id	sid	tid	token	lemma	pos
ap-3493	1	1	acta	acta	PROPN
ap-3493	1	2	polytechnica	polytechnica	PROPN
ap-3493	1	3	doi:10.14311	doi:10.14311	PROPN
ap-3493	1	4	/	/	SYM
ap-3493	1	5	ap.2016.56.0166	ap.2016.56.0166	PROPN
ap-3493	1	6	acta	acta	PROPN
ap-3493	1	7	polytechnica	polytechnica	PROPN
ap-3493	1	8	56(3):166–172	56(3):166–172	PROPN
ap-3493	1	9	,	,	PUNCT
ap-3493	1	10	2016	2016	NUM
ap-3493	1	11	©	©	PROPN
ap-3493	1	12	czech	czech	PROPN
ap-3493	1	13	technical	technical	PROPN
ap-3493	1	14	university	university	PROPN
ap-3493	1	15	in	in	ADP
ap-3493	1	16	prague	prague	PROPN
ap-3493	1	17	,	,	PUNCT
ap-3493	1	18	2016	2016	NUM
ap-3493	1	19	available	available	ADJ
ap-3493	1	20	online	online	ADV
ap-3493	1	21	at	at	ADP
ap-3493	1	22	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-3493	1	23	a	a	DET
ap-3493	1	24	superintegrable	superintegrable	ADJ
ap-3493	1	25	model	model	NOUN
ap-3493	1	26	with	with	ADP
ap-3493	1	27	reflections	reflection	NOUN
ap-3493	1	28	on	on	ADP
ap-3493	1	29	s3	s3	PROPN
ap-3493	1	30	and	and	CCONJ
ap-3493	1	31	the	the	DET
ap-3493	1	32	rank	rank	NOUN
ap-3493	1	33	two	two	NUM
ap-3493	1	34	bannai	bannai	PROPN
ap-3493	1	35	-	-	PUNCT
ap-3493	1	36	ito	ito	PROPN
ap-3493	1	37	algebra	algebra	PROPN
ap-3493	1	38	hendrik	hendrik	PROPN
ap-3493	1	39	de	de	X
ap-3493	1	40	biea,∗	biea,∗	PROPN
ap-3493	1	41	,	,	PUNCT
ap-3493	1	42	vincent	vincent	PROPN
ap-3493	1	43	x.	x.	PROPN
ap-3493	1	44	genestb	genestb	PROPN
ap-3493	1	45	,	,	PUNCT
ap-3493	1	46	jean	jean	PROPN
ap-3493	1	47	-	-	PUNCT
ap-3493	1	48	michel	michel	PROPN
ap-3493	1	49	lemayc	lemayc	PROPN
ap-3493	1	50	,	,	PUNCT
ap-3493	1	51	luc	luc	PROPN
ap-3493	1	52	vinetc	vinetc	VERB
ap-3493	1	53	a	a	DET
ap-3493	1	54	department	department	NOUN
ap-3493	1	55	of	of	ADP
ap-3493	1	56	mathematical	mathematical	ADJ
ap-3493	1	57	analysis	analysis	NOUN
ap-3493	1	58	,	,	PUNCT
ap-3493	1	59	faculty	faculty	NOUN
ap-3493	1	60	of	of	ADP
ap-3493	1	61	engineering	engineering	NOUN
ap-3493	1	62	and	and	CCONJ
ap-3493	1	63	architecture	architecture	NOUN
ap-3493	1	64	,	,	PUNCT
ap-3493	1	65	ghent	ghent	PROPN
ap-3493	1	66	university	university	PROPN
ap-3493	1	67	,	,	PUNCT
ap-3493	1	68	galglaan	galglaan	VERB
ap-3493	1	69	2	2	NUM
ap-3493	1	70	,	,	PUNCT
ap-3493	1	71	9000	9000	NUM
ap-3493	1	72	ghent	ghent	NOUN
ap-3493	1	73	,	,	PUNCT
ap-3493	1	74	belgium	belgium	PROPN
ap-3493	1	75	b	b	PROPN
ap-3493	1	76	department	department	PROPN
ap-3493	1	77	of	of	ADP
ap-3493	1	78	mathematics	mathematics	PROPN
ap-3493	1	79	,	,	PUNCT
ap-3493	1	80	massachusetts	massachusetts	PROPN
ap-3493	1	81	institute	institute	PROPN
ap-3493	1	82	of	of	ADP
ap-3493	1	83	technology	technology	PROPN
