245	145	21	1	1	NUM
ejpam-5245	145	22	2(∂u	2(∂u	NOUN
ejpam-5245	145	23	+	+	X
ejpam-5245	145	24	1	1	NUM
ejpam-5245	145	25	ε∂v	ε∂v	NOUN
ejpam-5245	145	26	)	)	PUNCT
ejpam-5245	145	27	and	and	CCONJ
ejpam-5245	145	28	∂w̄	∂w̄	PROPN
ejpam-5245	145	29	=	=	SYM
ejpam-5245	145	30	1	1	NUM
ejpam-5245	145	31	2(∂u	2(∂u	NOUN
ejpam-5245	145	32	−	−	PROPN
ejpam-5245	145	33	1	1	NUM
ejpam-5245	145	34	ε∂v	ε∂v	NOUN
ejpam-5245	145	35	)	)	PUNCT
ejpam-5245	145	36	.	.	PUNCT
ejpam-5245	146	1	the	the	DET
ejpam-5245	146	2	casimir	casimir	NOUN
ejpam-5245	146	3	operator	operator	NOUN
ejpam-5245	146	4	is	be	AUX
ejpam-5245	146	5	:	:	PUNCT
ejpam-5245	146	6	dρτ	dρτ	NOUN
ejpam-5245	146	7	(	(	PUNCT
ejpam-5245	146	8	c	c	X
ejpam-5245	146	9	)	)	PUNCT
ejpam-5245	146	10	=	=	VERB
ejpam-5245	147	1	dρz	dρz	ADV
ejpam-5245	147	2	2−4a2−4b2	2−4a2−4b2	NUM
ejpam-5245	147	3	τ	τ	X
ejpam-5245	147	4	=	=	SYM
ejpam-5245	147	5	−8πivτ∂u	−8πivτ∂u	PROPN
ejpam-5245	147	6	−	−	PROPN
ejpam-5245	147	7	4v2∂2v	4v2∂2v	NUM
ejpam-5245	147	8	.	.	PUNCT
ejpam-5245	148	1	(	(	PUNCT
ejpam-5245	148	2	38	38	NUM
ejpam-5245	148	3	)	)	PUNCT
ejpam-5245	148	4	in	in	ADP
ejpam-5245	148	5	the	the	DET
ejpam-5245	148	6	following	following	NOUN
ejpam-5245	148	7	we	we	PRON
ejpam-5245	148	8	will	will	AUX
ejpam-5245	148	9	find	find	VERB
ejpam-5245	148	10	some	some	DET
ejpam-5245	148	11	eigenfunctions	eigenfunction	NOUN
ejpam-5245	148	12	,	,	PUNCT
ejpam-5245	148	13	and	and	CCONJ
ejpam-5245	148	14	the	the	DET
ejpam-5245	148	15	special	special	ADJ
ejpam-5245	148	16	role	role	NOUN
ejpam-5245	148	17	of	of	ADP
ejpam-5245	148	18	them	they	PRON
ejpam-5245	148	19	will	will	AUX
ejpam-5245	148	20	become	become	VERB
ejpam-5245	148	21	obvious	obvious	ADJ
ejpam-5245	148	22	later	later	ADV
ejpam-5245	148	23	.	.	PUNCT
ejpam-5245	149	1	2.1	2.1	NUM
ejpam-5245	149	2	.	.	PUNCT
ejpam-5245	150	1	joint	joint	ADJ
ejpam-5245	150	2	eigenvector	eigenvector	NOUN
ejpam-5245	150	3	of	of	ADP
ejpam-5245	150	4	dρk(c	dρk(c	PROPN
ejpam-5245	150	5	)	)	PUNCT
ejpam-5245	150	6	with	with	ADP
ejpam-5245	150	7	dρnk	dρnk	ADJ
ejpam-5245	150	8	first	first	ADV
ejpam-5245	151	1	,	,	PUNCT
ejpam-5245	151	2	we	we	PRON
ejpam-5245	151	3	calculate	calculate	VERB
ejpam-5245	151	4	the	the	DET
ejpam-5245	151	5	eigenvector	eigenvector	NOUN
ejpam-5245	151	6	of	of	ADP
ejpam-5245	151	7	the	the	DET
ejpam-5245	151	8	derived	derive	VERB
ejpam-5245	151	9	representation	representation	NOUN
ejpam-5245	151	10	dρnk	dρnk	NOUN
ejpam-5245	151	11	:	:	PUNCT
ejpam-5245	151	12	[	[	PUNCT
ejpam-5245	151	13	dρnk	dρnk	ADJ
ejpam-5245	151	14	f	f	X
ejpam-5245	151	15	]	]	X
ejpam-5245	151	16	(	(	PUNCT
ejpam-5245	151	17	w	w	PROPN
ejpam-5245	151	18	,	,	PUNCT
ejpam-5245	151	19	w̄	w̄	NOUN
ejpam-5245	151	20	)	)	PUNCT
ejpam-5245	151	21	=	=	PUNCT
ejpam-5245	151	22	−∂uf(w	−∂uf(w	NOUN
ejpam-5245	151	23	,	,	PUNCT
ejpam-5245	151	24	w̄	w̄	NOUN
ejpam-5245	151	25	)	)	PUNCT
ejpam-5245	151	26	=	=	PUNCT
ejpam-5245	152	1	−(∂w	−(∂w	ADV
ejpam-5245	152	2	+	+	CCONJ
ejpam-5245	152	3	∂w̄)f(w	∂w̄)f(w	ADJ
ejpam-5245	152	4	,	,	PUNCT
ejpam-5245	152	5	w̄	w̄	NOUN
ejpam-5245	152	6	)	)	PUNCT
ejpam-5245	152	7	=	=	SYM
ejpam-5245	153	1	0	0	X
ejpam-5245	153	2	.	.	PUNCT
ejpam-5245	154	1	(	(	PUNCT
ejpam-5245	154	2	39	39	NUM
ejpam-5245	154	3	)	)	PUNCT
ejpam-5245	154	4	the	the	DET
ejpam-5245	154	5	solution	solution	NOUN
ejpam-5245	154	6	is	be	AUX
ejpam-5245	154	7	f(w	f(w	PROPN
ejpam-5245	154	8	,	,	PUNCT
ejpam-5245	154	9	w̄	w̄	NOUN
ejpam-5245	154	10	)	)	PUNCT
ejpam-5245	154	11	=	=	SYM
ejpam-5245	154	12	ϕ(v	ϕ(v	PROPN
ejpam-5245	154	13	)	)	PUNCT
ejpam-5245	154	14	,	,	PUNCT
ejpam-5245	154	15	where	where	SCONJ
ejpam-5245	154	16	ϕ	ϕ	NOUN
ejpam-5245	154	17	is	be	AUX
ejpam-5245	154	18	an	an	DET
ejpam-5245	154	19	arbitrary	arbitrary	ADJ
ejpam-5245	154	20	function	function	NOUN
ejpam-5245	154	21	.	.	PUNCT
ejpam-5245	155	1	then	then	ADV
ejpam-5245	155	2	,	,	PUNCT
ejpam-5245	155	3	we	we	PRON
ejpam-5245	155	4	solve	solve	VERB
ejpam-5245	155	5	the	the	DET
ejpam-5245	155	6	differential	differential	ADJ
ejpam-5245	155	7	equation	equation	NOUN
ejpam-5245	155	8	dρk(c)ϕ(v	dρk(c)ϕ(v	PUNCT
ejpam-5245	155	9	)	)	PUNCT
ejpam-5245	155	10	=	=	SYM
ejpam-5245	155	11	(	(	PUNCT
ejpam-5245	155	12	1	1	NUM
ejpam-5245	155	13	+	+	NUM
ejpam-5245	155	14	s2)ϕ(v	s2)ϕ(v	NOUN
ejpam-5245	155	15	)	)	PUNCT
ejpam-5245	155	16	,	,	PUNCT
ejpam-5245	155	17	s	s	VERB
ejpam-5245	155	18	∈	∈	PROPN
ejpam-5245	155	19	r	r	NOUN
ejpam-5245	155	20	,	,	PUNCT
ejpam-5245	155	21	where	where	SCONJ
ejpam-5245	155	22	dρk(c	dρk(c	PROPN
ejpam-5245	155	23	)	)	PUNCT
ejpam-5245	155	24	is	be	AUX
ejpam-5245	155	25	the	the	DET
ejpam-5245	155	26	casimir	casimir	NOUN
ejpam-5245	155	27	operator(25	operator(25	NOUN
ejpam-5245	155	28	)	)	PUNCT
ejpam-5245	155	29	,	,	PUNCT
ejpam-5245	155	30	and	and	CCONJ
ejpam-5245	155	31	k	k	PROPN
ejpam-5245	155	32	=	=	NOUN
ejpam-5245	155	33	0	0	PROPN
ejpam-5245	155	34	for	for	ADP
ejpam-5245	155	35	simplicity	simplicity	NOUN
ejpam-5245	155	36	.	.	PUNCT
ejpam-5245	156	1	this	this	DET
ejpam-5245	156	2	equation	equation	NOUN
ejpam-5245	156	3	becomes	become	VERB
ejpam-5245	156	4	−4v2	−4v2	NUM
ejpam-5245	156	5	d2ϕ	d2ϕ	PROPN
ejpam-5245	156	6	dv2	dv2	NOUN
ejpam-5245	156	7	(	(	PUNCT
ejpam-5245	156	8	v)−	v)−	PROPN
ejpam-5245	156	9	(	(	PUNCT
ejpam-5245	156	10	1	1	NUM
ejpam-5245	156	11	+	+	NUM
ejpam-5245	156	12	s2)ϕ(v	s2)ϕ(v	NOUN
ejpam-5245	156	13	)	)	PUNCT
ejpam-5245	156	14	=	=	SYM
ejpam-5245	157	1	0	0	X
ejpam-5245	157	2	.	.	PUNCT
ejpam-5245	158	1	(	(	PUNCT
ejpam-5245	158	2	40	40	NUM
ejpam-5245	158	3	)	)	PUNCT
ejpam-5245	158	4	it	it	PRON
ejpam-5245	158	5	is	be	AUX
ejpam-5245	158	6	a	a	DET
ejpam-5245	158	7	cauchy	cauchy	PROPN
ejpam-5245	158	8	-	-	PUNCT
ejpam-5245	158	9	euler	euler	NOUN
ejpam-5245	158	10	equation	equation	NOUN
ejpam-5245	158	11	,	,	PUNCT
ejpam-5245	158	12	therefore	therefore	ADV
ejpam-5245	158	13	the	the	DET
ejpam-5245	158	14	solution	solution	NOUN
ejpam-5245	158	15	takes	take	VERB
ejpam-5245	158	16	the	the	DET
ejpam-5245	158	17	form	form	NOUN
ejpam-5245	158	18	ϕ(v	ϕ(v	PUNCT
ejpam-5245	158	19	)	)	PUNCT
ejpam-5245	158	20	=	=	SYM
ejpam-5245	158	21	vm	vm	PROPN
ejpam-5245	158	22	.	.	PROPN
ejpam-5245	158	23	differentiating	differentiate	VERB
ejpam-5245	158	24	gives	give	VERB
ejpam-5245	158	25	d2ϕ	d2ϕ	PROPN
ejpam-5245	158	26	dv2	dv2	NOUN
ejpam-5245	158	27	(	(	PUNCT
ejpam-5245	158	28	v	v	NOUN
ejpam-5245	158	29	)	)	PUNCT
ejpam-5245	158	30	=	=	PUNCT
ejpam-5245	158	31	m(m−	m(m−	NOUN
ejpam-5245	158	32	1)vm−2	1)vm−2	NUM
ejpam-5245	158	33	,	,	PUNCT
ejpam-5245	158	34	and	and	CCONJ
ejpam-5245	158	35	substituting	substitute	VERB
ejpam-5245	158	36	into	into	ADP
ejpam-5245	158	37	(	(	PUNCT
ejpam-5245	158	38	40	40	NUM
ejpam-5245	158	39	)	)	PUNCT
ejpam-5245	158	40	leeds	leed	NOUN
ejpam-5245	158	41	to	to	ADP
ejpam-5245	158	42	−4m(m−	−4m(m−	PROPN
ejpam-5245	158	43	1)vm	1)vm	PROPN
ejpam-5245	158	44	−	−	NOUN
ejpam-5245	158	45	(	(	PUNCT
ejpam-5245	158	46	1	1	NUM
ejpam-5245	158	47	+	+	NUM
ejpam-5245	158	48	s2)vm	s2)vm	NOUN
ejpam-5245	158	49	=	=	SYM
ejpam-5245	158	50	0	0	NUM
ejpam-5245	158	51	⇒	⇒	NOUN
ejpam-5245	158	52	−4m(m−	−4m(m−	PROPN
ejpam-5245	159	1	1)−	1)−	PROPN
ejpam-5245	159	2	(	(	PUNCT
ejpam-5245	159	3	1	1	NUM
ejpam-5245	159	4	+	+	NUM
ejpam-5245	159	5	s2	s2	NOUN
ejpam-5245	159	6	)	)	PUNCT
ejpam-5245	159	7	=	=	SYM
ejpam-5245	159	8	0	0	NUM
ejpam-5245	159	9	⇒	⇒	NOUN
ejpam-5245	159	10	m	m	VERB
ejpam-5245	159	11	=	=	ADJ
ejpam-5245	159	12	1±	1±	NUM
ejpam-5245	159	13	is	be	AUX
ejpam-5245	159	14	2	2	NUM
ejpam-5245	159	15	.	.	PUNCT
ejpam-5245	160	1	hence	hence	ADV
ejpam-5245	160	2	,	,	PUNCT
ejpam-5245	160	3	the	the	DET
ejpam-5245	160	4	set	set	NOUN
ejpam-5245	160	5	of	of	ADP
ejpam-5245	160	6	fundamental	fundamental	ADJ
ejpam-5245	160	7	solution	solution	NOUN
ejpam-5245	160	8	is	be	AUX
ejpam-5245	160	9	{	{	PUNCT
ejpam-5245	160	10	v	v	NUM
ejpam-5245	160	11	1+is	1+is	NUM
ejpam-5245	160	12	2	2	NUM
ejpam-5245	160	13	,	,	PUNCT
ejpam-5245	160	14	v	v	PRON
ejpam-5245	160	15	1−is	1−is	NOUN
ejpam-5245	160	16	2	2	NUM
ejpam-5245	160	17	}	}	PUNCT
ejpam-5245	160	18	.	.	PUNCT
ejpam-5245	161	1	(	(	PUNCT
ejpam-5245	161	2	41	41	NUM
ejpam-5245	161	3	)	)	PUNCT
ejpam-5245	161	4	f.	f.	NOUN
ejpam-5245	161	5	a.	a.	PROPN
ejpam-5245	161	6	alabbad	alabbad	PROPN
ejpam-5245	161	7	/	/	SYM
ejpam-5245	161	8	eur	eur	PROPN
ejpam-5245	161	9	.	.	PUNCT
ejpam-5245	162	1	j.	j.	PROPN
ejpam-5245	162	2	pure	pure	PROPN
ejpam-5245	162	3	appl	appl	PROPN
ejpam-5245	162	4	.	.	PROPN
ejpam-5245	162	5	math	math	PROPN
ejpam-5245	162	6	,	,	PUNCT
ejpam-5245	162	7	17	17	NUM
ejpam-5245	162	8	(	(	PUNCT
ejpam-5245	162	9	3	3	NUM
ejpam-5245	162	10	)	)	PUNCT
ejpam-5245	162	11	(	(	PUNCT
ejpam-5245	162	12	2024	2024	NUM
ejpam-5245	162	13	)	)	PUNCT
ejpam-5245	162	14	,	,	PUNCT
ejpam-5245	162	15	2092	2092	NUM
ejpam-5245	162	16	-	-	SYM
ejpam-5245	162	17	2105	2105	NUM
ejpam-5245	162	18	2099	2099	NUM
ejpam-5245	162	19	2.2	2.2	NUM
ejpam-5245	162	20	.	.	PUNCT
ejpam-5245	163	1	joint	joint	ADJ
ejpam-5245	163	2	eigenvector	eigenvector	NOUN
ejpam-5245	163	3	of	of	ADP
ejpam-5245	163	4	dρτ	dρτ	NOUN
ejpam-5245	163	5	(	(	PUNCT
ejpam-5245	163	6	c	c	NOUN
ejpam-5245	163	7	)	)	PUNCT
ejpam-5245	163	8	with	with	ADP
ejpam-5245	163	9	dρzτ	dρzτ	PROPN
ejpam-5245	163	10	to	to	PART
ejpam-5245	163	11	begin	begin	VERB
ejpam-5245	163	12	,	,	PUNCT
ejpam-5245	163	13	we	we	PRON
ejpam-5245	163	14	look	look	VERB
ejpam-5245	163	15	for	for	ADP
ejpam-5245	163	16	an	an	DET
ejpam-5245	163	17	eigenvector	eigenvector	NOUN
ejpam-5245	163	18	of	of	ADP
ejpam-5245	163	19	the	the	DET
ejpam-5245	163	20	derived	derive	VERB
ejpam-5245	163	21	representation	representation	NOUN
ejpam-5245	163	22	dρzτ	dρzτ	NOUN
ejpam-5245	163	23	(	(	PUNCT
ejpam-5245	163	24	37	37	NUM
ejpam-5245	163	25	)	)	PUNCT
ejpam-5245	163	26	with	with	ADP
ejpam-5245	163	27	τ	τ	PROPN
ejpam-5245	163	28	=	=	SYM
ejpam-5245	163	29	0	0	PROPN
ejpam-5245	163	30	.	.	PUNCT
ejpam-5245	164	1	to	to	PART
ejpam-5245	164	2	do	do	VERB
ejpam-5245	164	3	that	that	PRON
ejpam-5245	164	4	,	,	PUNCT
ejpam-5245	164	5	we	we	PRON
ejpam-5245	164	6	solve	solve	VERB
ejpam-5245	164	7	the	the	DET
ejpam-5245	164	8	equation	equation	NOUN
ejpam-5245	164	9	dρzτ	dρzτ	PROPN
ejpam-5245	164	10	f(w	f(w	PROPN
ejpam-5245	164	11	,	,	PUNCT
ejpam-5245	164	12	w̄	w̄	NOUN
ejpam-5245	164	13	)	)	PUNCT
ejpam-5245	164	14	=	=	SYM
ejpam-5245	164	15	0	0	PUNCT
ejpam-5245	164	16	using	use	VERB
ejpam-5245	164	17	the	the	DET
ejpam-5245	164	18	method	method	NOUN
ejpam-5245	164	19	of	of	ADP
ejpam-5245	164	20	characteristics	characteristic	NOUN
ejpam-5245	164	21	:	:	PUNCT
ejpam-5245	164	22	du	du	PROPN
ejpam-5245	164	23	1	1	NUM
ejpam-5245	164	24	+	+	CCONJ
ejpam-5245	164	25	u2	u2	PROPN
ejpam-5245	164	26	=	=	SYM
ejpam-5245	164	27	dv	dv	PROPN
ejpam-5245	164	28	2uv	2uv	NOUN
ejpam-5245	164	29	=	=	X
ejpam-5245	164	30	df	df	PROPN
ejpam-5245	164	31	2πiτvf	2πiτvf	NUM
ejpam-5245	164	32	.	.	PUNCT
ejpam-5245	165	1	du	du	PROPN
ejpam-5245	165	2	1	1	NUM
ejpam-5245	165	3	+	+	CCONJ
ejpam-5245	165	4	u2	u2	PROPN
ejpam-5245	165	5	=	=	PROPN
ejpam-5245	165	6	dv	dv	PROPN
ejpam-5245	165	7	2uv	2uv	ADJ
ejpam-5245	165	8	⇒	⇒	NOUN
ejpam-5245	165	9	2udu	2udu	PROPN
ejpam-5245	165	10	1	1	NUM
ejpam-5245	165	11	+	+	CCONJ
ejpam-5245	165	12	u2	u2	NOUN
ejpam-5245	165	13	=	=	SYM
ejpam-5245	165	14	dv	dv	PROPN
ejpam-5245	165	15	v	v	ADP
ejpam-5245	165	16	⇒	⇒	NOUN
ejpam-5245	165	17	2c1	2c1	NUM
ejpam-5245	166	1	=	=	SYM
ejpam-5245	166	2	v	v	ADP
ejpam-5245	166	3	1	1	NUM
ejpam-5245	166	4	+	+	CCONJ
ejpam-5245	166	5	u2	u2	NOUN
ejpam-5245	166	6	.	.	PUNCT
ejpam-5245	167	1	we	we	PRON
ejpam-5245	167	2	need	need	VERB
ejpam-5245	167	3	to	to	PART
ejpam-5245	167	4	obtain	obtain	VERB
ejpam-5245	167	5	another	another	DET
ejpam-5245	167	6	integral	integral	ADJ
ejpam-5245	167	7	curve	curve	NOUN
ejpam-5245	167	8	which	which	PRON
ejpam-5245	167	9	involves	involve	VERB
ejpam-5245	167	10	f	f	PROPN
ejpam-5245	167	11	.	.	PUNCT
ejpam-5245	168	1	since	since	SCONJ
ejpam-5245	168	2	τ	τ	PROPN
ejpam-5245	168	3	=	=	SYM
ejpam-5245	168	4	0	0	PROPN
ejpam-5245	168	5	,	,	PUNCT
ejpam-5245	168	6	then	then	ADV
ejpam-5245	168	7	dv	dv	PROPN
ejpam-5245	168	8	2uv	2uv	PROPN
ejpam-5245	168	9	=	=	X
ejpam-5245	168	10	df	df	PROPN
ejpam-5245	168	11	2πiτvf	2πiτvf	NUM
ejpam-5245	168	12	⇒	⇒	NOUN
ejpam-5245	168	13	df	df	PROPN
ejpam-5245	168	14	f	f	PROPN
ejpam-5245	168	15	=	=	SYM
ejpam-5245	168	16	0	0	PROPN
ejpam-5245	168	17	⇒	⇒	PROPN
ejpam-5245	168	18	c2	c2	PROPN
ejpam-5245	168	19	=	=	SYM
ejpam-5245	168	20	f.	f.	PROPN
ejpam-5245	168	21	hence	hence	ADV
ejpam-5245	168	22	,	,	PUNCT
ejpam-5245	168	23	the	the	DET
ejpam-5245	168	24	general	general	ADJ
ejpam-5245	168	25	solution	solution	NOUN
ejpam-5245	168	26	is	be	AUX
ejpam-5245	168	27	of	of	ADP
ejpam-5245	168	28	the	the	DET
ejpam-5245	168	29	form	form	NOUN
ejpam-5245	168	30	c2	c2	PROPN
ejpam-5245	168	31	=	=	PUNCT
ejpam-5245	168	32	ψ(c1	ψ(c1	PROPN
ejpam-5245	168	33	)	)	PUNCT
ejpam-5245	168	34	,	,	PUNCT
ejpam-5245	168	35	that	that	PRON
ejpam-5245	168	36	is	be	AUX
ejpam-5245	168	37	f(w	f(w	PROPN
ejpam-5245	168	38	,	,	PUNCT
ejpam-5245	168	39	w̄	w̄	NOUN
ejpam-5245	168	40	)	)	PUNCT
ejpam-5245	169	1	=	=	SYM
ejpam-5245	169	2	ψ	ψ	X
ejpam-5245	169	3	(	(	PUNCT
ejpam-5245	169	4	v	v	NUM
ejpam-5245	169	5	2(1	2(1	NUM
ejpam-5245	169	6	+	+	CCONJ
ejpam-5245	169	7	u2	u2	NOUN
ejpam-5245	169	8	)	)	PUNCT
ejpam-5245	169	9	)	)	PUNCT
ejpam-5245	169	10	,	,	PUNCT
ejpam-5245	169	11	w	w	NOUN
ejpam-5245	169	12	=	=	SYM
ejpam-5245	169	13	u+	u+	NUM
ejpam-5245	169	14	εv	εv	NOUN
ejpam-5245	169	15	,	,	PUNCT
ejpam-5245	169	16	(	(	PUNCT
ejpam-5245	169	17	42	42	NUM
ejpam-5245	169	18	)	)	PUNCT
ejpam-5245	169	19	where	where	SCONJ
ejpam-5245	169	20	ψ	ψ	NOUN
ejpam-5245	169	21	is	be	AUX
ejpam-5245	169	22	an	an	DET
ejpam-5245	169	23	arbitrary	arbitrary	ADJ
ejpam-5245	169	24	function	function	NOUN
ejpam-5245	169	25	.	.	PUNCT
ejpam-5245	170	1	to	to	PART
ejpam-5245	170	2	specify	specify	VERB
ejpam-5245	170	3	this	this	DET
ejpam-5245	170	4	function	function	NOUN
ejpam-5245	170	5	,	,	PUNCT
ejpam-5245	170	6	we	we	PRON
ejpam-5245	170	7	solve	solve	VERB
ejpam-5245	170	8	the	the	DET
ejpam-5245	170	9	equation	equation	NOUN
ejpam-5245	170	10	dρτ	dρτ	NOUN
ejpam-5245	170	11	(	(	PUNCT
ejpam-5245	170	12	c)ψ	c)ψ	X
ejpam-5245	170	13	(	(	PUNCT
ejpam-5245	170	14	v	v	NUM
ejpam-5245	170	15	2(1	2(1	NUM
ejpam-5245	170	16	+	+	CCONJ
ejpam-5245	170	17	u2	u2	NOUN
ejpam-5245	170	18	)	)	PUNCT
ejpam-5245	170	19	)	)	PUNCT
ejpam-5245	171	1	=	=	PUNCT
ejpam-5245	171	2	(	(	PUNCT
ejpam-5245	171	3	1	1	NUM
ejpam-5245	171	4	+	+	CCONJ
ejpam-5245	171	5	s2)ψ	s2)ψ	NOUN
ejpam-5245	171	6	(	(	PUNCT
ejpam-5245	171	7	v	v	NOUN
ejpam-5245	171	8	2(1	2(1	NUM
ejpam-5245	171	9	+	+	CCONJ
ejpam-5245	171	10	u2	u2	NOUN
ejpam-5245	171	11	)	)	PUNCT
ejpam-5245	171	12	)	)	PUNCT
ejpam-5245	171	13	,	,	PUNCT
ejpam-5245	171	14	(	(	PUNCT
ejpam-5245	171	15	43	43	NUM
ejpam-5245	171	16	)	)	PUNCT
ejpam-5245	171	17	where	where	SCONJ
ejpam-5245	171	18	dρτ	dρτ	NOUN
ejpam-5245	171	19	(	(	PUNCT
ejpam-5245	171	20	c	c	NOUN
ejpam-5245	171	21	)	)	PUNCT
ejpam-5245	171	22	is	be	AUX
ejpam-5245	171	23	the	the	DET
ejpam-5245	171	24	casimir	casimir	NOUN
ejpam-5245	171	25	operator(38	operator(38	NOUN
ejpam-5245	171	26	)	)	PUNCT
ejpam-5245	171	27	.	.	PUNCT
ejpam-5245	172	1	this	this	DET
ejpam-5245	172	2	equation	equation	NOUN
ejpam-5245	172	3	turns	turn	VERB
ejpam-5245	172	4	into	into	ADP
ejpam-5245	172	5	−4	−4	X
ejpam-5245	172	6	v2	v2	PROPN
ejpam-5245	172	7	(	(	PUNCT
ejpam-5245	172	8	1	1	NUM
ejpam-5245	172	9	+	+	CCONJ
ejpam-5245	172	10	u2)2	u2)2	ADP
ejpam-5245	172	11	d2ψ	d2ψ	ADJ
ejpam-5245	172	12	dv2	dv2	NOUN
ejpam-5245	172	13	(	(	PUNCT
ejpam-5245	172	14	v	v	NOUN
ejpam-5245	172	15	2(1	2(1	NUM
ejpam-5245	172	16	+	+	CCONJ
ejpam-5245	172	17	u2	u2	NOUN
ejpam-5245	172	18	)	)	PUNCT
ejpam-5245	172	19	)	)	PUNCT
ejpam-5245	173	1	−	−	PROPN
ejpam-5245	173	2	(	(	PUNCT
ejpam-5245	173	3	1	1	NUM
ejpam-5245	173	4	+	+	CCONJ
ejpam-5245	173	5	s2)ψ	s2)ψ	NOUN
ejpam-5245	173	6	(	(	PUNCT
ejpam-5245	173	7	v	v	NOUN
ejpam-5245	173	8	2(1	2(1	NUM
ejpam-5245	173	9	+	+	CCONJ
ejpam-5245	173	10	u2	u2	NOUN
ejpam-5245	173	11	)	)	PUNCT
ejpam-5245	173	12	)	)	PUNCT
ejpam-5245	174	1	=	=	PUNCT
ejpam-5245	174	2	0	0	X
ejpam-5245	174	3	.	.	PUNCT
ejpam-5245	175	1	(	(	PUNCT
ejpam-5245	175	2	44	44	NUM
ejpam-5245	175	3	)	)	PUNCT
ejpam-5245	175	4	using	use	VERB
ejpam-5245	175	5	the	the	DET
ejpam-5245	175	6	substitution	substitution	NOUN
ejpam-5245	175	7	t	t	NOUN
ejpam-5245	175	8	=	=	SYM
ejpam-5245	175	9	v	v	ADP
ejpam-5245	175	10	2(1+u2	2(1+u2	NUM
ejpam-5245	175	11	)	)	PUNCT
ejpam-5245	175	12	,	,	PUNCT
ejpam-5245	175	13	then	then	ADV
ejpam-5245	175	14	we	we	PRON
ejpam-5245	175	15	obtain	obtain	VERB
ejpam-5245	175	16	−4t2	−4t2	PUNCT
ejpam-5245	175	17	d2ψ	d2ψ	PROPN
ejpam-5245	175	18	dt2	dt2	PROPN
ejpam-5245	175	19	(	(	PUNCT
ejpam-5245	175	20	t)−	t)−	PROPN
ejpam-5245	175	21	(	(	PUNCT
ejpam-5245	175	22	1	1	NUM
ejpam-5245	175	23	+	+	NUM
ejpam-5245	175	24	s2)ψ(t	s2)ψ(t	NOUN
ejpam-5245	175	25	)	)	PUNCT
ejpam-5245	175	26	=	=	SYM
ejpam-5245	176	1	0	0	X
ejpam-5245	176	2	.	.	PUNCT
ejpam-5245	177	1	(	(	PUNCT
ejpam-5245	177	2	45	45	NUM
ejpam-5245	177	3	)	)	PUNCT
ejpam-5245	177	4	it	it	PRON
ejpam-5245	177	5	is	be	AUX
ejpam-5245	177	6	a	a	DET
ejpam-5245	177	7	cauchy	cauchy	PROPN
ejpam-5245	177	8	-	-	PUNCT
ejpam-5245	177	9	euler	euler	NOUN
ejpam-5245	177	10	equation	equation	NOUN
ejpam-5245	177	11	,	,	PUNCT
ejpam-5245	177	12	so	so	ADV
ejpam-5245	177	13	let	let	VERB
ejpam-5245	177	14	ψ(t	ψ(t	PRON
ejpam-5245	177	15	)	)	PUNCT
ejpam-5245	178	1	=	=	SYM
ejpam-5245	178	2	tm	tm	NOUN
ejpam-5245	178	3	and	and	CCONJ
ejpam-5245	178	4	substitute	substitute	NOUN
ejpam-5245	178	5	in	in	ADP
ejpam-5245	178	6	the	the	DET
ejpam-5245	178	7	differential	differential	ADJ
ejpam-5245	178	8	equation(45	equation(45	NOUN
ejpam-5245	178	9	)	)	PUNCT
ejpam-5245	178	10	,	,	PUNCT
ejpam-5245	178	11	then	then	ADV
ejpam-5245	178	12	m	m	VERB
ejpam-5245	178	13	=	=	ADJ
ejpam-5245	178	14	1+is	1+is	NUM
ejpam-5245	178	15	2	2	NUM
ejpam-5245	178	16	and	and	CCONJ
ejpam-5245	178	17	m	m	PROPN
ejpam-5245	178	18	=	=	SYM
ejpam-5245	178	19	1−is	1−is	NUM
ejpam-5245	178	20	2	2	NUM
ejpam-5245	178	21	are	be	AUX
ejpam-5245	178	22	two	two	NUM
ejpam-5245	178	23	distinct	distinct	ADJ
ejpam-5245	178	24	possible	possible	ADJ
ejpam-5245	178	25	values	value	NOUN
ejpam-5245	178	26	of	of	ADP
ejpam-5245	178	27	m.	m.	NOUN
ejpam-5245	178	28	therefore	therefore	ADV
ejpam-5245	178	29	,	,	PUNCT
ejpam-5245	178	30	the	the	DET
ejpam-5245	178	31	set	set	NOUN
ejpam-5245	178	32	of	of	ADP
ejpam-5245	178	33	fundamental	fundamental	ADJ
ejpam-5245	178	34	solution	solution	NOUN
ejpam-5245	178	35	is	be	AUX
ejpam-5245	178	36	{	{	PUNCT
ejpam-5245	178	37	t	t	PROPN
ejpam-5245	178	38	1+is	1+is	NUM
ejpam-5245	178	39	2	2	NUM
ejpam-5245	178	40	,	,	PUNCT
ejpam-5245	178	41	t	t	PROPN
ejpam-5245	178	42	1−is	1−is	NUM
ejpam-5245	178	43	2	2	NUM
ejpam-5245	178	44	}	}	PUNCT
ejpam-5245	178	45	.	.	PUNCT
ejpam-5245	179	1	finally	finally	ADV
ejpam-5245	179	2	,	,	PUNCT
ejpam-5245	179	3	the	the	DET
ejpam-5245	179	4	set	set	NOUN
ejpam-5245	179	5	of	of	ADP
ejpam-5245	179	6	fundamental	fundamental	ADJ
ejpam-5245	179	7	solution	solution	NOUN
ejpam-5245	179	8	for	for	ADP
ejpam-5245	179	9	the	the	DET
ejpam-5245	179	10	equation(44	equation(44	NOUN
ejpam-5245	179	11	)	)	PUNCT
ejpam-5245	179	12	is	be	AUX
ejpam-5245	179	13	{	{	PUNCT
ejpam-5245	179	14	(	(	PUNCT
ejpam-5245	179	15	v	v	NOUN
ejpam-5245	179	16	2(1	2(1	NUM
ejpam-5245	179	17	+	+	CCONJ
ejpam-5245	179	18	u2	u2	NOUN
ejpam-5245	179	19	)	)	PUNCT
ejpam-5245	179	20	)	)	PUNCT
ejpam-5245	180	1	1+is	1+is	NUM
ejpam-5245	180	2	2	2	NUM
ejpam-5245	180	3	,	,	PUNCT
ejpam-5245	180	4	(	(	PUNCT
ejpam-5245	180	5	v	v	NUM
ejpam-5245	180	6	2(1	2(1	NUM
ejpam-5245	180	7	+	+	CCONJ
ejpam-5245	180	8	u2	u2	NOUN
ejpam-5245	180	9	)	)	PUNCT
ejpam-5245	180	10	)	)	PUNCT
ejpam-5245	181	1	1−is	1−is	NUM
ejpam-5245	181	2	2	2	NUM
ejpam-5245	181	3	}	}	PUNCT
ejpam-5245	181	4	.	.	PUNCT
ejpam-5245	182	1	(	(	PUNCT
ejpam-5245	182	2	46	46	NUM
ejpam-5245	182	3	)	)	PUNCT
ejpam-5245	182	4	f.	f.	PROPN
ejpam-5245	182	5	a.	a.	PROPN
ejpam-5245	182	6	alabbad	alabbad	PROPN
ejpam-5245	182	7	/	/	SYM
ejpam-5245	182	8	eur	eur	PROPN
ejpam-5245	182	9	.	.	PUNCT
ejpam-5245	183	1	j.	j.	PROPN
ejpam-5245	183	2	pure	pure	PROPN
ejpam-5245	183	3	appl	appl	PROPN
ejpam-5245	183	4	.	.	PROPN
ejpam-5245	183	5	math	math	PROPN
ejpam-5245	183	6	,	,	PUNCT
ejpam-5245	183	7	17	17	NUM
ejpam-5245	183	8	(	(	PUNCT
ejpam-5245	183	9	3	3	NUM
ejpam-5245	183	10	)	)	PUNCT
ejpam-5245	183	11	(	(	PUNCT
ejpam-5245	183	12	2024	2024	NUM
ejpam-5245	183	13	)	)	PUNCT
ejpam-5245	183	14	,	,	PUNCT
ejpam-5245	183	15	2092	2092	NUM
ejpam-5245	183	16	-	-	SYM
ejpam-5245	183	17	2105	2105	NUM
ejpam-5245	183	18	2100	2100	NUM
ejpam-5245	183	19	3	3	NUM
ejpam-5245	183	20	.	.	PUNCT
ejpam-5245	183	21	induced	induce	VERB
ejpam-5245	183	22	covariant	covariant	ADJ
ejpam-5245	183	23	transform	transform	NOUN
ejpam-5245	183	24	definition	definition	NOUN
ejpam-5245	183	25	3	3	NUM
ejpam-5245	183	26	.	.	PUNCT
ejpam-5245	184	1	[	[	X
ejpam-5245	184	2	8	8	NUM
ejpam-5245	184	3	]	]	PUNCT
ejpam-5245	184	4	,	,	PUNCT
ejpam-5245	184	5	§	§	PROPN
ejpam-5245	184	6	5.1	5.1	NUM
ejpam-5245	184	7	let	let	VERB
ejpam-5245	184	8	h	h	NOUN
ejpam-5245	184	9	be	be	AUX
ejpam-5245	184	10	a	a	DET
ejpam-5245	184	11	closed	closed	ADJ
ejpam-5245	184	12	subgroup	subgroup	NOUN
ejpam-5245	184	13	of	of	ADP
ejpam-5245	184	14	g	g	PROPN
ejpam-5245	184	15	and	and	CCONJ
ejpam-5245	184	16	f	f	PROPN
ejpam-5245	184	17	∈	∈	PROPN
ejpam-5245	184	18	h	h	NOUN
ejpam-5245	184	19	such	such	ADJ
ejpam-5245	184	20	that	that	SCONJ
ejpam-5245	184	21	ρ(h)f	ρ(h)f	PROPN
ejpam-5245	184	22	=	=	PUNCT
ejpam-5245	184	23	χ(h)f	χ(h)f	PROPN
ejpam-5245	184	24	(	(	PUNCT
ejpam-5245	184	25	47	47	NUM
ejpam-5245	184	26	)	)	PUNCT
ejpam-5245	184	27	for	for	ADP
ejpam-5245	184	28	some	some	DET
ejpam-5245	184	29	character	character	NOUN
ejpam-5245	184	30	χ	χ	NOUN
ejpam-5245	184	31	of	of	ADP
ejpam-5245	184	32	h	h	PRON
ejpam-5245	184	33	where	where	SCONJ
ejpam-5245	184	34	h	h	NOUN
ejpam-5245	184	35	∈	∈	PROPN
ejpam-5245	184	36	h	h	NOUN
ejpam-5245	184	37	and	and	CCONJ
ejpam-5245	184	38	ρ	ρ	PROPN
ejpam-5245	184	39	is	be	AUX
ejpam-5245	184	40	a	a	DET
ejpam-5245	184	41	unitary	unitary	ADJ
ejpam-5245	184	42	representation	representation	NOUN
ejpam-5245	184	43	of	of	ADP
ejpam-5245	184	44	a	a	DET
ejpam-5245	184	45	lie	lie	NOUN
ejpam-5245	184	46	group	group	NOUN
ejpam-5245	184	47	g	g	PROPN
ejpam-5245	184	48	in	in	ADP
ejpam-5245	184	49	a	a	DET
ejpam-5245	184	50	hilbert	hilbert	NOUN
ejpam-5245	184	51	space	space	NOUN
ejpam-5245	184	52	h.	h.	PROPN
ejpam-5245	184	53	for	for	ADP
ejpam-5245	184	54	a	a	DET
ejpam-5245	184	55	section	section	NOUN
ejpam-5245	184	56	s	s	VERB
ejpam-5245	184	57	from	from	ADP
ejpam-5245	184	58	g	g	NOUN
ejpam-5245	184	59	/	/	SYM
ejpam-5245	184	60	h	h	NOUN
ejpam-5245	184	61	to	to	ADP
ejpam-5245	184	62	g	g	NOUN
ejpam-5245	184	63	,	,	PUNCT
ejpam-5245	184	64	the	the	DET
ejpam-5245	184	65	induced	induce	VERB
ejpam-5245	184	66	covariant	covariant	NOUN
ejpam-5245	184	67	transform	transform	NOUN
ejpam-5245	184	68	wρ	wρ	ADP
ejpam-5245	184	69	f	f	PROPN
ejpam-5245	184	70	is	be	AUX
ejpam-5245	184	71	a	a	DET
ejpam-5245	184	72	map	map	NOUN
ejpam-5245	184	73	from	from	ADP
ejpam-5245	184	74	the	the	DET
ejpam-5245	184	75	hilbert	hilbert	PROPN
ejpam-5245	184	76	space	space	NOUN
ejpam-5245	184	77	h	h	NOUN
ejpam-5245	184	78	to	to	ADP
ejpam-5245	184	79	a	a	DET
ejpam-5245	184	80	space	space	NOUN
ejpam-5245	184	81	of	of	ADP
ejpam-5245	184	82	function	function	NOUN
ejpam-5245	184	83	on	on	ADP
ejpam-5245	184	84	g	g	PROPN
ejpam-5245	184	85	/	/	SYM
ejpam-5245	184	86	h	h	NOUN
ejpam-5245	184	87	given	give	VERB
ejpam-5245	184	88	as	as	SCONJ
ejpam-5245	184	89	follows	follow	VERB
ejpam-5245	184	90	:	:	PUNCT
ejpam-5245	184	91	wf	wf	PROPN
ejpam-5245	184	92	:	:	PUNCT
ejpam-5245	184	93	υ	υ	PROPN
ejpam-5245	184	94	7→	7→	PROPN
ejpam-5245	184	95	υ̃(x	υ̃(x	PROPN
ejpam-5245	184	96	)	)	PUNCT
ejpam-5245	184	97	=	=	SYM
ejpam-5245	184	98	⟨υ	⟨υ	PROPN
ejpam-5245	184	99	,	,	PUNCT
ejpam-5245	184	100	ρ(s(x))f⟩	ρ(s(x))f⟩	PROPN
ejpam-5245	184	101	,	,	PUNCT
ejpam-5245	184	102	x	x	PUNCT
ejpam-5245	184	103	∈	∈	PROPN
ejpam-5245	184	104	g	g	PROPN
ejpam-5245	184	105	/	/	SYM
ejpam-5245	184	106	h.	h.	PROPN
ejpam-5245	184	107	(	(	PUNCT
ejpam-5245	184	108	48	48	NUM
ejpam-5245	184	109	)	)	PUNCT
ejpam-5245	184	110	the	the	DET
ejpam-5245	184	111	map	map	NOUN
ejpam-5245	184	112	υ	υ	PROPN
ejpam-5245	184	113	7→	7→	PROPN
ejpam-5245	184	114	υ̃(x	υ̃(x	PROPN
ejpam-5245	184	115	)	)	PUNCT
ejpam-5245	184	116	=	=	SYM
ejpam-5245	184	117	υ̃(s(x	υ̃(s(x	PROPN
ejpam-5245	184	118	)	)	PUNCT
ejpam-5245	184	119	)	)	PUNCT
ejpam-5245	184	120	intertwines	intertwine	VERB
ejpam-5245	184	121	ρ	ρ	NOUN
ejpam-5245	184	122	with	with	ADP
ejpam-5245	184	123	the	the	DET
ejpam-5245	184	124	representation	representation	NOUN
ejpam-5245	184	125	ρχ	ρχ	INTJ
ejpam-5245	184	126	in	in	ADP
ejpam-5245	184	127	a	a	DET
ejpam-5245	184	128	certain	certain	ADJ
ejpam-5245	184	129	function	function	NOUN
ejpam-5245	184	130	space	space	NOUN
ejpam-5245	184	131	on	on	ADP
ejpam-5245	184	132	g	g	PROPN
ejpam-5245	184	133	/	/	SYM
ejpam-5245	184	134	h	h	NOUN
ejpam-5245	184	135	induced	induce	VERB
ejpam-5245	184	136	by	by	ADP
ejpam-5245	184	137	the	the	DET
ejpam-5245	184	138	character	character	NOUN
ejpam-5245	184	139	χ	χ	PROPN
ejpam-5245	184	140	of	of	ADP
ejpam-5245	184	141	h.	h.	PROPN
ejpam-5245	184	142	that	that	PRON
ejpam-5245	184	143	is	be	AUX
ejpam-5245	184	144	,	,	PUNCT
ejpam-5245	184	145	ρχ	ρχ	PROPN
ejpam-5245	184	146	◦	◦	NOUN
ejpam-5245	184	147	wρ	wρ	NOUN
ejpam-5245	184	148	f	f	PROPN
ejpam-5245	184	149	=	=	NOUN
ejpam-5245	184	150	wρ	wρ	PROPN
ejpam-5245	184	151	f	f	PROPN
ejpam-5245	184	152	◦	◦	PROPN
ejpam-5245	184	153	ρ	ρ	PROPN
ejpam-5245	184	154	.	.	PUNCT
ejpam-5245	185	1	(	(	PUNCT
ejpam-5245	185	2	49	49	NUM
ejpam-5245	185	3	)	)	PUNCT
ejpam-5245	185	4	example	example	NOUN
ejpam-5245	186	1	1	1	NUM
ejpam-5245	186	2	.	.	PUNCT
ejpam-5245	186	3	we	we	PRON
ejpam-5245	186	4	will	will	AUX
ejpam-5245	186	5	find	find	VERB
ejpam-5245	186	6	the	the	DET
ejpam-5245	186	7	induced	induced	ADJ
ejpam-5245	186	8	wavelet	wavelet	NOUN
ejpam-5245	186	9	transform	transform	NOUN
ejpam-5245	186	10	with	with	ADP
ejpam-5245	186	11	n	n	DET
ejpam-5245	186	12	-eigenvector	-eigenvector	NOUN
ejpam-5245	186	13	that	that	PRON
ejpam-5245	186	14	intertwines	intertwine	VERB
ejpam-5245	186	15	respectively	respectively	ADV
ejpam-5245	186	16	the	the	DET
ejpam-5245	186	17	representation	representation	NOUN
ejpam-5245	186	18	ρk	ρk	ADP
ejpam-5245	186	19	(	(	PUNCT
ejpam-5245	186	20	17	17	NUM
ejpam-5245	186	21	)	)	PUNCT
ejpam-5245	187	1	where	where	SCONJ
ejpam-5245	187	2	k	k	NOUN
ejpam-5245	188	1	=	=	NOUN
ejpam-5245	188	2	0	0	NUM
ejpam-5245	188	3	with	with	ADP
ejpam-5245	188	4	the	the	DET
ejpam-5245	188	5	representation	representation	NOUN
ejpam-5245	188	6	ρτ	ρτ	X
ejpam-5245	188	7	(	(	PUNCT
ejpam-5245	188	8	31	31	NUM
ejpam-5245	188	9	)	)	PUNCT
ejpam-5245	188	10	.	.	PUNCT
ejpam-5245	189	1	we	we	PRON
ejpam-5245	189	2	take	take	VERB
ejpam-5245	189	3	the	the	DET
ejpam-5245	189	4	fiducial	fiducial	ADJ
ejpam-5245	189	5	vector	vector	NOUN
ejpam-5245	189	6	φ0(w	φ0(w	PROPN
ejpam-5245	189	7	,	,	PUNCT
ejpam-5245	189	8	w̄	w̄	NOUN
ejpam-5245	189	9	)	)	PUNCT
ejpam-5245	189	10	=	=	PUNCT
ejpam-5245	190	1	v	v	ADP
ejpam-5245	190	2	1+is	1+is	NUM
ejpam-5245	190	3	2	2	NUM
ejpam-5245	190	4	(	(	PUNCT
ejpam-5245	190	5	41	41	NUM
ejpam-5245	190	6	)	)	PUNCT
ejpam-5245	190	7	which	which	PRON
ejpam-5245	190	8	would	would	AUX
ejpam-5245	190	9	be	be	AUX
ejpam-5245	190	10	the	the	DET
ejpam-5245	190	11	eigenvector	eigenvector	NOUN
ejpam-5245	190	12	for	for	ADP
ejpam-5245	190	13	the	the	DET
ejpam-5245	190	14	representation	representation	NOUN
ejpam-5245	190	15	ρk	ρk	ADP
ejpam-5245	190	16	(	(	PUNCT
ejpam-5245	190	17	1	1	NUM
ejpam-5245	190	18	n	n	NOUN
ejpam-5245	190	19	0	0	NUM
ejpam-5245	190	20	1	1	NUM
ejpam-5245	190	21	)	)	PUNCT
ejpam-5245	190	22	.	.	PUNCT
ejpam-5245	191	1	that	that	PRON
ejpam-5245	191	2	is	be	AUX
ejpam-5245	191	3	ρk	ρk	NOUN
ejpam-5245	191	4	(	(	PUNCT
ejpam-5245	191	5	1	1	NUM
ejpam-5245	191	6	n	n	NOUN
ejpam-5245	191	7	0	0	NUM
ejpam-5245	191	8	1	1	NUM
ejpam-5245	191	9	)	)	PUNCT
ejpam-5245	191	10	φ0	φ0	PROPN
ejpam-5245	191	11	=	=	NOUN
ejpam-5245	191	12	χτ	χτ	PROPN
ejpam-5245	191	13	(	(	PUNCT
ejpam-5245	191	14	1	1	NUM
ejpam-5245	191	15	n	n	NOUN
ejpam-5245	191	16	0	0	NUM
ejpam-5245	191	17	1	1	NUM
ejpam-5245	191	18	)	)	PUNCT
ejpam-5245	191	19	φ0	φ0	PROPN
ejpam-5245	191	20	.	.	PUNCT
ejpam-5245	192	1	(	(	PUNCT
ejpam-5245	192	2	50	50	NUM
ejpam-5245	192	3	)	)	PUNCT
ejpam-5245	192	4	then	then	ADV
ejpam-5245	192	5	,	,	PUNCT
ejpam-5245	192	6	the	the	DET
ejpam-5245	192	7	corresponding	corresponding	ADJ
ejpam-5245	192	8	induced	induce	VERB
ejpam-5245	192	9	covariant	covariant	ADJ
ejpam-5245	192	10	transform	transform	NOUN
ejpam-5245	192	11	is	be	AUX
ejpam-5245	192	12	:	:	PUNCT
ejpam-5245	192	13	[	[	PUNCT
ejpam-5245	192	14	wρk	wρk	VERB
ejpam-5245	192	15	φ0	φ0	PROPN
ejpam-5245	192	16	f	f	PROPN
ejpam-5245	192	17	]	]	X
ejpam-5245	192	18	(	(	PUNCT
ejpam-5245	192	19	ξ	ξ	X
ejpam-5245	192	20	)	)	PUNCT
ejpam-5245	192	21	=	=	SYM
ejpam-5245	192	22	⟨f	⟨f	X
ejpam-5245	192	23	,	,	PUNCT
ejpam-5245	192	24	ρk(s(ξ1	ρk(s(ξ1	NOUN
ejpam-5245	192	25	,	,	PUNCT
ejpam-5245	192	26	ξ2))φ0⟩	ξ2))φ0⟩	NOUN
ejpam-5245	192	27	=	=	SYM
ejpam-5245	192	28	〈	〈	PROPN
ejpam-5245	192	29	f	f	X
ejpam-5245	192	30	,	,	PUNCT
ejpam-5245	192	31	ρk	ρk	X
ejpam-5245	192	32	(	(	PUNCT
ejpam-5245	192	33	ξ1	ξ1	PROPN
ejpam-5245	192	34	0	0	NUM
ejpam-5245	192	35	ξ2	ξ2	NOUN
ejpam-5245	192	36	1	1	NUM
ejpam-5245	192	37	ξ1	ξ1	NOUN
ejpam-5245	192	38	)	)	PUNCT
ejpam-5245	192	39	v	v	ADP
ejpam-5245	192	40	1+is	1+is	NUM
ejpam-5245	192	41	2	2	NUM
ejpam-5245	192	42	〉	〉	NOUN
ejpam-5245	192	43	=	=	SYM
ejpam-5245	192	44	∫	∫	PROPN
ejpam-5245	192	45	h+	h+	X
ejpam-5245	192	46	f(w	f(w	PROPN
ejpam-5245	192	47	)	)	PUNCT
ejpam-5245	192	48	(	(	PUNCT
ejpam-5245	192	49	v	v	NOUN
ejpam-5245	192	50	|ξ1	|ξ1	NOUN
ejpam-5245	192	51	−	−	NUM
ejpam-5245	192	52	ξ2w|2	ξ2w|2	NOUN
ejpam-5245	192	53	)	)	PUNCT
ejpam-5245	192	54	1−is	1−is	NOUN
ejpam-5245	192	55	2	2	NUM
ejpam-5245	192	56	dudv	dudv	NOUN
ejpam-5245	192	57	v2	v2	PROPN
ejpam-5245	192	58	=	=	SYM
ejpam-5245	192	59	∫	∫	PROPN
ejpam-5245	192	60	h+	h+	X
ejpam-5245	192	61	f(w	f(w	PROPN
ejpam-5245	192	62	)	)	PUNCT
ejpam-5245	192	63	exp	exp	NOUN
ejpam-5245	192	64	{	{	PUNCT
ejpam-5245	192	65	−1−	−1−	NOUN
ejpam-5245	192	66	is	be	AUX
ejpam-5245	192	67	2	2	NUM
ejpam-5245	192	68	ϱ(w	ϱ(w	NOUN
ejpam-5245	192	69	;	;	PUNCT
ejpam-5245	192	70	ξ	ξ	X
ejpam-5245	192	71	)	)	PUNCT
ejpam-5245	192	72	}	}	PUNCT
ejpam-5245	192	73	dudv	dudv	ADP
ejpam-5245	192	74	v2	v2	PROPN
ejpam-5245	192	75	,	,	PUNCT
ejpam-5245	192	76	w	w	NOUN
ejpam-5245	192	77	=	=	SYM
ejpam-5245	192	78	u+	u+	NUM
ejpam-5245	192	79	iv	iv	NUM
ejpam-5245	192	80	,	,	PUNCT
ejpam-5245	192	81	(	(	PUNCT
ejpam-5245	192	82	51	51	NUM
ejpam-5245	192	83	)	)	PUNCT
ejpam-5245	192	84	where	where	SCONJ
ejpam-5245	192	85	ϱ(w	ϱ(w	PROPN
ejpam-5245	192	86	;	;	PUNCT
ejpam-5245	192	87	ξ	ξ	X
ejpam-5245	192	88	)	)	PUNCT
ejpam-5245	192	89	(	(	PUNCT
ejpam-5245	192	90	10	10	NUM
ejpam-5245	192	91	)	)	PUNCT
ejpam-5245	192	92	is	be	AUX
ejpam-5245	192	93	the	the	DET
ejpam-5245	192	94	signed	sign	VERB
ejpam-5245	192	95	distance	distance	NOUN
ejpam-5245	192	96	from	from	ADP
ejpam-5245	192	97	the	the	DET
ejpam-5245	192	98	point	point	NOUN
ejpam-5245	192	99	w	w	ADP
ejpam-5245	192	100	to	to	ADP
ejpam-5245	192	101	the	the	DET
ejpam-5245	192	102	horocycle	horocycle	NOUN
ejpam-5245	192	103	h(ξ	h(ξ	PROPN
ejpam-5245	192	104	)	)	PUNCT
ejpam-5245	192	105	,	,	PUNCT
ejpam-5245	192	106	ξ	ξ	X
ejpam-5245	192	107	=	=	SYM
ejpam-5245	192	108	(	(	PUNCT
ejpam-5245	192	109	ξ1	ξ1	NOUN
ejpam-5245	192	110	,	,	PUNCT
ejpam-5245	192	111	ξ2	ξ2	NOUN
ejpam-5245	192	112	)	)	PUNCT
ejpam-5245	192	113	.	.	PUNCT
ejpam-5245	193	1	4	4	X
ejpam-5245	193	2	.	.	X
ejpam-5245	193	3	contravariant	contravariant	PROPN
ejpam-5245	193	4	transform	transform	VERB
ejpam-5245	193	5	definition	definition	NOUN
ejpam-5245	193	6	4	4	NUM
ejpam-5245	193	7	.	.	PUNCT
ejpam-5245	194	1	[	[	X
ejpam-5245	194	2	6	6	NUM
ejpam-5245	194	3	]	]	PUNCT
ejpam-5245	194	4	,	,	PUNCT
ejpam-5245	194	5	§	§	PROPN
ejpam-5245	194	6	5	5	NUM
ejpam-5245	194	7	let	let	VERB
ejpam-5245	194	8	ρ	ρ	PROPN
ejpam-5245	194	9	be	be	AUX
ejpam-5245	194	10	a	a	DET
ejpam-5245	194	11	unitary	unitary	ADJ
ejpam-5245	194	12	square	square	ADJ
ejpam-5245	194	13	integrable	integrable	ADJ
ejpam-5245	194	14	representation	representation	NOUN
ejpam-5245	194	15	of	of	ADP
ejpam-5245	194	16	the	the	DET
ejpam-5245	194	17	group	group	NOUN
ejpam-5245	194	18	sl2(r	sl2(r	PROPN
ejpam-5245	194	19	)	)	PUNCT
ejpam-5245	194	20	on	on	ADP
ejpam-5245	194	21	a	a	DET
ejpam-5245	194	22	hilbert	hilbert	NOUN
ejpam-5245	194	23	space	space	NOUN
ejpam-5245	194	24	h	h	NOUN
ejpam-5245	194	25	and	and	CCONJ
ejpam-5245	194	26	h	h	NOUN
ejpam-5245	194	27	be	be	VERB
ejpam-5245	194	28	a	a	DET
ejpam-5245	194	29	closed	closed	ADJ
ejpam-5245	194	30	subgroup	subgroup	NOUN
ejpam-5245	194	31	of	of	ADP
ejpam-5245	194	32	sl2(r	sl2(r	PROPN
ejpam-5245	194	33	)	)	PUNCT
ejpam-5245	194	34	.	.	PUNCT
ejpam-5245	195	1	let	let	VERB
ejpam-5245	195	2	x	x	PUNCT
ejpam-5245	195	3	=	=	PUNCT
ejpam-5245	195	4	sl2(r)/h	sl2(r)/h	NOUN
ejpam-5245	195	5	be	be	AUX
ejpam-5245	195	6	a	a	DET
ejpam-5245	195	7	homogeneous	homogeneous	ADJ
ejpam-5245	195	8	space	space	NOUN
ejpam-5245	195	9	with	with	ADP
ejpam-5245	195	10	an	an	DET
ejpam-5245	195	11	invariant	invariant	ADJ
ejpam-5245	195	12	measure	measure	NOUN
ejpam-5245	195	13	dx	dx	PROPN
ejpam-5245	195	14	.	.	PUNCT
ejpam-5245	196	1	we	we	PRON
ejpam-5245	196	2	define	define	VERB
ejpam-5245	196	3	the	the	DET
ejpam-5245	196	4	function	function	NOUN
ejpam-5245	196	5	ws(x	ws(x	NOUN
ejpam-5245	196	6	)	)	PUNCT
ejpam-5245	196	7	=	=	SYM
ejpam-5245	196	8	f.	f.	PROPN
ejpam-5245	196	9	a.	a.	PROPN
ejpam-5245	196	10	alabbad	alabbad	PROPN
ejpam-5245	196	11	/	/	SYM
ejpam-5245	196	12	eur	eur	PROPN
ejpam-5245	196	13	.	.	PUNCT
ejpam-5245	197	1	j.	j.	PROPN
ejpam-5245	197	2	pure	pure	PROPN
ejpam-5245	197	3	appl	appl	PROPN
ejpam-5245	197	4	.	.	PROPN
ejpam-5245	197	5	math	math	PROPN
ejpam-5245	197	6	,	,	PUNCT
ejpam-5245	197	7	17	17	NUM
ejpam-5245	197	8	(	(	PUNCT
ejpam-5245	197	9	3	3	NUM
ejpam-5245	197	10	)	)	PUNCT
ejpam-5245	197	11	(	(	PUNCT
ejpam-5245	197	12	2024	2024	NUM
ejpam-5245	197	13	)	)	PUNCT
ejpam-5245	197	14	,	,	PUNCT
ejpam-5245	197	15	2092	2092	NUM
ejpam-5245	197	16	-	-	SYM
ejpam-5245	197	17	2105	2105	NUM
ejpam-5245	197	18	2101	2101	NUM
ejpam-5245	197	19	ρ(s(x))w0	ρ(s(x))w0	PROPN
ejpam-5245	197	20	,	,	PUNCT
ejpam-5245	197	21	where	where	SCONJ
ejpam-5245	197	22	w0	w0	PROPN
ejpam-5245	197	23	∈	∈	PROPN
ejpam-5245	197	24	h	h	NOUN
ejpam-5245	197	25	and	and	CCONJ
ejpam-5245	197	26	s	s	NOUN
ejpam-5245	197	27	is	be	AUX
ejpam-5245	197	28	a	a	DET
ejpam-5245	197	29	section	section	NOUN
ejpam-5245	197	30	map	map	NOUN
ejpam-5245	197	31	.	.	PUNCT
ejpam-5245	198	1	the	the	DET
ejpam-5245	198	2	contravariant	contravariant	PROPN
ejpam-5245	198	3	transform	transform	NOUN
ejpam-5245	198	4	mρ	mρ	X
ejpam-5245	198	5	w0	w0	PROPN
ejpam-5245	198	6	is	be	AUX
ejpam-5245	198	7	a	a	DET
ejpam-5245	198	8	map	map	NOUN
ejpam-5245	198	9	l2(x	l2(x	NOUN
ejpam-5245	198	10	)	)	PUNCT
ejpam-5245	199	1	→	→	SYM
ejpam-5245	199	2	h	h	PRON
ejpam-5245	199	3	defined	define	VERB
ejpam-5245	199	4	by	by	ADP
ejpam-5245	199	5	mρ	mρ	NOUN
ejpam-5245	199	6	w0	w0	PROPN
ejpam-5245	199	7	f	f	PROPN
ejpam-5245	199	8	=	=	SYM
ejpam-5245	199	9	∫	∫	PROPN
ejpam-5245	199	10	x	x	SYM
ejpam-5245	199	11	f(x)ws(x	f(x)ws(x	PROPN
ejpam-5245	199	12	)	)	PUNCT
ejpam-5245	199	13	dx	dx	PROPN
ejpam-5245	199	14	,	,	PUNCT
ejpam-5245	199	15	x	x	X
ejpam-5245	199	16	∈	∈	NOUN
ejpam-5245	199	17	x.	x.	NOUN
ejpam-5245	199	18	(	(	PUNCT
ejpam-5245	199	19	52	52	NUM
ejpam-5245	199	20	)	)	PUNCT
ejpam-5245	199	21	for	for	ADP
ejpam-5245	199	22	an	an	DET
ejpam-5245	199	23	admissible	admissible	ADJ
ejpam-5245	199	24	vector	vector	NOUN
ejpam-5245	199	25	w0	w0	NOUN
ejpam-5245	199	26	[	[	X
ejpam-5245	199	27	1	1	NUM
ejpam-5245	199	28	]	]	PUNCT
ejpam-5245	199	29	,	,	PUNCT
ejpam-5245	199	30	definition	definition	NOUN
ejpam-5245	199	31	8.1.1	8.1.1	NUM
ejpam-5245	199	32	,	,	PUNCT
ejpam-5245	199	33	the	the	DET
ejpam-5245	199	34	contravariant	contravariant	ADJ
ejpam-5245	199	35	transform	transform	NOUN
ejpam-5245	199	36	in	in	ADP
ejpam-5245	199	37	this	this	DET
ejpam-5245	199	38	setup	setup	NOUN
ejpam-5245	199	39	is	be	AUX
ejpam-5245	199	40	known	know	VERB
ejpam-5245	199	41	as	as	ADP
ejpam-5245	199	42	a	a	DET
ejpam-5245	199	43	reconstruction	reconstruction	NOUN
ejpam-5245	199	44	formula	formula	NOUN
ejpam-5245	199	45	.	.	PUNCT
ejpam-5245	200	1	example	example	NOUN
ejpam-5245	201	1	2	2	NUM
ejpam-5245	201	2	.	.	X
ejpam-5245	202	1	for	for	ADP
ejpam-5245	202	2	the	the	DET
ejpam-5245	202	3	representation	representation	NOUN
ejpam-5245	202	4	ρτ	ρτ	X
ejpam-5245	202	5	(	(	PUNCT
ejpam-5245	202	6	31	31	NUM
ejpam-5245	202	7	)	)	PUNCT
ejpam-5245	202	8	with	with	ADP
ejpam-5245	202	9	τ	τ	PROPN
ejpam-5245	202	10	=	=	SYM
ejpam-5245	202	11	0	0	PROPN
ejpam-5245	202	12	,	,	PUNCT
ejpam-5245	202	13	we	we	PRON
ejpam-5245	202	14	take	take	VERB
ejpam-5245	202	15	the	the	DET
ejpam-5245	202	16	k	k	NOUN
ejpam-5245	202	17	-	-	NOUN
ejpam-5245	202	18	eigenvector	eigenvector	NOUN
ejpam-5245	202	19	ϕ0(w	ϕ0(w	NOUN
ejpam-5245	202	20	,	,	PUNCT
ejpam-5245	202	21	w̄	w̄	NOUN
ejpam-5245	202	22	)	)	PUNCT
ejpam-5245	202	23	=	=	PRON
ejpam-5245	203	1	(	(	PUNCT
ejpam-5245	203	2	v	v	NUM
ejpam-5245	203	3	2	2	NUM
ejpam-5245	203	4	+	+	NOUN
ejpam-5245	203	5	2u2	2u2	NUM
ejpam-5245	203	6	)	)	PUNCT
ejpam-5245	203	7	1+is	1+is	NUM
ejpam-5245	203	8	2	2	NUM
ejpam-5245	203	9	(	(	PUNCT
ejpam-5245	203	10	46	46	NUM
ejpam-5245	203	11	)	)	PUNCT
ejpam-5245	203	12	.	.	PUNCT
ejpam-5245	204	1	then	then	ADV
ejpam-5245	204	2	,	,	PUNCT
ejpam-5245	204	3	the	the	DET
ejpam-5245	204	4	corresponding	corresponding	ADJ
ejpam-5245	204	5	contravariant	contravariant	ADJ
ejpam-5245	204	6	transform	transform	NOUN
ejpam-5245	204	7	is	be	AUX
ejpam-5245	204	8	:	:	PUNCT
ejpam-5245	204	9	[	[	PUNCT
ejpam-5245	204	10	mρτ	mρτ	PROPN
ejpam-5245	204	11	ϕ0	ϕ0	PROPN
ejpam-5245	204	12	f	f	X
ejpam-5245	204	13	]	]	X
ejpam-5245	204	14	(	(	PUNCT
ejpam-5245	204	15	w	w	NOUN
ejpam-5245	204	16	)	)	PUNCT
ejpam-5245	204	17	=	=	SYM
ejpam-5245	204	18	∫	∫	PROPN
ejpam-5245	204	19	h(ξ	h(ξ	PROPN
ejpam-5245	204	20	)	)	PUNCT
ejpam-5245	204	21	f(ξ)ρτ	f(ξ)ρτ	PROPN
ejpam-5245	204	22	(	(	PUNCT
ejpam-5245	204	23	s(ξ1	s(ξ1	NOUN
ejpam-5245	204	24	,	,	PUNCT
ejpam-5245	204	25	ξ2))ϕ0	ξ2))ϕ0	PROPN
ejpam-5245	204	26	dξ	dξ	PROPN
ejpam-5245	204	27	=	=	SYM
ejpam-5245	204	28	∫	∫	PROPN
ejpam-5245	204	29	r2	r2	PROPN
ejpam-5245	204	30	f(ξ)ρτ	f(ξ)ρτ	PROPN
ejpam-5245	204	31	(	(	PUNCT
ejpam-5245	204	32	(	(	PUNCT
ejpam-5245	204	33	ξ1	ξ1	NOUN
ejpam-5245	204	34	0	0	NUM
ejpam-5245	204	35	ξ2	ξ2	NOUN
ejpam-5245	204	36	1	1	NUM
ejpam-5245	204	37	ξ1	ξ1	NOUN
ejpam-5245	204	38	)	)	PUNCT
ejpam-5245	204	39	)	)	PUNCT
ejpam-5245	205	1	(	(	PUNCT
ejpam-5245	205	2	v	v	NUM
ejpam-5245	205	3	2(1	2(1	NUM
ejpam-5245	205	4	+	+	CCONJ
ejpam-5245	205	5	u2	u2	NOUN
ejpam-5245	205	6	)	)	PUNCT
ejpam-5245	205	7	)	)	PUNCT
ejpam-5245	206	1	1+is	1+is	NUM
ejpam-5245	206	2	2	2	NUM
ejpam-5245	206	3	dξ1dξ2	dξ1dξ2	NOUN
ejpam-5245	206	4	=	=	SYM
ejpam-5245	206	5	∫	∫	PROPN
ejpam-5245	206	6	r2	r2	PROPN
ejpam-5245	206	7	f(ξ	f(ξ	PROPN
ejpam-5245	206	8	)	)	PUNCT
ejpam-5245	206	9	(	(	PUNCT
ejpam-5245	206	10	vξ21	vξ21	PROPN
ejpam-5245	206	11	2ξ21(ξ1	2ξ21(ξ1	NUM
ejpam-5245	206	12	−	−	NOUN
ejpam-5245	207	1	ξ2u)2	ξ2u)2	PROPN
ejpam-5245	207	2	+	+	PUNCT
ejpam-5245	207	3	2u2	2u2	NUM
ejpam-5245	207	4	)	)	PUNCT
ejpam-5245	207	5	1+is	1+is	NUM
ejpam-5245	207	6	2	2	NUM
ejpam-5245	207	7	dξ1dξ2	dξ1dξ2	NOUN
ejpam-5245	207	8	,	,	PUNCT
ejpam-5245	207	9	w	w	NOUN
ejpam-5245	207	10	=	=	PUNCT
ejpam-5245	207	11	u+	u+	NOUN
ejpam-5245	207	12	εv	εv	NOUN
ejpam-5245	207	13	.	.	PUNCT
ejpam-5245	208	1	(	(	PUNCT
ejpam-5245	208	2	53	53	NUM
ejpam-5245	208	3	)	)	PUNCT
ejpam-5245	208	4	proposition	proposition	NOUN
ejpam-5245	208	5	1	1	NUM
ejpam-5245	208	6	.	.	PUNCT
ejpam-5245	209	1	[	[	X
ejpam-5245	209	2	6	6	NUM
ejpam-5245	209	3	]	]	PUNCT
ejpam-5245	209	4	,	,	PUNCT
ejpam-5245	209	5	prop	prop	NOUN
ejpam-5245	209	6	.	.	PUNCT
ejpam-5245	210	1	6.4	6.4	NUM
ejpam-5245	210	2	contravariant	contravariant	ADJ
ejpam-5245	210	3	transform	transform	NOUN
ejpam-5245	210	4	mw0	mw0	NOUN
ejpam-5245	210	5	intertwines	intertwine	NOUN
ejpam-5245	210	6	left	leave	VERB
ejpam-5245	210	7	regular	regular	ADJ
ejpam-5245	210	8	representation	representation	NOUN
ejpam-5245	210	9	λ	λ	PROPN
ejpam-5245	210	10	on	on	ADP
ejpam-5245	210	11	l2(sl2(r	l2(sl2(r	NOUN
ejpam-5245	210	12	)	)	PUNCT
ejpam-5245	210	13	)	)	PUNCT
ejpam-5245	210	14	and	and	CCONJ
ejpam-5245	210	15	ρ	ρ	NUM
ejpam-5245	210	16	:	:	PUNCT
ejpam-5245	210	17	mw0λ(g	mw0λ(g	NOUN
ejpam-5245	210	18	)	)	PUNCT
ejpam-5245	210	19	=	=	PUNCT
ejpam-5245	211	1	ρ(g)mw0	ρ(g)mw0	X
ejpam-5245	211	2	.	.	PUNCT
ejpam-5245	212	1	(	(	PUNCT
ejpam-5245	212	2	54	54	NUM
ejpam-5245	212	3	)	)	PUNCT
ejpam-5245	212	4	let	let	VERB
ejpam-5245	212	5	ρ	ρ	NOUN
ejpam-5245	212	6	be	be	AUX
ejpam-5245	212	7	an	an	DET
ejpam-5245	212	8	irreducible	irreducible	ADJ
ejpam-5245	212	9	square	square	ADJ
ejpam-5245	212	10	integrable	integrable	ADJ
ejpam-5245	212	11	representation	representation	NOUN
ejpam-5245	212	12	and	and	CCONJ
ejpam-5245	212	13	φ0	φ0	PROPN
ejpam-5245	212	14	and	and	CCONJ
ejpam-5245	212	15	w0	w0	PROPN
ejpam-5245	212	16	be	be	VERB
ejpam-5245	212	17	admissible	admissible	ADJ
ejpam-5245	212	18	vectors	vector	NOUN
ejpam-5245	212	19	.	.	PUNCT
ejpam-5245	213	1	the	the	DET
ejpam-5245	213	2	covariant	covariant	PROPN
ejpam-5245	213	3	transform	transform	NOUN
ejpam-5245	213	4	intertwines	intertwine	VERB
ejpam-5245	213	5	ρ	ρ	PROPN
ejpam-5245	213	6	and	and	CCONJ
ejpam-5245	213	7	the	the	DET
ejpam-5245	213	8	left	left	ADJ
ejpam-5245	213	9	regular	regular	ADJ
ejpam-5245	213	10	representation	representation	NOUN
ejpam-5245	213	11	λ	λ	PROPN
ejpam-5245	213	12	:	:	PUNCT
ejpam-5245	213	13	wφ0ρ(g	wφ0ρ(g	NUM
ejpam-5245	213	14	)	)	PUNCT
ejpam-5245	213	15	=	=	SYM
ejpam-5245	214	1	λ(g)wφ0	λ(g)wφ0	X
ejpam-5245	214	2	.	.	PUNCT
ejpam-5245	215	1	combining	combine	VERB
ejpam-5245	215	2	with	with	ADP
ejpam-5245	215	3	(	(	PUNCT
ejpam-5245	215	4	54	54	NUM
ejpam-5245	215	5	)	)	PUNCT
ejpam-5245	215	6	,	,	PUNCT
ejpam-5245	215	7	we	we	PRON
ejpam-5245	215	8	see	see	VERB
ejpam-5245	215	9	that	that	SCONJ
ejpam-5245	215	10	the	the	DET
ejpam-5245	215	11	composition	composition	NOUN
ejpam-5245	215	12	mw0	mw0	NOUN
ejpam-5245	215	13	◦	◦	NOUN
ejpam-5245	215	14	wf	wf	PROPN
ejpam-5245	215	15	intertwines	intertwine	VERB
ejpam-5245	215	16	ρ	ρ	NOUN
ejpam-5245	215	17	with	with	ADP
ejpam-5245	215	18	itself	itself	PRON
ejpam-5245	215	19	.	.	PUNCT
ejpam-5245	216	1	that	that	PRON
ejpam-5245	216	2	is	be	AUX
ejpam-5245	216	3	,	,	PUNCT
ejpam-5245	216	4	(	(	PUNCT
ejpam-5245	216	5	mw0	mw0	NOUN
ejpam-5245	216	6	◦	◦	NOUN
ejpam-5245	216	7	wφ0	wφ0	NOUN
ejpam-5245	216	8	)	)	PUNCT
ejpam-5245	216	9	◦	◦	NOUN
ejpam-5245	216	10	ρ(g	ρ(g	NOUN
ejpam-5245	216	11	)	)	PUNCT
ejpam-5245	216	12	=	=	PUNCT
ejpam-5245	217	1	ρ(g	ρ(g	ADJ
ejpam-5245	217	2	)	)	PUNCT
ejpam-5245	217	3	◦	◦	NOUN
ejpam-5245	217	4	(	(	PUNCT
ejpam-5245	217	5	mw0	mw0	NOUN
ejpam-5245	217	6	◦	◦	NOUN
ejpam-5245	217	7	wφ0	wφ0	NOUN
ejpam-5245	217	8	)	)	PUNCT
ejpam-5245	217	9	.	.	PUNCT
ejpam-5245	218	1	(	(	PUNCT
ejpam-5245	218	2	55	55	NUM
ejpam-5245	218	3	)	)	PUNCT
ejpam-5245	218	4	thus	thus	ADV
ejpam-5245	218	5	,	,	PUNCT
ejpam-5245	218	6	from	from	ADP
ejpam-5245	218	7	the	the	DET
ejpam-5245	218	8	schur	schur	PROPN
ejpam-5245	218	9	’s	’s	PART
ejpam-5245	218	10	lemma	lemma	PROPN
ejpam-5245	218	11	we	we	PRON
ejpam-5245	218	12	have	have	VERB
ejpam-5245	218	13	the	the	DET
ejpam-5245	218	14	relation	relation	NOUN
ejpam-5245	218	15	mw0	mw0	NOUN
ejpam-5245	218	16	◦	◦	NOUN
ejpam-5245	218	17	wφ0	wφ0	NOUN
ejpam-5245	218	18	=	=	SYM
ejpam-5245	218	19	ki	ki	PROPN
ejpam-5245	218	20	,	,	PUNCT
ejpam-5245	218	21	(	(	PUNCT
ejpam-5245	218	22	56	56	NUM
ejpam-5245	218	23	)	)	PUNCT
ejpam-5245	218	24	for	for	ADP
ejpam-5245	218	25	some	some	DET
ejpam-5245	218	26	constant	constant	ADJ
ejpam-5245	218	27	k	k	PROPN
ejpam-5245	218	28	∈	∈	PROPN
ejpam-5245	218	29	c.	c.	NOUN
ejpam-5245	218	30	on	on	ADP
ejpam-5245	218	31	the	the	DET
ejpam-5245	218	32	other	other	ADJ
ejpam-5245	218	33	hand	hand	NOUN
ejpam-5245	218	34	,	,	PUNCT
ejpam-5245	218	35	and	and	CCONJ
ejpam-5245	218	36	from	from	ADP
ejpam-5245	218	37	the	the	DET
ejpam-5245	218	38	orthogonality	orthogonality	NOUN
ejpam-5245	218	39	relations	relation	NOUN
ejpam-5245	218	40	[	[	X
ejpam-5245	218	41	1	1	NUM
ejpam-5245	218	42	]	]	PUNCT
ejpam-5245	218	43	,	,	PUNCT
ejpam-5245	218	44	§	§	PROPN
ejpam-5245	218	45	8.2	8.2	NUM
ejpam-5245	218	46	:	:	PUNCT
ejpam-5245	218	47	⟨wφ1f1,wφ2f2⟩	⟨wφ1f1,wφ2f2⟩	NOUN
ejpam-5245	218	48	=	=	PUNCT
ejpam-5245	219	1	⟨f1	⟨f1	ADJ
ejpam-5245	219	2	,	,	PUNCT
ejpam-5245	219	3	f2⟩⟨cφ2	f2⟩⟨cφ2	NOUN
ejpam-5245	219	4	,	,	PUNCT
ejpam-5245	219	5	cφ1⟩	cφ1⟩	PROPN
ejpam-5245	219	6	,	,	PUNCT
ejpam-5245	219	7	(	(	PUNCT
ejpam-5245	219	8	57	57	NUM
ejpam-5245	219	9	)	)	PUNCT
ejpam-5245	219	10	where	where	SCONJ
ejpam-5245	219	11	c	c	NOUN
ejpam-5245	219	12	is	be	AUX
ejpam-5245	219	13	a	a	DET
ejpam-5245	219	14	unique	unique	ADJ
ejpam-5245	219	15	positive	positive	ADJ
ejpam-5245	219	16	,	,	PUNCT
ejpam-5245	219	17	self	self	NOUN
ejpam-5245	219	18	adjoint	adjoint	NOUN
ejpam-5245	219	19	and	and	CCONJ
ejpam-5245	219	20	invertible	invertible	ADJ
ejpam-5245	219	21	operator	operator	NOUN
ejpam-5245	219	22	in	in	ADP
ejpam-5245	219	23	the	the	DET
ejpam-5245	219	24	hilbert	hilbert	NOUN
ejpam-5245	219	25	space	space	NOUN
ejpam-5245	219	26	.	.	PUNCT
ejpam-5245	220	1	this	this	DET
ejpam-5245	220	2	operator	operator	NOUN
ejpam-5245	220	3	is	be	AUX
ejpam-5245	220	4	known	know	VERB
ejpam-5245	220	5	as	as	ADP
ejpam-5245	220	6	duflo	duflo	NOUN
ejpam-5245	220	7	-	-	PUNCT
ejpam-5245	220	8	moore	moore	NOUN
ejpam-5245	220	9	operator	operator	NOUN
ejpam-5245	220	10	.	.	PUNCT
ejpam-5245	221	1	if	if	SCONJ
ejpam-5245	221	2	f1	f1	PROPN
ejpam-5245	221	3	,	,	PUNCT
ejpam-5245	221	4	f2	f2	PROPN
ejpam-5245	221	5	∈	∈	PROPN
ejpam-5245	221	6	h	h	NOUN
ejpam-5245	221	7	,	,	PUNCT
ejpam-5245	221	8	we	we	PRON
ejpam-5245	221	9	have	have	VERB
ejpam-5245	221	10	⟨mw0	⟨mw0	NOUN
ejpam-5245	221	11	◦	◦	NOUN
ejpam-5245	221	12	wφ0f1	wφ0f1	NOUN
ejpam-5245	221	13	,	,	PUNCT
ejpam-5245	221	14	f2⟩	f2⟩	VERB
ejpam-5245	222	1	=	=	PUNCT
ejpam-5245	222	2	⟨wφ0f1,ww0f2⟩	⟨wφ0f1,ww0f2⟩	NOUN
ejpam-5245	222	3	=	=	PUNCT
ejpam-5245	223	1	⟨f1	⟨f1	ADJ
ejpam-5245	223	2	,	,	PUNCT
ejpam-5245	223	3	f2⟩⟨cw0	f2⟩⟨cw0	PRON
ejpam-5245	223	4	,	,	PUNCT
ejpam-5245	223	5	cφ0⟩	cφ0⟩	PROPN
ejpam-5245	223	6	=	=	SYM
ejpam-5245	223	7	⟨⟨cφ0	⟨⟨cφ0	NUM
ejpam-5245	223	8	,	,	PUNCT
ejpam-5245	223	9	cw0⟩f1	cw0⟩f1	PROPN
ejpam-5245	223	10	,	,	PUNCT
ejpam-5245	223	11	f2⟩.	f2⟩.	X
ejpam-5245	223	12	(	(	PUNCT
ejpam-5245	223	13	58	58	NUM
ejpam-5245	223	14	)	)	PUNCT
ejpam-5245	223	15	f.	f.	PROPN
ejpam-5245	223	16	a.	a.	PROPN
ejpam-5245	223	17	alabbad	alabbad	PROPN
ejpam-5245	223	18	/	/	SYM
ejpam-5245	223	19	eur	eur	PROPN
ejpam-5245	223	20	.	.	PUNCT
ejpam-5245	224	1	j.	j.	PROPN
ejpam-5245	224	2	pure	pure	PROPN
ejpam-5245	224	3	appl	appl	PROPN
ejpam-5245	224	4	.	.	PROPN
ejpam-5245	224	5	math	math	PROPN
ejpam-5245	224	6	,	,	PUNCT
ejpam-5245	224	7	17	17	NUM
ejpam-5245	224	8	(	(	PUNCT
ejpam-5245	224	9	3	3	NUM
ejpam-5245	224	10	)	)	PUNCT
ejpam-5245	224	11	(	(	PUNCT
ejpam-5245	224	12	2024	2024	NUM
ejpam-5245	224	13	)	)	PUNCT
ejpam-5245	224	14	,	,	PUNCT
ejpam-5245	224	15	2092	2092	NUM
ejpam-5245	224	16	-	-	SYM
ejpam-5245	224	17	2105	2105	NUM
ejpam-5245	224	18	2102	2102	NUM
ejpam-5245	224	19	thus	thus	ADV
ejpam-5245	224	20	mw0	mw0	VERB
ejpam-5245	224	21	◦	◦	NOUN
ejpam-5245	224	22	wφ0	wφ0	NOUN
ejpam-5245	224	23	=	=	SYM
ejpam-5245	224	24	⟨cφ0	⟨cφ0	PROPN
ejpam-5245	224	25	,	,	PUNCT
ejpam-5245	224	26	cw0⟩i	cw0⟩i	PROPN
ejpam-5245	224	27	.	.	PROPN
ejpam-5245	224	28	(	(	PUNCT
ejpam-5245	224	29	59	59	NUM
ejpam-5245	224	30	)	)	PUNCT
ejpam-5245	224	31	and	and	CCONJ
ejpam-5245	224	32	for	for	ADP
ejpam-5245	224	33	non	non	ADJ
ejpam-5245	224	34	-	-	ADJ
ejpam-5245	224	35	orthogonal	orthogonal	ADJ
ejpam-5245	224	36	vectors	vector	NOUN
ejpam-5245	224	37	w0	w0	PROPN
ejpam-5245	224	38	and	and	CCONJ
ejpam-5245	224	39	φ0	φ0	PROPN
ejpam-5245	224	40	,	,	PUNCT
ejpam-5245	224	41	we	we	PRON
ejpam-5245	224	42	get	get	VERB
ejpam-5245	224	43	⟨cφ0	⟨cφ0	NOUN
ejpam-5245	224	44	,	,	PUNCT
ejpam-5245	225	1	cw0⟩	cw0⟩	PROPN
ejpam-5245	225	2	=	=	PROPN
ejpam-5245	225	3	k	k	PROPN
ejpam-5245	225	4	̸=	̸=	PROPN
ejpam-5245	225	5	0	0	NUM
ejpam-5245	225	6	.	.	PROPN
ejpam-5245	225	7	4.1	4.1	NUM
ejpam-5245	225	8	.	.	PUNCT
ejpam-5245	225	9	inversion	inversion	NOUN
ejpam-5245	225	10	formula	formula	NOUN
ejpam-5245	225	11	we	we	PRON
ejpam-5245	225	12	will	will	AUX
ejpam-5245	225	13	find	find	VERB
ejpam-5245	225	14	the	the	DET
ejpam-5245	225	15	inversion	inversion	NOUN
ejpam-5245	225	16	formula	formula	NOUN
ejpam-5245	225	17	for	for	ADP
ejpam-5245	225	18	the	the	DET
ejpam-5245	225	19	covariant	covariant	ADJ
ejpam-5245	225	20	transform	transform	NOUN
ejpam-5245	225	21	(	(	PUNCT
ejpam-5245	225	22	51	51	NUM
ejpam-5245	225	23	)	)	PUNCT
ejpam-5245	225	24	from	from	ADP
ejpam-5245	225	25	the	the	DET
ejpam-5245	225	26	relation	relation	NOUN
ejpam-5245	225	27	(	(	PUNCT
ejpam-5245	225	28	59	59	NUM
ejpam-5245	225	29	)	)	PUNCT
ejpam-5245	225	30	with	with	ADP
ejpam-5245	225	31	the	the	DET
ejpam-5245	225	32	contravariant	contravariant	PROPN
ejpam-5245	225	33	transform	transform	NOUN
ejpam-5245	225	34	mρτ	mρτ	PROPN
ejpam-5245	225	35	ϕ0	ϕ0	PROPN
ejpam-5245	225	36	(	(	PUNCT
ejpam-5245	225	37	53	53	NUM
ejpam-5245	225	38	):	):	PUNCT
ejpam-5245	225	39	f(w	f(w	PROPN
ejpam-5245	225	40	)	)	PUNCT
ejpam-5245	226	1	=	=	SYM
ejpam-5245	226	2	1	1	NUM
ejpam-5245	226	3	⟨cφ0	⟨cφ0	PROPN
ejpam-5245	226	4	,	,	PUNCT
ejpam-5245	227	1	cϕ0⟩	cϕ0⟩	PROPN
ejpam-5245	227	2	[	[	PUNCT
ejpam-5245	227	3	mρτ	mρτ	PROPN
ejpam-5245	227	4	ϕ0	ϕ0	PROPN
ejpam-5245	227	5	(	(	PUNCT
ejpam-5245	227	6	wρk	wρk	VERB
ejpam-5245	227	7	φ0	φ0	PROPN
ejpam-5245	227	8	f	f	PROPN
ejpam-5245	227	9	)	)	PUNCT
ejpam-5245	227	10	]	]	PUNCT
ejpam-5245	228	1	(	(	PUNCT
ejpam-5245	228	2	w	w	NOUN
ejpam-5245	228	3	)	)	PUNCT
ejpam-5245	228	4	=	=	SYM
ejpam-5245	228	5	1	1	NUM
ejpam-5245	228	6	⟨cφ0	⟨cφ0	NOUN
ejpam-5245	228	7	,	,	PUNCT
ejpam-5245	228	8	cϕ0⟩	cϕ0⟩	PROPN
ejpam-5245	228	9	∫	∫	PROPN
ejpam-5245	228	10	r2	r2	PROPN
ejpam-5245	228	11	wρk	wρk	VERB
ejpam-5245	228	12	φ0	φ0	PROPN
ejpam-5245	228	13	f(ξ	f(ξ	PROPN
ejpam-5245	228	14	)	)	PUNCT
ejpam-5245	228	15	(	(	PUNCT
ejpam-5245	228	16	vξ21	vξ21	PROPN
ejpam-5245	228	17	2ξ21(ξ1	2ξ21(ξ1	NUM
ejpam-5245	228	18	−	−	NOUN
ejpam-5245	229	1	ξ2u)2	ξ2u)2	PROPN
ejpam-5245	229	2	+	+	PUNCT
ejpam-5245	229	3	2u2	2u2	NUM
ejpam-5245	229	4	)	)	PUNCT
ejpam-5245	229	5	1+is	1+is	NUM
ejpam-5245	229	6	2	2	NUM
ejpam-5245	229	7	dξ1dξ2	dξ1dξ2	NOUN
ejpam-5245	229	8	.	.	PUNCT
ejpam-5245	230	1	(	(	PUNCT
ejpam-5245	230	2	60	60	NUM
ejpam-5245	230	3	)	)	PUNCT
ejpam-5245	230	4	the	the	DET
ejpam-5245	230	5	function	function	NOUN
ejpam-5245	230	6	h(s	h(s	PROPN
ejpam-5245	230	7	)	)	PUNCT
ejpam-5245	231	1	=	=	PUNCT
ejpam-5245	231	2	⟨cφ0	⟨cφ0	PROPN
ejpam-5245	231	3	,	,	PUNCT
ejpam-5245	231	4	cϕ0⟩	cϕ0⟩	NOUN
ejpam-5245	231	5	must	must	AUX
ejpam-5245	231	6	be	be	AUX
ejpam-5245	231	7	explicitly	explicitly	ADV
ejpam-5245	231	8	identified	identify	VERB
ejpam-5245	231	9	.	.	PUNCT
ejpam-5245	232	1	the	the	DET
ejpam-5245	232	2	following	following	ADJ
ejpam-5245	232	3	result	result	NOUN
ejpam-5245	232	4	is	be	AUX
ejpam-5245	232	5	an	an	DET
ejpam-5245	232	6	inversion	inversion	NOUN
ejpam-5245	232	7	formula	formula	NOUN
ejpam-5245	232	8	similar	similar	ADJ
ejpam-5245	232	9	to	to	ADP
ejpam-5245	232	10	that	that	PRON
ejpam-5245	232	11	in	in	ADP
ejpam-5245	232	12	gelfand	gelfand	PROPN
ejpam-5245	232	13	’s	’s	PART
ejpam-5245	232	14	book	book	NOUN
ejpam-5245	233	1	[	[	X
ejpam-5245	233	2	3	3	NUM
ejpam-5245	233	3	]	]	PUNCT
ejpam-5245	233	4	,	,	PUNCT
ejpam-5245	233	5	chap	chap	NOUN
ejpam-5245	233	6	.	.	PUNCT
ejpam-5245	234	1	3	3	NUM
ejpam-5245	234	2	,	,	PUNCT
ejpam-5245	234	3	theorem	theorem	VERB
ejpam-5245	234	4	3.2	3.2	NUM
ejpam-5245	234	5	,	,	PUNCT
ejpam-5245	234	6	but	but	CCONJ
ejpam-5245	234	7	with	with	ADP
ejpam-5245	234	8	a	a	DET
ejpam-5245	234	9	difference	difference	NOUN
ejpam-5245	234	10	in	in	ADP
ejpam-5245	234	11	the	the	DET
ejpam-5245	234	12	eigenvector	eigenvector	NOUN
ejpam-5245	234	13	and	and	CCONJ
ejpam-5245	234	14	with	with	ADP
ejpam-5245	234	15	a	a	DET
ejpam-5245	234	16	different	different	ADJ
ejpam-5245	234	17	method	method	NOUN
ejpam-5245	234	18	.	.	PUNCT
ejpam-5245	235	1	theorem	theorem	NOUN
ejpam-5245	235	2	2	2	NUM
ejpam-5245	235	3	.	.	X
ejpam-5245	236	1	for	for	ADP
ejpam-5245	236	2	f	f	PROPN
ejpam-5245	236	3	∈	∈	PROPN
ejpam-5245	236	4	l2(r2	l2(r2	NOUN
ejpam-5245	236	5	+	+	PROPN
ejpam-5245	236	6	,	,	PUNCT
ejpam-5245	236	7	dµ	dµ	PROPN
ejpam-5245	236	8	)	)	PUNCT
ejpam-5245	236	9	,	,	PUNCT
ejpam-5245	236	10	we	we	PRON
ejpam-5245	236	11	have	have	VERB
ejpam-5245	236	12	the	the	DET
ejpam-5245	236	13	inversion	inversion	NOUN
ejpam-5245	236	14	formula	formula	NOUN
ejpam-5245	236	15	f(w	f(w	NOUN
ejpam-5245	236	16	)	)	PUNCT
ejpam-5245	236	17	=	=	SYM
ejpam-5245	237	1	1	1	NUM
ejpam-5245	237	2	2π2	2π2	NUM
ejpam-5245	237	3	∫	∫	NOUN
ejpam-5245	237	4	r	r	NOUN
ejpam-5245	237	5	s	s	PROPN
ejpam-5245	237	6	tanh	tanh	NOUN
ejpam-5245	237	7	πs	πs	ADP
ejpam-5245	237	8	2	2	NUM
ejpam-5245	237	9	(	(	PUNCT
ejpam-5245	237	10	∫	∫	PROPN
ejpam-5245	237	11	r2	r2	PROPN
ejpam-5245	237	12	wρk	wρk	VERB
ejpam-5245	237	13	φ0	φ0	PROPN
ejpam-5245	237	14	f(ξ)ρτ	f(ξ)ρτ	PROPN
ejpam-5245	237	15	(	(	PUNCT
ejpam-5245	237	16	s(ξ1	s(ξ1	NOUN
ejpam-5245	237	17	,	,	PUNCT
ejpam-5245	237	18	ξ2))ϕ0(w	ξ2))ϕ0(w	PROPN
ejpam-5245	237	19	)	)	PUNCT
ejpam-5245	237	20	dξ1dξ2	dξ1dξ2	NOUN
ejpam-5245	237	21	)	)	PUNCT
ejpam-5245	237	22	ds	ds	PROPN
ejpam-5245	237	23	,	,	PUNCT
ejpam-5245	237	24	(	(	PUNCT
ejpam-5245	237	25	61	61	NUM
ejpam-5245	237	26	)	)	PUNCT
ejpam-5245	237	27	where	where	SCONJ
ejpam-5245	237	28	ρτ	ρτ	X
ejpam-5245	237	29	(	(	PUNCT
ejpam-5245	237	30	s(ξ1	s(ξ1	NOUN
ejpam-5245	237	31	,	,	PUNCT
ejpam-5245	237	32	ξ2))ϕ0(w	ξ2))ϕ0(w	NOUN
ejpam-5245	237	33	)	)	PUNCT
ejpam-5245	237	34	=	=	PUNCT
ejpam-5245	238	1	(	(	PUNCT
ejpam-5245	238	2	vξ21	vξ21	PROPN
ejpam-5245	238	3	2ξ21(ξ1	2ξ21(ξ1	NUM
ejpam-5245	238	4	−	−	NOUN
ejpam-5245	239	1	ξ2u)2	ξ2u)2	PROPN
ejpam-5245	239	2	+	+	PUNCT
ejpam-5245	239	3	2u2	2u2	NUM
ejpam-5245	239	4	)	)	PUNCT
ejpam-5245	239	5	1+is	1+is	NUM
ejpam-5245	239	6	2	2	NUM
ejpam-5245	239	7	,	,	PUNCT
ejpam-5245	239	8	and	and	CCONJ
ejpam-5245	239	9	wρk	wρk	VERB
ejpam-5245	239	10	φ0f	φ0f	ADV
ejpam-5245	239	11	is	be	AUX
ejpam-5245	239	12	the	the	DET
ejpam-5245	239	13	covariant	covariant	ADJ
ejpam-5245	239	14	transform	transform	NOUN
ejpam-5245	239	15	(	(	PUNCT
ejpam-5245	239	16	51	51	NUM
ejpam-5245	239	17	)	)	PUNCT
ejpam-5245	239	18	.	.	PUNCT
ejpam-5245	240	1	proof	proof	NOUN
ejpam-5245	240	2	.	.	PUNCT
ejpam-5245	241	1	to	to	PART
ejpam-5245	241	2	find	find	VERB
ejpam-5245	241	3	the	the	DET
ejpam-5245	241	4	inversion	inversion	NOUN
ejpam-5245	241	5	formula	formula	NOUN
ejpam-5245	241	6	for	for	ADP
ejpam-5245	241	7	the	the	DET
ejpam-5245	241	8	covariant	covariant	ADJ
ejpam-5245	241	9	transform	transform	NOUN
ejpam-5245	241	10	(	(	PUNCT
ejpam-5245	241	11	51	51	NUM
ejpam-5245	241	12	)	)	PUNCT
ejpam-5245	241	13	,	,	PUNCT
ejpam-5245	241	14	we	we	PRON
ejpam-5245	241	15	need	need	VERB
ejpam-5245	241	16	to	to	PART
ejpam-5245	241	17	identify	identify	VERB
ejpam-5245	241	18	⟨cφ0	⟨cφ0	PROPN
ejpam-5245	241	19	,	,	PUNCT
ejpam-5245	241	20	cw0⟩	cw0⟩	PROPN
ejpam-5245	241	21	in	in	ADP
ejpam-5245	241	22	(	(	PUNCT
ejpam-5245	241	23	60	60	NUM
ejpam-5245	241	24	):	):	PUNCT
ejpam-5245	241	25	⟨cφ0	⟨cφ0	PROPN
ejpam-5245	241	26	,	,	PUNCT
ejpam-5245	241	27	cw0⟩	cw0⟩	PROPN
ejpam-5245	241	28	=	=	SYM
ejpam-5245	241	29	1	1	NUM
ejpam-5245	241	30	f(w	f(w	PROPN
ejpam-5245	241	31	)	)	PUNCT
ejpam-5245	241	32	[	[	PUNCT
ejpam-5245	241	33	mρτ	mρτ	PROPN
ejpam-5245	241	34	ϕ0	ϕ0	PROPN
ejpam-5245	241	35	(	(	PUNCT
ejpam-5245	241	36	wρk	wρk	VERB
ejpam-5245	241	37	φ0	φ0	PROPN
ejpam-5245	241	38	f	f	PROPN
ejpam-5245	241	39	)	)	PUNCT
ejpam-5245	241	40	]	]	PUNCT
ejpam-5245	242	1	(	(	PUNCT
ejpam-5245	242	2	w	w	NOUN
ejpam-5245	242	3	)	)	PUNCT
ejpam-5245	242	4	=	=	SYM
ejpam-5245	242	5	1	1	NUM
ejpam-5245	242	6	f(w	f(w	PROPN
ejpam-5245	242	7	)	)	PUNCT
ejpam-5245	242	8	∫	∫	PROPN
ejpam-5245	242	9	r2	r2	PROPN
ejpam-5245	242	10	wρk	wρk	VERB
ejpam-5245	242	11	φ0	φ0	PROPN
ejpam-5245	242	12	f(ξ	f(ξ	PROPN
ejpam-5245	242	13	)	)	PUNCT
ejpam-5245	242	14	(	(	PUNCT
ejpam-5245	242	15	vξ21	vξ21	PROPN
ejpam-5245	242	16	2ξ21(ξ1	2ξ21(ξ1	NUM
ejpam-5245	242	17	−	−	NOUN
ejpam-5245	243	1	ξ2u)2	ξ2u)2	PROPN
ejpam-5245	243	2	+	+	PUNCT
ejpam-5245	243	3	2u2	2u2	NUM
ejpam-5245	243	4	)	)	PUNCT
ejpam-5245	243	5	1+is	1+is	NUM
ejpam-5245	243	6	2	2	NUM
ejpam-5245	243	7	dξ1dξ2	dξ1dξ2	NOUN
ejpam-5245	243	8	.	.	PUNCT
ejpam-5245	243	9	(	(	PUNCT
ejpam-5245	243	10	62	62	NUM
ejpam-5245	243	11	)	)	PUNCT
ejpam-5245	243	12	to	to	PART
ejpam-5245	243	13	identify	identify	VERB
ejpam-5245	243	14	this	this	DET
ejpam-5245	243	15	function	function	NOUN
ejpam-5245	243	16	,	,	PUNCT
ejpam-5245	243	17	it	it	PRON
ejpam-5245	243	18	is	be	AUX
ejpam-5245	243	19	enough	enough	ADJ
ejpam-5245	243	20	to	to	PART
ejpam-5245	243	21	compute	compute	VERB
ejpam-5245	243	22	the	the	DET
ejpam-5245	243	23	composition	composition	NOUN
ejpam-5245	243	24	of	of	ADP
ejpam-5245	243	25	the	the	DET
ejpam-5245	243	26	covariant	covariant	ADJ
ejpam-5245	243	27	transform	transform	NOUN
ejpam-5245	243	28	and	and	CCONJ
ejpam-5245	243	29	the	the	DET
ejpam-5245	243	30	contravariant	contravariant	PROPN
ejpam-5245	243	31	transform	transform	NOUN
ejpam-5245	243	32	for	for	ADP
ejpam-5245	243	33	one	one	NUM
ejpam-5245	243	34	particular	particular	ADJ
ejpam-5245	243	35	function	function	NOUN
ejpam-5245	243	36	.	.	PUNCT
ejpam-5245	244	1	let	let	VERB
ejpam-5245	244	2	f0(w	f0(w	PRON
ejpam-5245	244	3	)	)	PUNCT
ejpam-5245	244	4	=	=	PUNCT
ejpam-5245	245	1	vis+	vis+	NOUN
ejpam-5245	245	2	1	1	NUM
ejpam-5245	245	3	2	2	NUM
ejpam-5245	245	4	(	(	PUNCT
ejpam-5245	245	5	1	1	NUM
ejpam-5245	245	6	+	+	NOUN
ejpam-5245	245	7	v)−	v)−	PROPN
ejpam-5245	245	8	is+1	is+1	NOUN
ejpam-5245	245	9	2	2	NUM
ejpam-5245	245	10	1	1	NUM
ejpam-5245	245	11	+	+	CCONJ
ejpam-5245	245	12	u2	u2	PROPN
ejpam-5245	245	13	∈	∈	PROPN
ejpam-5245	245	14	l2(r2	l2(r2	NOUN
ejpam-5245	245	15	+	+	NOUN
ejpam-5245	245	16	,	,	PUNCT
ejpam-5245	245	17	dµ(w	dµ(w	PUNCT
ejpam-5245	245	18	)	)	PUNCT
ejpam-5245	245	19	)	)	PUNCT
ejpam-5245	245	20	,	,	PUNCT
ejpam-5245	245	21	0	0	NUM
ejpam-5245	245	22	<	<	X
ejpam-5245	245	23	ℜ(is	ℜ(is	PROPN
ejpam-5245	245	24	)	)	PUNCT
ejpam-5245	245	25	<	<	X
ejpam-5245	245	26	1	1	X
ejpam-5245	245	27	.	.	PUNCT
ejpam-5245	245	28	(	(	PUNCT
ejpam-5245	245	29	63	63	NUM
ejpam-5245	245	30	)	)	PUNCT
ejpam-5245	245	31	we	we	PRON
ejpam-5245	245	32	compute	compute	VERB
ejpam-5245	245	33	the	the	DET
ejpam-5245	245	34	covariant	covariant	ADJ
ejpam-5245	245	35	transform	transform	NOUN
ejpam-5245	245	36	for	for	ADP
ejpam-5245	245	37	the	the	DET
ejpam-5245	245	38	function	function	NOUN
ejpam-5245	245	39	f0	f0	PROPN
ejpam-5245	245	40	:	:	PUNCT
ejpam-5245	245	41	wρk	wρk	VERB
ejpam-5245	245	42	φ0	φ0	PROPN
ejpam-5245	245	43	f0(ξ	f0(ξ	PROPN
ejpam-5245	245	44	)	)	PUNCT
ejpam-5245	245	45	=	=	SYM
ejpam-5245	246	1	∫	∫	PROPN
ejpam-5245	247	1	+	+	NUM
ejpam-5245	247	2	∞	∞	PROPN
ejpam-5245	247	3	0	0	NUM
ejpam-5245	247	4	∫	∫	PROPN
ejpam-5245	248	1	+	+	NUM
ejpam-5245	248	2	∞	∞	PROPN
ejpam-5245	248	3	−∞	−∞	ADP
ejpam-5245	248	4	vis+	vis+	PROPN
ejpam-5245	248	5	1	1	NUM
ejpam-5245	248	6	2	2	NUM
ejpam-5245	248	7	(	(	PUNCT
ejpam-5245	248	8	1	1	NUM
ejpam-5245	248	9	+	+	NOUN
ejpam-5245	248	10	v)−	v)−	PROPN
ejpam-5245	248	11	is+1	is+1	NOUN
ejpam-5245	248	12	2	2	NUM
ejpam-5245	248	13	1	1	NUM
ejpam-5245	248	14	+	+	CCONJ
ejpam-5245	248	15	u2	u2	PROPN
ejpam-5245	248	16	v	v	ADP
ejpam-5245	248	17	1−is	1−is	NUM
ejpam-5245	248	18	2	2	NUM
ejpam-5245	248	19	(	(	PUNCT
ejpam-5245	248	20	1	1	NUM
ejpam-5245	248	21	|ξ1	|ξ1	NOUN
ejpam-5245	248	22	−	−	NUM
ejpam-5245	248	23	ξ2w|2	ξ2w|2	NOUN
ejpam-5245	248	24	)	)	PUNCT
ejpam-5245	248	25	1−is	1−is	NOUN
ejpam-5245	248	26	2	2	NUM
ejpam-5245	248	27	dudv	dudv	NOUN
ejpam-5245	248	28	v2	v2	PROPN
ejpam-5245	248	29	.	.	PUNCT
ejpam-5245	249	1	(	(	PUNCT
ejpam-5245	249	2	64	64	NUM
ejpam-5245	249	3	)	)	PUNCT
ejpam-5245	249	4	f.	f.	NOUN
ejpam-5245	249	5	a.	a.	PROPN
ejpam-5245	249	6	alabbad	alabbad	PROPN
ejpam-5245	249	7	/	/	SYM
ejpam-5245	249	8	eur	eur	PROPN
ejpam-5245	249	9	.	.	PUNCT
ejpam-5245	250	1	j.	j.	PROPN
ejpam-5245	250	2	pure	pure	PROPN
ejpam-5245	250	3	appl	appl	PROPN
ejpam-5245	250	4	.	.	PROPN
ejpam-5245	250	5	math	math	PROPN
ejpam-5245	250	6	,	,	PUNCT
ejpam-5245	250	7	17	17	NUM
ejpam-5245	250	8	(	(	PUNCT
ejpam-5245	250	9	3	3	NUM
ejpam-5245	250	10	)	)	PUNCT
ejpam-5245	250	11	(	(	PUNCT
ejpam-5245	250	12	2024	2024	NUM
ejpam-5245	250	13	)	)	PUNCT
ejpam-5245	250	14	,	,	PUNCT
ejpam-5245	250	15	2092	2092	NUM
ejpam-5245	250	16	-	-	SYM
ejpam-5245	250	17	2105	2105	NUM
ejpam-5245	250	18	2103	2103	NUM
ejpam-5245	250	19	and	and	CCONJ
ejpam-5245	250	20	for	for	ADP
ejpam-5245	250	21	ξ	ξ	PROPN
ejpam-5245	250	22	=	=	SYM
ejpam-5245	250	23	(	(	PUNCT
ejpam-5245	250	24	ξ1	ξ1	PROPN
ejpam-5245	250	25	,	,	PUNCT
ejpam-5245	250	26	0	0	NUM
ejpam-5245	250	27	)	)	PUNCT
ejpam-5245	250	28	,	,	PUNCT
ejpam-5245	250	29	this	this	DET
ejpam-5245	250	30	value	value	NOUN
ejpam-5245	250	31	becomes	become	VERB
ejpam-5245	250	32	wρk	wρk	NOUN
ejpam-5245	250	33	φ0	φ0	PROPN
ejpam-5245	250	34	f0(ξ	f0(ξ	PROPN
ejpam-5245	250	35	)	)	PUNCT
ejpam-5245	250	36	=	=	SYM
ejpam-5245	251	1	∫	∫	PROPN
ejpam-5245	252	1	+	+	NUM
ejpam-5245	252	2	∞	∞	PROPN
ejpam-5245	252	3	0	0	NUM
ejpam-5245	252	4	∫	∫	PROPN
ejpam-5245	253	1	+	+	NUM
ejpam-5245	253	2	∞	∞	PROPN
ejpam-5245	253	3	−∞	−∞	ADP
ejpam-5245	253	4	vis+	vis+	PROPN
ejpam-5245	253	5	1	1	NUM
ejpam-5245	253	6	2	2	NUM
ejpam-5245	253	7	(	(	PUNCT
ejpam-5245	253	8	1	1	NUM
ejpam-5245	253	9	+	+	NOUN
ejpam-5245	253	10	v)−	v)−	PROPN
ejpam-5245	253	11	is+1	is+1	NOUN
ejpam-5245	253	12	2	2	NUM
ejpam-5245	253	13	1	1	NUM
ejpam-5245	253	14	+	+	CCONJ
ejpam-5245	253	15	u2	u2	PROPN
ejpam-5245	253	16	v	v	ADP
ejpam-5245	253	17	1−is	1−is	NUM
ejpam-5245	253	18	2	2	NUM
ejpam-5245	253	19	−2	−2	NOUN
ejpam-5245	253	20	(	(	PUNCT
ejpam-5245	253	21	ξ21	ξ21	NOUN
ejpam-5245	253	22	)	)	PUNCT
ejpam-5245	253	23	is−1	is−1	NOUN
ejpam-5245	253	24	2	2	NUM
ejpam-5245	253	25	dudv	dudv	NOUN
ejpam-5245	253	26	=	=	PUNCT
ejpam-5245	253	27	(	(	PUNCT
ejpam-5245	253	28	ξ21	ξ21	NOUN
ejpam-5245	253	29	)	)	PUNCT
ejpam-5245	253	30	is−1	is−1	PROPN
ejpam-5245	253	31	2	2	NUM
ejpam-5245	253	32	∫	∫	NOUN
ejpam-5245	254	1	+	+	NOUN
ejpam-5245	254	2	∞	∞	PROPN
ejpam-5245	254	3	0	0	NUM
ejpam-5245	254	4	v	v	NOUN
ejpam-5245	254	5	is	be	AUX
ejpam-5245	254	6	2	2	NUM
ejpam-5245	254	7	−1(1	−1(1	ADJ
ejpam-5245	254	8	+	+	CCONJ
ejpam-5245	254	9	v)−	v)−	PROPN
ejpam-5245	254	10	is+1	is+1	PROPN
ejpam-5245	254	11	2	2	NUM
ejpam-5245	254	12	(	(	PUNCT
ejpam-5245	254	13	∫	∫	PROPN
ejpam-5245	255	1	+	+	PROPN
ejpam-5245	255	2	∞	∞	PROPN
ejpam-5245	255	3	−∞	−∞	ADP
ejpam-5245	255	4	1	1	NUM
ejpam-5245	255	5	1	1	NUM
ejpam-5245	255	6	+	+	CCONJ
ejpam-5245	255	7	u2	u2	PROPN
ejpam-5245	255	8	du	du	PROPN
ejpam-5245	255	9	)	)	PUNCT
ejpam-5245	255	10	dv	dv	PROPN
ejpam-5245	255	11	=	=	PUNCT
ejpam-5245	255	12	(	(	PUNCT
ejpam-5245	255	13	ξ21	ξ21	NOUN
ejpam-5245	255	14	)	)	PUNCT
ejpam-5245	255	15	is−1	is−1	PROPN
ejpam-5245	255	16	2	2	NUM
ejpam-5245	255	17	∫	∫	NOUN
ejpam-5245	256	1	+	+	NOUN
ejpam-5245	256	2	∞	∞	PROPN
ejpam-5245	256	3	0	0	NUM
ejpam-5245	256	4	v	v	NOUN
ejpam-5245	256	5	is	be	AUX
ejpam-5245	256	6	2	2	NUM
ejpam-5245	256	7	−1(1	−1(1	ADJ
ejpam-5245	256	8	+	+	CCONJ
ejpam-5245	256	9	v)−	v)−	PROPN
ejpam-5245	256	10	is+1	is+1	NOUN
ejpam-5245	256	11	2	2	NUM
ejpam-5245	256	12	π	π	PROPN
ejpam-5245	256	13	dv	dv	PROPN
ejpam-5245	256	14	=	=	NOUN
ejpam-5245	256	15	πe	πe	PROPN
ejpam-5245	256	16	is−1	is−1	PROPN
ejpam-5245	256	17	2	2	NUM
ejpam-5245	256	18	ϱ(i;ξ)b	ϱ(i;ξ)b	NOUN
ejpam-5245	256	19	(	(	PUNCT
ejpam-5245	256	20	is	be	AUX
ejpam-5245	256	21	2	2	NUM
ejpam-5245	256	22	,	,	PUNCT
ejpam-5245	256	23	1	1	NUM
ejpam-5245	256	24	2	2	NUM
ejpam-5245	256	25	)	)	PUNCT
ejpam-5245	256	26	,	,	PUNCT
ejpam-5245	256	27	(	(	PUNCT
ejpam-5245	256	28	65	65	NUM
ejpam-5245	256	29	)	)	PUNCT
ejpam-5245	256	30	where	where	SCONJ
ejpam-5245	256	31	ϱ(i	ϱ(i	PROPN
ejpam-5245	256	32	;	;	PUNCT
ejpam-5245	256	33	ξ	ξ	X
ejpam-5245	256	34	)	)	PUNCT
ejpam-5245	256	35	is	be	AUX
ejpam-5245	256	36	the	the	DET
ejpam-5245	256	37	distance	distance	NOUN
ejpam-5245	256	38	from	from	ADP
ejpam-5245	256	39	the	the	DET
ejpam-5245	256	40	point	point	NOUN
ejpam-5245	256	41	i	i	PRON
ejpam-5245	256	42	to	to	ADP
ejpam-5245	256	43	the	the	DET
ejpam-5245	256	44	horocycle	horocycle	NOUN
ejpam-5245	256	45	h(ξ	h(ξ	PROPN
ejpam-5245	256	46	)	)	PUNCT
ejpam-5245	256	47	and	and	CCONJ
ejpam-5245	256	48	b	b	PROPN
ejpam-5245	256	49	is	be	AUX
ejpam-5245	256	50	the	the	DET
ejpam-5245	256	51	beta	beta	ADJ
ejpam-5245	256	52	function	function	NOUN
ejpam-5245	256	53	.	.	PUNCT
ejpam-5245	257	1	then	then	ADV
ejpam-5245	257	2	,	,	PUNCT
ejpam-5245	257	3	we	we	PRON
ejpam-5245	257	4	find	find	VERB
ejpam-5245	257	5	the	the	DET
ejpam-5245	257	6	function	function	NOUN
ejpam-5245	257	7	(	(	PUNCT
ejpam-5245	257	8	62	62	NUM
ejpam-5245	257	9	)	)	PUNCT
ejpam-5245	257	10	with	with	ADP
ejpam-5245	257	11	(	(	PUNCT
ejpam-5245	257	12	ξ1	ξ1	NOUN
ejpam-5245	257	13	,	,	PUNCT
ejpam-5245	257	14	ξ2	ξ2	NOUN
ejpam-5245	257	15	)	)	PUNCT
ejpam-5245	257	16	=	=	SYM
ejpam-5245	257	17	(	(	PUNCT
ejpam-5245	257	18	ξ1	ξ1	NOUN
ejpam-5245	257	19	,	,	PUNCT
ejpam-5245	257	20	1	1	NUM
ejpam-5245	257	21	)	)	PUNCT
ejpam-5245	257	22	and	and	CCONJ
ejpam-5245	257	23	f(w	f(w	PROPN
ejpam-5245	257	24	)	)	PUNCT
ejpam-5245	257	25	=	=	SYM
ejpam-5245	258	1	f0(i	f0(i	NOUN
ejpam-5245	258	2	):	):	PUNCT
ejpam-5245	258	3	⟨cφ0	⟨cφ0	PROPN
ejpam-5245	258	4	,	,	PUNCT
ejpam-5245	258	5	cw0⟩	cw0⟩	PROPN
ejpam-5245	258	6	=	=	SYM
ejpam-5245	258	7	1	1	NUM
ejpam-5245	258	8	f0(i	f0(i	ADJ
ejpam-5245	258	9	)	)	PUNCT
ejpam-5245	258	10	∫	∫	PROPN
ejpam-5245	258	11	r	r	PROPN
ejpam-5245	258	12	wρk	wρk	NOUN
ejpam-5245	258	13	φ0	φ0	PROPN
ejpam-5245	258	14	f0((ξ1	f0((ξ1	PROPN
ejpam-5245	258	15	,	,	PUNCT
ejpam-5245	258	16	1	1	NUM
ejpam-5245	258	17	)	)	PUNCT
ejpam-5245	258	18	)	)	PUNCT
ejpam-5245	259	1	(	(	PUNCT
ejpam-5245	259	2	ξ21	ξ21	NOUN
ejpam-5245	259	3	2ξ21(ξ1	2ξ21(ξ1	NUM
ejpam-5245	259	4	)	)	PUNCT
ejpam-5245	259	5	2	2	NUM
ejpam-5245	259	6	)	)	PUNCT
ejpam-5245	259	7	1+is	1+is	NUM
ejpam-5245	259	8	2	2	NUM
ejpam-5245	259	9	dξ1	dξ1	NOUN
ejpam-5245	259	10	=	=	SYM
ejpam-5245	259	11	2	2	NUM
ejpam-5245	259	12	is+1	is+1	NUM
ejpam-5245	259	13	2	2	NUM
ejpam-5245	259	14	πb	πb	NOUN
ejpam-5245	259	15	(	(	PUNCT
ejpam-5245	259	16	is	be	AUX
ejpam-5245	259	17	2	2	NUM
ejpam-5245	259	18	,	,	PUNCT
ejpam-5245	259	19	1	1	NUM
ejpam-5245	259	20	2	2	NUM
ejpam-5245	259	21	)	)	PUNCT
ejpam-5245	260	1	∫	∫	NOUN
ejpam-5245	260	2	r	r	PROPN
ejpam-5245	260	3	e	e	PROPN
ejpam-5245	260	4	is−1	is−1	PROPN
ejpam-5245	260	5	2	2	NUM
ejpam-5245	260	6	ϱ(i;(ξ1,1	ϱ(i;(ξ1,1	NOUN
ejpam-5245	260	7	)	)	PUNCT
ejpam-5245	260	8	)	)	PUNCT
ejpam-5245	261	1	(	(	PUNCT
ejpam-5245	261	2	2ξ21	2ξ21	NUM
ejpam-5245	261	3	)	)	PUNCT
ejpam-5245	261	4	−	−	PROPN
ejpam-5245	262	1	1+is	1+is	NUM
ejpam-5245	262	2	2	2	NUM
ejpam-5245	262	3	dξ1	dξ1	NOUN
ejpam-5245	262	4	=	=	SYM
ejpam-5245	262	5	πb	πb	NOUN
ejpam-5245	262	6	(	(	PUNCT
ejpam-5245	262	7	is	be	AUX
ejpam-5245	262	8	2	2	NUM
ejpam-5245	262	9	,	,	PUNCT
ejpam-5245	262	10	1	1	NUM
ejpam-5245	262	11	2	2	NUM
ejpam-5245	262	12	)	)	PUNCT
ejpam-5245	262	13	∫	∫	PROPN
ejpam-5245	263	1	r	r	NOUN
ejpam-5245	263	2	(	(	PUNCT
ejpam-5245	263	3	ξ21	ξ21	NOUN
ejpam-5245	263	4	+	+	CCONJ
ejpam-5245	263	5	1	1	NUM
ejpam-5245	263	6	)	)	PUNCT
ejpam-5245	263	7	is−1	is−1	NOUN
ejpam-5245	263	8	2	2	NUM
ejpam-5245	263	9	(	(	PUNCT
ejpam-5245	263	10	ξ21	ξ21	NOUN
ejpam-5245	263	11	)	)	PUNCT
ejpam-5245	263	12	−	−	PROPN
ejpam-5245	263	13	1+is	1+is	NUM
ejpam-5245	263	14	2	2	NUM
ejpam-5245	263	15	dξ1	dξ1	NOUN
ejpam-5245	263	16	.	.	PUNCT
ejpam-5245	264	1	(	(	PUNCT
ejpam-5245	264	2	66	66	NUM
ejpam-5245	264	3	)	)	PUNCT
ejpam-5245	264	4	put	put	VERB
ejpam-5245	264	5	u	u	NOUN
ejpam-5245	264	6	=	=	PUNCT
ejpam-5245	264	7	(	(	PUNCT
ejpam-5245	264	8	ξ21	ξ21	PROPN
ejpam-5245	264	9	+	+	SYM
ejpam-5245	264	10	1)−1	1)−1	NUM
ejpam-5245	264	11	,	,	PUNCT
ejpam-5245	264	12	then	then	ADV
ejpam-5245	264	13	(	(	PUNCT
ejpam-5245	264	14	66	66	NUM
ejpam-5245	264	15	)	)	PUNCT
ejpam-5245	264	16	becomes	become	VERB
ejpam-5245	264	17	⟨cφ0	⟨cφ0	PROPN
ejpam-5245	264	18	,	,	PUNCT
ejpam-5245	264	19	cw0⟩	cw0⟩	PROPN
ejpam-5245	264	20	=	=	PUNCT
ejpam-5245	264	21	πb	πb	NOUN
ejpam-5245	264	22	(	(	PUNCT
ejpam-5245	264	23	is	be	AUX
ejpam-5245	264	24	2	2	NUM
ejpam-5245	264	25	,	,	PUNCT
ejpam-5245	264	26	1	1	NUM
ejpam-5245	264	27	2	2	NUM
ejpam-5245	264	28	)	)	PUNCT
ejpam-5245	264	29	∫	∫	PROPN
ejpam-5245	265	1	1	1	NUM
ejpam-5245	265	2	0	0	NUM
ejpam-5245	265	3	u	u	NOUN
ejpam-5245	265	4	1	1	NUM
ejpam-5245	265	5	2	2	NUM
ejpam-5245	265	6	−1(1−	−1(1−	NOUN
ejpam-5245	265	7	u)−	u)−	PROPN
ejpam-5245	265	8	is	be	AUX
ejpam-5245	265	9	2	2	NUM
ejpam-5245	265	10	−1	−1	NOUN
ejpam-5245	265	11	du	du	NOUN
ejpam-5245	265	12	=	=	PUNCT
ejpam-5245	265	13	πb	πb	NOUN
ejpam-5245	265	14	(	(	PUNCT
ejpam-5245	265	15	is	be	AUX
ejpam-5245	265	16	2	2	NUM
ejpam-5245	265	17	,	,	PUNCT
ejpam-5245	265	18	1	1	NUM
ejpam-5245	265	19	2	2	NUM
ejpam-5245	265	20	)	)	PUNCT
ejpam-5245	265	21	b(−	b(−	NOUN
ejpam-5245	265	22	is	be	AUX
ejpam-5245	265	23	2	2	NUM
ejpam-5245	265	24	,	,	PUNCT
ejpam-5245	265	25	1	1	NUM
ejpam-5245	265	26	2	2	NUM
ejpam-5245	265	27	)	)	PUNCT
ejpam-5245	265	28	=	=	PUNCT
ejpam-5245	266	1	π	π	X
ejpam-5245	266	2	γ	γ	X
ejpam-5245	266	3	(	(	PUNCT
ejpam-5245	266	4	is2	is2	PROPN
ejpam-5245	266	5	)	)	PUNCT
ejpam-5245	266	6	γ	γ	PROPN
ejpam-5245	266	7	(	(	PUNCT
ejpam-5245	266	8	1	1	NUM
ejpam-5245	266	9	2	2	NUM
ejpam-5245	266	10	)	)	PUNCT
ejpam-5245	266	11	γ	γ	X
ejpam-5245	266	12	(	(	PUNCT
ejpam-5245	266	13	is+1	is+1	PROPN
ejpam-5245	266	14	2	2	NUM
ejpam-5245	266	15	)	)	PUNCT
ejpam-5245	266	16	γ(−is	γ(−is	NOUN
ejpam-5245	266	17	2	2	NUM
ejpam-5245	266	18	)	)	PUNCT
ejpam-5245	266	19	γ(12	γ(12	PROPN
ejpam-5245	266	20	)	)	PUNCT
ejpam-5245	266	21	γ(−is+1	γ(−is+1	NOUN
ejpam-5245	266	22	2	2	NUM
ejpam-5245	266	23	)	)	PUNCT
ejpam-5245	266	24	=	=	SYM
ejpam-5245	266	25	π2	π2	PROPN
ejpam-5245	266	26	∣∣∣∣γ	∣∣∣∣γ	PROPN
ejpam-5245	266	27	(	(	PUNCT
ejpam-5245	266	28	is	be	AUX
ejpam-5245	266	29	2	2	NUM
ejpam-5245	266	30	)	)	PUNCT
ejpam-5245	266	31	∣∣∣∣2	∣∣∣∣2	PROPN
ejpam-5245	266	32	∣∣∣∣γ	∣∣∣∣γ	PROPN
ejpam-5245	266	33	(	(	PUNCT
ejpam-5245	266	34	is+	is+	VERB
ejpam-5245	266	35	1	1	NUM
ejpam-5245	266	36	2	2	NUM
ejpam-5245	266	37	)	)	PUNCT
ejpam-5245	266	38	∣∣∣∣−2	∣∣∣∣−2	PUNCT
ejpam-5245	267	1	=	=	SYM
ejpam-5245	267	2	π2	π2	ADP
ejpam-5245	267	3	2	2	NUM
ejpam-5245	267	4	s	s	NOUN
ejpam-5245	267	5	coth	coth	NOUN
ejpam-5245	267	6	πs	πs	ADP
ejpam-5245	267	7	2	2	NUM
ejpam-5245	267	8	.	.	PUNCT
ejpam-5245	268	1	(	(	PUNCT
ejpam-5245	268	2	67	67	NUM
ejpam-5245	268	3	)	)	PUNCT
ejpam-5245	268	4	substituting	substitute	VERB
ejpam-5245	268	5	this	this	DET
ejpam-5245	268	6	value	value	NOUN
ejpam-5245	268	7	in	in	ADP
ejpam-5245	268	8	(	(	PUNCT
ejpam-5245	268	9	60	60	NUM
ejpam-5245	268	10	)	)	PUNCT
ejpam-5245	268	11	,	,	PUNCT
ejpam-5245	268	12	we	we	PRON
ejpam-5245	268	13	obtain	obtain	VERB
ejpam-5245	268	14	f(w	f(w	NOUN
ejpam-5245	268	15	)	)	PUNCT
ejpam-5245	268	16	=	=	PUNCT
ejpam-5245	269	1	1	1	NUM
ejpam-5245	269	2	2π2	2π2	NUM
ejpam-5245	269	3	s	s	PART
ejpam-5245	269	4	tanh	tanh	NOUN
ejpam-5245	269	5	πs	πs	ADP
ejpam-5245	269	6	2	2	NUM
ejpam-5245	269	7	∫	∫	NOUN
ejpam-5245	269	8	r2	r2	PROPN
ejpam-5245	269	9	wρk	wρk	NOUN
ejpam-5245	269	10	φ0	φ0	PROPN
ejpam-5245	269	11	f(ξ	f(ξ	PROPN
ejpam-5245	269	12	)	)	PUNCT
ejpam-5245	269	13	(	(	PUNCT
ejpam-5245	269	14	vξ21	vξ21	PROPN
ejpam-5245	269	15	2ξ21(ξ1	2ξ21(ξ1	NUM
ejpam-5245	269	16	−	−	NOUN
ejpam-5245	270	1	ξ2u)2	ξ2u)2	PROPN
ejpam-5245	270	2	+	+	PUNCT
ejpam-5245	270	3	2u2	2u2	NUM
ejpam-5245	270	4	)	)	PUNCT
ejpam-5245	270	5	1+is	1+is	NUM
ejpam-5245	270	6	2	2	NUM
ejpam-5245	270	7	dξ1dξ2	dξ1dξ2	NOUN
ejpam-5245	270	8	.	.	PUNCT
ejpam-5245	270	9	(	(	PUNCT
ejpam-5245	270	10	68	68	NUM
ejpam-5245	270	11	)	)	PUNCT
ejpam-5245	270	12	and	and	CCONJ
ejpam-5245	270	13	for	for	ADP
ejpam-5245	270	14	s	s	PROPN
ejpam-5245	270	15	∈	∈	PROPN
ejpam-5245	270	16	r	r	NOUN
ejpam-5245	270	17	,	,	PUNCT
ejpam-5245	270	18	we	we	PRON
ejpam-5245	270	19	get	get	VERB
ejpam-5245	270	20	the	the	DET
ejpam-5245	270	21	inversion	inversion	NOUN
ejpam-5245	270	22	formula	formula	NOUN
ejpam-5245	270	23	f.	f.	PROPN
ejpam-5245	270	24	a.	a.	PROPN
ejpam-5245	270	25	alabbad	alabbad	PROPN
ejpam-5245	270	26	/	/	SYM
ejpam-5245	270	27	eur	eur	PROPN
ejpam-5245	270	28	.	.	PUNCT
ejpam-5245	271	1	j.	j.	PROPN
ejpam-5245	271	2	pure	pure	PROPN
ejpam-5245	271	3	appl	appl	PROPN
ejpam-5245	271	4	.	.	PROPN
ejpam-5245	271	5	math	math	PROPN
ejpam-5245	271	6	,	,	PUNCT
ejpam-5245	271	7	17	17	NUM
ejpam-5245	271	8	(	(	PUNCT
ejpam-5245	271	9	3	3	NUM
ejpam-5245	271	10	)	)	PUNCT
ejpam-5245	271	11	(	(	PUNCT
ejpam-5245	271	12	2024	2024	NUM
ejpam-5245	271	13	)	)	PUNCT
ejpam-5245	271	14	,	,	PUNCT
ejpam-5245	271	15	2092	2092	NUM
ejpam-5245	271	16	-	-	SYM
ejpam-5245	271	17	2105	2105	NUM
ejpam-5245	271	18	2104	2104	NUM
ejpam-5245	271	19	f(w	f(w	PROPN
ejpam-5245	271	20	)	)	PUNCT
ejpam-5245	271	21	=	=	SYM
ejpam-5245	272	1	1	1	NUM
ejpam-5245	272	2	2π2	2π2	NUM
ejpam-5245	272	3	∫	∫	NOUN
ejpam-5245	272	4	r	r	NOUN
ejpam-5245	272	5	s	s	PROPN
ejpam-5245	272	6	tanh	tanh	NOUN
ejpam-5245	272	7	πs	πs	ADP
ejpam-5245	272	8	2	2	NUM
ejpam-5245	272	9	(	(	PUNCT
ejpam-5245	272	10	∫	∫	PROPN
ejpam-5245	272	11	r2	r2	PROPN
ejpam-5245	272	12	wρk	wρk	VERB
ejpam-5245	272	13	φ0	φ0	PROPN
ejpam-5245	272	14	f(ξ)ρτ	f(ξ)ρτ	PROPN
ejpam-5245	272	15	(	(	PUNCT
ejpam-5245	272	16	s(ξ1	s(ξ1	NOUN
ejpam-5245	272	17	,	,	PUNCT
ejpam-5245	272	18	ξ2))ϕ0(w	ξ2))ϕ0(w	PROPN
ejpam-5245	272	19	)	)	PUNCT
ejpam-5245	272	20	dξ1dξ2	dξ1dξ2	NOUN
ejpam-5245	272	21	)	)	PUNCT
ejpam-5245	272	22	ds	ds	PROPN
ejpam-5245	272	23	,	,	PUNCT
ejpam-5245	272	24	(	(	PUNCT
ejpam-5245	272	25	69	69	NUM
ejpam-5245	272	26	)	)	PUNCT
ejpam-5245	272	27	where	where	SCONJ
ejpam-5245	272	28	ρτ	ρτ	X
ejpam-5245	272	29	(	(	PUNCT
ejpam-5245	272	30	s(ξ1	s(ξ1	NOUN
ejpam-5245	272	31	,	,	PUNCT
ejpam-5245	272	32	ξ2))ϕ0(w	ξ2))ϕ0(w	NOUN
ejpam-5245	272	33	)	)	PUNCT
ejpam-5245	272	34	=	=	PUNCT
ejpam-5245	273	1	(	(	PUNCT
ejpam-5245	273	2	vξ21	vξ21	PROPN
ejpam-5245	273	3	2ξ21(ξ1	2ξ21(ξ1	NUM
ejpam-5245	273	4	−	−	NOUN
ejpam-5245	274	1	ξ2u)2	ξ2u)2	PROPN
ejpam-5245	274	2	+	+	PUNCT
ejpam-5245	274	3	2u2	2u2	NUM
ejpam-5245	274	4	)	)	PUNCT
ejpam-5245	274	5	1+is	1+is	NUM
ejpam-5245	274	6	2	2	NUM
ejpam-5245	274	7	.	.	PUNCT
ejpam-5245	275	1	(	(	PUNCT
ejpam-5245	275	2	70	70	NUM
ejpam-5245	275	3	)	)	PUNCT
ejpam-5245	275	4	the	the	DET
ejpam-5245	275	5	inversion	inversion	NOUN
ejpam-5245	275	6	formula	formula	NOUN
ejpam-5245	275	7	is	be	AUX
ejpam-5245	275	8	equivalent	equivalent	ADJ
ejpam-5245	275	9	to	to	ADP
ejpam-5245	275	10	the	the	DET
ejpam-5245	275	11	decomposition	decomposition	NOUN
ejpam-5245	275	12	of	of	ADP
ejpam-5245	275	13	the	the	DET
ejpam-5245	275	14	unitary	unitary	ADJ
ejpam-5245	275	15	representation	representation	NOUN
ejpam-5245	275	16	ρk	ρk	ADP
ejpam-5245	275	17	,	,	PUNCT
ejpam-5245	275	18	k	k	PROPN
ejpam-5245	275	19	=	=	SYM
ejpam-5245	275	20	0	0	NUM
ejpam-5245	275	21	(	(	PUNCT
ejpam-5245	275	22	17	17	NUM
ejpam-5245	275	23	)	)	PUNCT
ejpam-5245	275	24	into	into	ADP
ejpam-5245	275	25	irreducible	irreducible	ADJ
ejpam-5245	275	26	components	component	NOUN
ejpam-5245	275	27	.	.	PUNCT
ejpam-5245	276	1	we	we	PRON
ejpam-5245	276	2	will	will	AUX
ejpam-5245	276	3	describe	describe	VERB
ejpam-5245	276	4	the	the	DET
ejpam-5245	276	5	irreducible	irreducible	ADJ
ejpam-5245	276	6	invariant	invariant	ADJ
ejpam-5245	276	7	subspaces	subspace	NOUN
ejpam-5245	276	8	hs	hs	PRON
ejpam-5245	276	9	.	.	PROPN
ejpam-5245	276	10	consider	consider	VERB
ejpam-5245	276	11	the	the	DET
ejpam-5245	276	12	eigenspace	eigenspace	NOUN
ejpam-5245	276	13	{	{	PUNCT
ejpam-5245	276	14	f	f	PROPN
ejpam-5245	276	15	∈	∈	PROPN
ejpam-5245	276	16	l2(h+	l2(h+	PROPN
ejpam-5245	276	17	)	)	PUNCT
ejpam-5245	276	18	:	:	PUNCT
ejpam-5245	277	1	dρk(c)f	dρk(c)f	NOUN
ejpam-5245	277	2	=	=	SYM
ejpam-5245	277	3	(	(	PUNCT
ejpam-5245	277	4	1	1	NUM
ejpam-5245	277	5	+	+	CCONJ
ejpam-5245	277	6	s2)f	s2)f	NOUN
ejpam-5245	277	7	}	}	PUNCT
ejpam-5245	277	8	.	.	PUNCT
ejpam-5245	278	1	(	(	PUNCT
ejpam-5245	278	2	71	71	NUM
ejpam-5245	278	3	)	)	PUNCT
ejpam-5245	278	4	this	this	DET
ejpam-5245	278	5	space	space	NOUN
ejpam-5245	278	6	is	be	AUX
ejpam-5245	278	7	spanned	span	VERB
ejpam-5245	278	8	by	by	ADP
ejpam-5245	278	9	the	the	DET
ejpam-5245	278	10	functions	function	NOUN
ejpam-5245	278	11	(	(	PUNCT
ejpam-5245	278	12	70	70	NUM
ejpam-5245	278	13	)	)	PUNCT
ejpam-5245	278	14	.	.	PUNCT
ejpam-5245	279	1	thus	thus	ADV
ejpam-5245	279	2	,	,	PUNCT
ejpam-5245	279	3	the	the	DET
ejpam-5245	279	4	elements	element	NOUN
ejpam-5245	279	5	of	of	ADP
ejpam-5245	279	6	this	this	DET
ejpam-5245	279	7	eigenspace	eigenspace	NOUN
ejpam-5245	279	8	can	can	AUX
ejpam-5245	279	9	be	be	AUX
ejpam-5245	279	10	presented	present	VERB
ejpam-5245	279	11	as	as	ADP
ejpam-5245	279	12	a	a	DET
ejpam-5245	279	13	continuous	continuous	ADJ
ejpam-5245	279	14	linear	linear	NOUN
ejpam-5245	279	15	combination	combination	NOUN
ejpam-5245	279	16	over	over	ADP
ejpam-5245	279	17	a	a	DET
ejpam-5245	279	18	set	set	NOUN
ejpam-5245	279	19	of	of	ADP
ejpam-5245	279	20	such	such	ADJ
ejpam-5245	279	21	functions	function	NOUN
ejpam-5245	279	22	,	,	PUNCT
ejpam-5245	279	23	that	that	PRON
ejpam-5245	279	24	is	be	AUX
ejpam-5245	279	25	fs(w	fs(w	ADJ
ejpam-5245	279	26	)	)	PUNCT
ejpam-5245	280	1	=	=	SYM
ejpam-5245	280	2	∫	∫	PROPN
ejpam-5245	280	3	r2	r2	PROPN
ejpam-5245	280	4	wρk	wρk	VERB
ejpam-5245	280	5	φ0	φ0	PROPN
ejpam-5245	280	6	f(ξ	f(ξ	PROPN
ejpam-5245	280	7	)	)	PUNCT
ejpam-5245	280	8	(	(	PUNCT
ejpam-5245	280	9	vξ21	vξ21	PROPN
ejpam-5245	280	10	2ξ21(ξ1	2ξ21(ξ1	NUM
ejpam-5245	280	11	−	−	NOUN
ejpam-5245	281	1	ξ2u)2	ξ2u)2	PROPN
ejpam-5245	281	2	+	+	PUNCT
ejpam-5245	281	3	2u2	2u2	NUM
ejpam-5245	281	4	)	)	PUNCT
ejpam-5245	281	5	1+is	1+is	NUM
ejpam-5245	281	6	2	2	NUM
ejpam-5245	281	7	dξ1dξ2	dξ1dξ2	NOUN
ejpam-5245	281	8	,	,	PUNCT
ejpam-5245	281	9	(	(	PUNCT
ejpam-5245	281	10	72	72	NUM
ejpam-5245	281	11	)	)	PUNCT
ejpam-5245	281	12	where	where	SCONJ
ejpam-5245	281	13	fs	f	NOUN
ejpam-5245	281	14	belongs	belong	VERB
ejpam-5245	281	15	to	to	ADP
ejpam-5245	281	16	the	the	DET
ejpam-5245	281	17	space	space	NOUN
ejpam-5245	281	18	hs	hs	PROPN
ejpam-5245	281	19	⊂	⊂	PROPN
ejpam-5245	281	20	l2(h+	l2(h+	PROPN
ejpam-5245	281	21	)	)	PUNCT
ejpam-5245	281	22	.	.	PUNCT
ejpam-5245	282	1	introduce	introduce	VERB
ejpam-5245	282	2	the	the	DET
ejpam-5245	282	3	projection	projection	NOUN
ejpam-5245	282	4	operator	operator	NOUN
ejpam-5245	282	5	ps	ps	NOUN
ejpam-5245	282	6	:	:	PUNCT
ejpam-5245	282	7	l2(h+	l2(h+	PROPN
ejpam-5245	282	8	)	)	PUNCT
ejpam-5245	282	9	→	→	SYM
ejpam-5245	282	10	hs	hs	X
ejpam-5245	282	11	by	by	ADP
ejpam-5245	282	12	psf	psf	NOUN
ejpam-5245	282	13	=	=	SYM
ejpam-5245	282	14	fs	fs	PROPN
ejpam-5245	282	15	.	.	PUNCT
ejpam-5245	283	1	thus	thus	ADV
ejpam-5245	283	2	,	,	PUNCT
ejpam-5245	283	3	the	the	DET
ejpam-5245	283	4	problem	problem	NOUN
ejpam-5245	283	5	of	of	ADP
ejpam-5245	283	6	decomposing	decompose	VERB
ejpam-5245	283	7	the	the	DET
ejpam-5245	283	8	space	space	NOUN
ejpam-5245	283	9	l2(h+	l2(h+	PROPN
ejpam-5245	283	10	)	)	PUNCT
ejpam-5245	283	11	into	into	ADP
ejpam-5245	283	12	irreducible	irreducible	ADJ
ejpam-5245	283	13	subspaces	subspace	NOUN
ejpam-5245	283	14	consists	consist	VERB
ejpam-5245	283	15	in	in	ADP
ejpam-5245	283	16	expanding	expand	VERB
ejpam-5245	283	17	the	the	DET
ejpam-5245	283	18	functions	function	NOUN
ejpam-5245	283	19	f	f	PROPN
ejpam-5245	283	20	∈	∈	PROPN
ejpam-5245	283	21	l2(h+	l2(h+	PROPN
ejpam-5245	283	22	)	)	PUNCT
ejpam-5245	283	23	in	in	ADP
ejpam-5245	283	24	their	their	PRON
ejpam-5245	283	25	projections	projection	NOUN
ejpam-5245	283	26	fs	fs	VERB
ejpam-5245	283	27	.	.	PUNCT
ejpam-5245	284	1	the	the	DET
ejpam-5245	284	2	solution	solution	NOUN
ejpam-5245	284	3	of	of	ADP
ejpam-5245	284	4	this	this	DET
ejpam-5245	284	5	problem	problem	NOUN
ejpam-5245	284	6	is	be	AUX
ejpam-5245	284	7	given	give	VERB
ejpam-5245	284	8	by	by	ADP
ejpam-5245	284	9	(	(	PUNCT
ejpam-5245	284	10	69	69	NUM
ejpam-5245	284	11	)	)	PUNCT
ejpam-5245	284	12	,	,	PUNCT
ejpam-5245	284	13	since	since	SCONJ
ejpam-5245	284	14	this	this	DET
ejpam-5245	284	15	formula	formula	NOUN
ejpam-5245	284	16	can	can	AUX
ejpam-5245	284	17	be	be	AUX
ejpam-5245	284	18	written	write	VERB
ejpam-5245	284	19	as	as	SCONJ
ejpam-5245	284	20	follows	follow	VERB
ejpam-5245	284	21	:	:	PUNCT
ejpam-5245	284	22	f(w	f(w	NUM
ejpam-5245	284	23	)	)	PUNCT
ejpam-5245	284	24	=	=	SYM
ejpam-5245	285	1	1	1	NUM
ejpam-5245	285	2	2π2	2π2	NUM
ejpam-5245	285	3	∫	∫	NOUN
ejpam-5245	285	4	r	r	NOUN
ejpam-5245	285	5	s	s	PROPN
ejpam-5245	285	6	tanh	tanh	NOUN
ejpam-5245	285	7	πs	πs	ADP
ejpam-5245	285	8	2	2	NUM
ejpam-5245	285	9	fsds	fsds	NOUN
ejpam-5245	285	10	,	,	PUNCT
ejpam-5245	285	11	fs	fs	ADP
ejpam-5245	285	12	=	=	PUNCT
ejpam-5245	285	13	psf	psf	NOUN
ejpam-5245	285	14	.	.	PUNCT
ejpam-5245	286	1	(	(	PUNCT
ejpam-5245	286	2	73	73	NUM
ejpam-5245	286	3	)	)	PUNCT
ejpam-5245	286	4	5	5	NUM
ejpam-5245	286	5	.	.	PUNCT
ejpam-5245	286	6	conclusion	conclusion	NOUN
ejpam-5245	286	7	in	in	ADP
ejpam-5245	286	8	this	this	DET
ejpam-5245	286	9	paper	paper	NOUN
ejpam-5245	286	10	,	,	PUNCT
ejpam-5245	286	11	we	we	PRON
ejpam-5245	286	12	obtain	obtain	VERB
ejpam-5245	286	13	the	the	DET
ejpam-5245	286	14	covariant	covariant	NOUN
ejpam-5245	286	15	and	and	CCONJ
ejpam-5245	286	16	contravariant	contravariant	PROPN
ejpam-5245	286	17	transforms	transform	VERB
ejpam-5245	286	18	using	use	VERB
ejpam-5245	286	19	the	the	DET
ejpam-5245	286	20	representation	representation	NOUN
ejpam-5245	286	21	itself	itself	PRON
ejpam-5245	286	22	like	like	ADP
ejpam-5245	286	23	in	in	ADP
ejpam-5245	286	24	gelfand	gelfand	PROPN
ejpam-5245	286	25	’s	’s	PART
ejpam-5245	286	26	approach	approach	NOUN
ejpam-5245	286	27	[	[	X
ejpam-5245	286	28	5	5	NUM
ejpam-5245	286	29	]	]	PUNCT
ejpam-5245	286	30	,	,	PUNCT
ejpam-5245	286	31	but	but	CCONJ
ejpam-5245	286	32	the	the	DET
ejpam-5245	286	33	eigenvectors	eigenvector	NOUN
ejpam-5245	286	34	are	be	AUX
ejpam-5245	286	35	selected	select	VERB
ejpam-5245	286	36	by	by	ADP
ejpam-5245	286	37	the	the	DET
ejpam-5245	286	38	derived	derive	VERB
ejpam-5245	286	39	representation	representation	NOUN
ejpam-5245	286	40	as	as	ADP
ejpam-5245	286	41	in	in	ADP
ejpam-5245	286	42	bargmann	bargmann	PROPN
ejpam-5245	286	43	’s	’s	PART
ejpam-5245	286	44	works	work	NOUN
ejpam-5245	286	45	[	[	X
ejpam-5245	286	46	2	2	NUM
ejpam-5245	286	47	]	]	PUNCT
ejpam-5245	286	48	.	.	PUNCT
ejpam-5245	287	1	we	we	PRON
ejpam-5245	287	2	use	use	VERB
ejpam-5245	287	3	the	the	DET
ejpam-5245	287	4	relation	relation	NOUN
ejpam-5245	287	5	between	between	ADP
ejpam-5245	287	6	these	these	PRON
ejpam-5245	287	7	transforms	transform	VERB
ejpam-5245	287	8	to	to	PART
ejpam-5245	287	9	find	find	VERB
ejpam-5245	287	10	the	the	DET
ejpam-5245	287	11	inversion	inversion	NOUN
ejpam-5245	287	12	formula	formula	NOUN
ejpam-5245	287	13	.	.	PUNCT
ejpam-5245	288	1	thus	thus	ADV
ejpam-5245	288	2	,	,	PUNCT
ejpam-5245	288	3	the	the	DET
ejpam-5245	288	4	original	original	ADJ
ejpam-5245	288	5	contribution	contribution	NOUN
ejpam-5245	288	6	is	be	AUX
ejpam-5245	288	7	using	use	VERB
ejpam-5245	288	8	the	the	DET
ejpam-5245	288	9	covariant	covariant	ADJ
ejpam-5245	288	10	transform	transform	NOUN
ejpam-5245	288	11	to	to	PART
ejpam-5245	288	12	find	find	VERB
ejpam-5245	288	13	the	the	DET
ejpam-5245	288	14	inversion	inversion	NOUN
ejpam-5245	288	15	formula	formula	NOUN
ejpam-5245	288	16	with	with	ADP
ejpam-5245	288	17	eigenvectors	eigenvector	NOUN
ejpam-5245	288	18	selected	select	VERB
ejpam-5245	288	19	by	by	ADP
ejpam-5245	288	20	the	the	DET
ejpam-5245	288	21	derived	derive	VERB
ejpam-5245	288	22	representation	representation	NOUN
ejpam-5245	288	23	.	.	PUNCT
ejpam-5245	289	1	this	this	DET
ejpam-5245	289	2	new	new	ADJ
ejpam-5245	289	3	method	method	NOUN
ejpam-5245	289	4	will	will	AUX
ejpam-5245	289	5	be	be	AUX
ejpam-5245	289	6	easier	easy	ADJ
ejpam-5245	289	7	to	to	PART
ejpam-5245	289	8	adopt	adopt	VERB
ejpam-5245	289	9	for	for	ADP
ejpam-5245	289	10	problems	problem	NOUN
ejpam-5245	289	11	of	of	ADP
ejpam-5245	289	12	decomposing	decompose	VERB
ejpam-5245	289	13	a	a	DET
ejpam-5245	289	14	system	system	NOUN
ejpam-5245	289	15	into	into	ADP
ejpam-5245	289	16	elementary	elementary	ADJ
ejpam-5245	289	17	bits	bit	NOUN
ejpam-5245	289	18	in	in	ADP
ejpam-5245	289	19	theoretical	theoretical	ADJ
ejpam-5245	289	20	physics	physics	NOUN
ejpam-5245	289	21	.	.	PUNCT
ejpam-5245	290	1	also	also	ADV
ejpam-5245	290	2	,	,	PUNCT
ejpam-5245	290	3	it	it	PRON
ejpam-5245	290	4	is	be	AUX
ejpam-5245	290	5	not	not	PART
ejpam-5245	290	6	restricted	restrict	VERB
ejpam-5245	290	7	to	to	ADP
ejpam-5245	290	8	sl2(r	sl2(r	PROPN
ejpam-5245	290	9	)	)	PUNCT
ejpam-5245	290	10	,	,	PUNCT
ejpam-5245	290	11	it	it	PRON
ejpam-5245	290	12	can	can	AUX
ejpam-5245	290	13	be	be	AUX
ejpam-5245	290	14	successfully	successfully	ADV
ejpam-5245	290	15	used	use	VERB
ejpam-5245	290	16	for	for	ADP
ejpam-5245	290	17	many	many	ADJ
ejpam-5245	290	18	other	other	ADJ
ejpam-5245	290	19	cases	case	NOUN
ejpam-5245	290	20	.	.	PUNCT
ejpam-5245	291	1	acknowledgements	acknowledgement	NOUN
ejpam-5245	291	2	i	i	PRON
ejpam-5245	291	3	would	would	AUX
ejpam-5245	291	4	like	like	VERB
ejpam-5245	291	5	to	to	PART
ejpam-5245	291	6	express	express	VERB
ejpam-5245	291	7	my	my	PRON
ejpam-5245	291	8	deepest	deep	ADJ
ejpam-5245	291	9	gratitude	gratitude	NOUN
ejpam-5245	291	10	to	to	ADP
ejpam-5245	291	11	dr	dr	PROPN
ejpam-5245	291	12	.	.	PROPN
ejpam-5245	291	13	vladimir	vladimir	PROPN
ejpam-5245	291	14	kisil	kisil	PROPN
ejpam-5245	291	15	,	,	PUNCT
ejpam-5245	291	16	for	for	ADP
ejpam-5245	291	17	his	his	PRON
ejpam-5245	291	18	guidance	guidance	NOUN
ejpam-5245	291	19	,	,	PUNCT
ejpam-5245	291	20	feedback	feedback	NOUN
ejpam-5245	291	21	and	and	CCONJ
ejpam-5245	291	22	support	support	NOUN
ejpam-5245	291	23	.	.	PUNCT
ejpam-5245	292	1	references	reference	NOUN
ejpam-5245	292	2	2105	2105	NUM
ejpam-5245	292	3	references	reference	NOUN
ejpam-5245	292	4	[	[	X
ejpam-5245	292	5	1	1	NUM
ejpam-5245	292	6	]	]	PUNCT
ejpam-5245	292	7	syed	syed	ADJ
ejpam-5245	292	8	twareque	twareque	PROPN
ejpam-5245	292	9	ali	ali	PROPN
ejpam-5245	292	10	,	,	PUNCT
ejpam-5245	292	11	jean	jean	PROPN
ejpam-5245	292	12	-	-	PUNCT
ejpam-5245	292	13	pierre	pierre	PROPN
ejpam-5245	292	14	antoine	antoine	PROPN
ejpam-5245	292	15	,	,	PUNCT
ejpam-5245	292	16	jean	jean	PROPN
ejpam-5245	292	17	-	-	PUNCT
ejpam-5245	292	18	pierre	pierre	PROPN
ejpam-5245	292	19	gazeau	gazeau	NOUN
ejpam-5245	292	20	,	,	PUNCT
ejpam-5245	292	21	et	et	PROPN
ejpam-5245	292	22	al	al	PROPN
ejpam-5245	292	23	.	.	PUNCT
ejpam-5245	292	24	coherent	coherent	ADJ
ejpam-5245	292	25	states	state	NOUN
ejpam-5245	292	26	,	,	PUNCT
ejpam-5245	292	27	wavelets	wavelet	NOUN
ejpam-5245	292	28	and	and	CCONJ
ejpam-5245	292	29	their	their	PRON
ejpam-5245	292	30	generalizations	generalization	NOUN
ejpam-5245	292	31	,	,	PUNCT
ejpam-5245	292	32	volume	volume	NOUN
ejpam-5245	292	33	3	3	NUM
ejpam-5245	292	34	.	.	PUNCT
ejpam-5245	292	35	springer	springer	NOUN
ejpam-5245	292	36	,	,	PUNCT
ejpam-5245	292	37	2000	2000	NUM
ejpam-5245	292	38	.	.	PUNCT
ejpam-5245	293	1	[	[	X
ejpam-5245	293	2	2	2	NUM
ejpam-5245	293	3	]	]	PUNCT
ejpam-5245	293	4	valentine	valentine	PROPN
ejpam-5245	293	5	bargmann	bargmann	PROPN
ejpam-5245	293	6	.	.	PUNCT
ejpam-5245	294	1	irreducible	irreducible	ADJ
ejpam-5245	294	2	unitary	unitary	ADJ
ejpam-5245	294	3	representations	representation	NOUN
ejpam-5245	294	4	of	of	ADP
ejpam-5245	294	5	the	the	DET
ejpam-5245	294	6	lorentz	lorentz	PROPN
ejpam-5245	294	7	group	group	NOUN
ejpam-5245	294	8	.	.	PUNCT
ejpam-5245	295	1	annals	annal	NOUN
ejpam-5245	295	2	of	of	ADP
ejpam-5245	295	3	mathematics	mathematic	NOUN
ejpam-5245	295	4	,	,	PUNCT
ejpam-5245	295	5	pages	page	NOUN
ejpam-5245	295	6	568–640	568–640	NUM
ejpam-5245	295	7	,	,	PUNCT
ejpam-5245	295	8	1947	1947	NUM
ejpam-5245	295	9	.	.	PUNCT
ejpam-5245	296	1	[	[	X
ejpam-5245	296	2	3	3	X
ejpam-5245	296	3	]	]	X
ejpam-5245	296	4	i	i	PRON
ejpam-5245	296	5	m	m	VERB
ejpam-5245	296	6	gelfand	gelfand	PROPN
ejpam-5245	296	7	,	,	PUNCT
ejpam-5245	296	8	sg	sg	PROPN
ejpam-5245	296	9	gindikin	gindikin	PROPN
ejpam-5245	296	10	,	,	PUNCT
ejpam-5245	296	11	and	and	CCONJ
ejpam-5245	296	12	mi	mi	PROPN
ejpam-5245	296	13	graev	graev	PROPN
ejpam-5245	296	14	.	.	PUNCT
ejpam-5245	297	1	selected	select	VERB
ejpam-5245	297	2	topics	topic	NOUN
ejpam-5245	297	3	in	in	ADP
ejpam-5245	297	4	integral	integral	ADJ
ejpam-5245	297	5	geometry	geometry	NOUN
ejpam-5245	297	6	,	,	PUNCT
ejpam-5245	297	7	translations	translation	NOUN
ejpam-5245	297	8	of	of	ADP
ejpam-5245	297	9	math	math	NOUN
ejpam-5245	297	10	.	.	PUNCT
ejpam-5245	298	1	monographs	monograph	NOUN
ejpam-5245	298	2	,	,	PUNCT
ejpam-5245	298	3	ams	am	NOUN
ejpam-5245	298	4	,	,	PUNCT
ejpam-5245	298	5	providence	providence	NOUN
ejpam-5245	298	6	,	,	PUNCT
ejpam-5245	298	7	ri	ri	PROPN
ejpam-5245	298	8	,	,	PUNCT
ejpam-5245	298	9	2003	2003	NUM
ejpam-5245	298	10	.	.	PUNCT
ejpam-5245	299	1	[	[	X
ejpam-5245	299	2	4	4	X
ejpam-5245	299	3	]	]	PUNCT
ejpam-5245	299	4	izrail	izrail	NOUN
ejpam-5245	299	5	moiseevich	moiseevich	PROPN
ejpam-5245	299	6	gelfand	gelfand	PROPN
ejpam-5245	299	7	,	,	PUNCT
ejpam-5245	299	8	mark	mark	PROPN
ejpam-5245	299	9	i	i	PROPN
ejpam-5245	299	10	graev	graev	PROPN
ejpam-5245	299	11	,	,	PUNCT
ejpam-5245	299	12	and	and	CCONJ
ejpam-5245	299	13	naum	naum	PROPN
ejpam-5245	299	14	iakovlevich	iakovlevich	PROPN
ejpam-5245	299	15	vilenkin	vilenkin	PROPN
ejpam-5245	299	16	.	.	PUNCT
ejpam-5245	300	1	generalized	generalized	ADJ
ejpam-5245	300	2	functions	function	NOUN
ejpam-5245	300	3	-	-	PUNCT
ejpam-5245	300	4	volume	volume	NOUN
ejpam-5245	300	5	5	5	NUM
ejpam-5245	300	6	.	.	PUNCT
ejpam-5245	300	7	integral	integral	ADJ
ejpam-5245	300	8	geometry	geometry	NOUN
ejpam-5245	300	9	and	and	CCONJ
ejpam-5245	300	10	representation	representation	NOUN
ejpam-5245	300	11	theory	theory	NOUN
ejpam-5245	300	12	.	.	PUNCT
ejpam-5245	301	1	academic	academic	ADJ
ejpam-5245	301	2	press	press	NOUN
ejpam-5245	301	3	,	,	PUNCT
ejpam-5245	301	4	1966	1966	NUM
ejpam-5245	301	5	.	.	PUNCT
ejpam-5245	302	1	[	[	X
ejpam-5245	302	2	5	5	NUM
ejpam-5245	302	3	]	]	PUNCT
ejpam-5245	302	4	izrail	izrail	NOUN
ejpam-5245	302	5	moiseevich	moiseevich	PROPN
ejpam-5245	302	6	gel’fand	gel’fand	PROPN
ejpam-5245	302	7	and	and	CCONJ
ejpam-5245	302	8	mark	mark	PROPN
ejpam-5245	302	9	aronovich	aronovich	PROPN
ejpam-5245	302	10	naimark	naimark	PROPN
ejpam-5245	302	11	.	.	PUNCT
ejpam-5245	303	1	unitary	unitary	ADJ
ejpam-5245	303	2	representations	representation	NOUN
ejpam-5245	303	3	of	of	ADP
ejpam-5245	303	4	the	the	DET
ejpam-5245	303	5	lorentz	lorentz	PROPN
ejpam-5245	303	6	group	group	NOUN
ejpam-5245	303	7	.	.	PUNCT
ejpam-5245	304	1	izvestiya	izvestiya	PROPN
ejpam-5245	304	2	rossiiskoi	rossiiskoi	PROPN
ejpam-5245	304	3	akademii	akademii	PROPN
ejpam-5245	304	4	nauk	nauk	PROPN
ejpam-5245	304	5	.	.	PROPN
ejpam-5245	304	6	seriya	seriya	PROPN
ejpam-5245	304	7	matematicheskaya	matematicheskaya	PROPN
ejpam-5245	304	8	,	,	PUNCT
ejpam-5245	304	9	11(5):411–504	11(5):411–504	NUM
ejpam-5245	304	10	,	,	PUNCT
ejpam-5245	304	11	1947	1947	NUM
ejpam-5245	304	12	.	.	PUNCT
ejpam-5245	305	1	[	[	X
ejpam-5245	305	2	6	6	NUM
ejpam-5245	305	3	]	]	X
ejpam-5245	305	4	vladimir	vladimir	PROPN
ejpam-5245	305	5	v	v	NOUN
ejpam-5245	305	6	kisil	kisil	PROPN
ejpam-5245	305	7	.	.	PUNCT
ejpam-5245	306	1	the	the	DET
ejpam-5245	306	2	real	real	ADJ
ejpam-5245	306	3	and	and	CCONJ
ejpam-5245	306	4	complex	complex	ADJ
ejpam-5245	306	5	techniques	technique	NOUN
ejpam-5245	306	6	in	in	ADP
ejpam-5245	306	7	harmonic	harmonic	ADJ
ejpam-5245	306	8	analysis	analysis	NOUN
ejpam-5245	306	9	from	from	ADP
ejpam-5245	306	10	the	the	DET
ejpam-5245	306	11	point	point	NOUN
ejpam-5245	306	12	of	of	ADP
ejpam-5245	306	13	view	view	NOUN
ejpam-5245	306	14	of	of	ADP
ejpam-5245	306	15	covariant	covariant	ADJ
ejpam-5245	306	16	transform	transform	NOUN
ejpam-5245	306	17	.	.	PUNCT
ejpam-5245	307	1	arxiv	arxiv	PROPN
ejpam-5245	307	2	preprint	preprint	PROPN
ejpam-5245	307	3	arxiv:1209.5072	arxiv:1209.5072	ADP
ejpam-5245	307	4	,	,	PUNCT
ejpam-5245	307	5	2012	2012	NUM
ejpam-5245	307	6	.	.	PUNCT
ejpam-5245	308	1	[	[	X
ejpam-5245	308	2	7	7	NUM
ejpam-5245	308	3	]	]	X
ejpam-5245	308	4	vladimir	vladimir	PROPN
ejpam-5245	308	5	v.	v.	ADP
ejpam-5245	308	6	kisil	kisil	PROPN
ejpam-5245	308	7	.	.	PUNCT
ejpam-5245	309	1	induced	induce	VERB
ejpam-5245	309	2	representations	representation	NOUN
ejpam-5245	309	3	and	and	CCONJ
ejpam-5245	309	4	hypercomplex	hypercomplex	NOUN
ejpam-5245	309	5	numbers	number	NOUN
ejpam-5245	309	6	.	.	PUNCT
ejpam-5245	310	1	advances	advance	NOUN
ejpam-5245	310	2	in	in	ADP
ejpam-5245	310	3	applied	apply	VERB
ejpam-5245	310	4	clifford	clifford	PROPN
ejpam-5245	310	5	algebras	algebras	PROPN
ejpam-5245	310	6	,	,	PUNCT
ejpam-5245	310	7	23(2):417–440	23(2):417–440	PROPN
ejpam-5245	310	8	,	,	PUNCT
ejpam-5245	310	9	2013	2013	NUM
ejpam-5245	310	10	.	.	PUNCT
ejpam-5245	311	1	[	[	X
ejpam-5245	311	2	8	8	NUM
ejpam-5245	311	3	]	]	X
ejpam-5245	311	4	vladimir	vladimir	PROPN
ejpam-5245	311	5	v.	v.	ADP
ejpam-5245	311	6	kisil	kisil	PROPN
ejpam-5245	311	7	.	.	PROPN
ejpam-5245	311	8	symmetry	symmetry	PROPN
ejpam-5245	311	9	,	,	PUNCT
ejpam-5245	311	10	geometry	geometry	NOUN
ejpam-5245	311	11	,	,	PUNCT
ejpam-5245	311	12	and	and	CCONJ
ejpam-5245	311	13	quantization	quantization	NOUN
ejpam-5245	311	14	with	with	ADP
ejpam-5245	311	15	hypercomplex	hypercomplex	ADJ
ejpam-5245	311	16	numbers	number	NOUN
ejpam-5245	311	17	.	.	PUNCT
ejpam-5245	312	1	arxiv	arxiv	PROPN
ejpam-5245	312	2	preprint	preprint	NOUN
ejpam-5245	312	3	arxiv:1611.05650	arxiv:1611.05650	NOUN
ejpam-5245	312	4	,	,	PUNCT
ejpam-5245	312	5	2016	2016	NUM
ejpam-5245	312	6	.	.	PUNCT
ejpam-5245	313	1	[	[	X
ejpam-5245	313	2	9	9	NUM
ejpam-5245	313	3	]	]	X
ejpam-5245	313	4	v.v	v.v	PROPN
ejpam-5245	313	5	.	.	PROPN
ejpam-5245	313	6	kisil	kisil	PROPN
ejpam-5245	313	7	.	.	PUNCT
ejpam-5245	313	8	geometry	geometry	NOUN
ejpam-5245	313	9	of	of	ADP
ejpam-5245	313	10	mobius	mobius	ADJ
ejpam-5245	313	11	transformations	transformation	NOUN
ejpam-5245	313	12	:	:	PUNCT
ejpam-5245	313	13	elliptic	elliptic	ADJ
ejpam-5245	313	14	,	,	PUNCT
ejpam-5245	313	15	parabolic	parabolic	ADJ
ejpam-5245	313	16	and	and	CCONJ
ejpam-5245	313	17	hyperbolic	hyperbolic	ADJ
ejpam-5245	313	18	actions	action	NOUN
ejpam-5245	313	19	of	of	ADP
ejpam-5245	313	20	sl2(r	sl2(r	PROPN
ejpam-5245	313	21	)	)	PUNCT
ejpam-5245	313	22	(	(	PUNCT
ejpam-5245	313	23	with	with	ADP
ejpam-5245	313	24	dvd	dvd	NOUN
ejpam-5245	313	25	-	-	PUNCT
ejpam-5245	313	26	rom	rom	NOUN
ejpam-5245	313	27	)	)	PUNCT
ejpam-5245	313	28	.	.	PUNCT
ejpam-5245	314	1	world	world	NOUN
ejpam-5245	314	2	scientific	scientific	ADJ
ejpam-5245	314	3	publishing	publishing	NOUN
ejpam-5245	314	4	company	company	NOUN
ejpam-5245	314	5	,	,	PUNCT
ejpam-5245	314	6	2012	2012	NUM
ejpam-5245	314	7	.	.	PUNCT