ap-3493	1	84	,	,	PUNCT
ap-3493	1	85	77	77	NUM
ap-3493	1	86	massachusetts	massachusetts	PROPN
ap-3493	1	87	ave	ave	PROPN
ap-3493	1	88	.	.	PROPN
ap-3493	1	89	,	,	PUNCT
ap-3493	1	90	cambridge	cambridge	PROPN
ap-3493	1	91	,	,	PUNCT
ap-3493	1	92	ma	ma	PROPN
ap-3493	1	93	02139	02139	NUM
ap-3493	1	94	,	,	PUNCT
ap-3493	1	95	usa	usa	PROPN
ap-3493	1	96	c	c	PROPN
ap-3493	1	97	centre	centre	PROPN
ap-3493	1	98	de	de	X
ap-3493	1	99	recherches	recherche	NOUN
ap-3493	1	100	mathématiques	mathématique	NOUN
ap-3493	1	101	,	,	PUNCT
ap-3493	1	102	université	université	PROPN
ap-3493	1	103	de	de	PROPN
ap-3493	1	104	montréal	montréal	PROPN
ap-3493	1	105	,	,	PUNCT
ap-3493	1	106	c.p	c.p	PROPN
ap-3493	1	107	.	.	PROPN
ap-3493	1	108	6128	6128	NUM
ap-3493	1	109	,	,	PUNCT
ap-3493	1	110	succ	succ	PROPN
ap-3493	1	111	.	.	PUNCT
ap-3493	1	112	centre	centre	PROPN
ap-3493	1	113	-	-	PUNCT
ap-3493	1	114	ville	ville	PROPN
ap-3493	1	115	,	,	PUNCT
ap-3493	1	116	montréal	montréal	PROPN
ap-3493	1	117	,	,	PUNCT
ap-3493	1	118	qc	qc	PROPN
ap-3493	1	119	,	,	PUNCT
ap-3493	1	120	canada	canada	PROPN
ap-3493	1	121	,	,	PUNCT
ap-3493	1	122	h3c	h3c	VERB
ap-3493	1	123	3j7	3j7	NUM
ap-3493	1	124	∗	∗	NOUN
ap-3493	1	125	corresponding	correspond	VERB
ap-3493	1	126	author	author	NOUN
ap-3493	1	127	:	:	PUNCT
ap-3493	1	128	hendrik.debie@ugent.be	hendrik.debie@ugent.be	PROPN
ap-3493	1	129	abstract	abstract	NOUN
ap-3493	1	130	.	.	PUNCT
ap-3493	2	1	a	a	DET
ap-3493	2	2	quantum	quantum	ADJ
ap-3493	2	3	superintegrable	superintegrable	ADJ
ap-3493	2	4	model	model	NOUN
ap-3493	2	5	with	with	ADP
ap-3493	2	6	reflections	reflection	NOUN
ap-3493	2	7	on	on	ADP
ap-3493	2	8	the	the	DET
ap-3493	2	9	three	three	NUM
ap-3493	2	10	-	-	PUNCT
ap-3493	2	11	sphere	sphere	NOUN
ap-3493	2	12	is	be	AUX
ap-3493	2	13	presented	present	VERB
ap-3493	2	14	.	.	PUNCT
ap-3493	3	1	its	its	PRON
ap-3493	3	2	symmetry	symmetry	NOUN
ap-3493	3	3	algebra	algebra	NOUN
ap-3493	3	4	is	be	AUX
ap-3493	3	5	identified	identify	VERB
ap-3493	3	6	with	with	ADP
ap-3493	3	7	the	the	DET
ap-3493	3	8	rank	rank	NOUN
ap-3493	3	9	-	-	PUNCT
ap-3493	3	10	two	two	NUM
ap-3493	3	11	bannai	bannai	PROPN
ap-3493	3	12	-	-	PUNCT
ap-3493	3	13	ito	ito	PROPN
ap-3493	3	14	algebra	algebra	NOUN
ap-3493	3	15	.	.	PUNCT
ap-3493	4	1	it	it	PRON
ap-3493	4	2	is	be	AUX
ap-3493	4	3	shown	show	VERB
ap-3493	4	4	that	that	SCONJ
ap-3493	4	5	the	the	DET
ap-3493	4	6	hamiltonian	hamiltonian	NOUN
ap-3493	4	7	of	of	ADP
ap-3493	4	8	the	the	DET
ap-3493	4	9	system	system	NOUN
ap-3493	4	10	can	can	AUX
ap-3493	4	11	be	be	AUX
ap-3493	4	12	constructed	construct	VERB
ap-3493	4	13	from	from	ADP
ap-3493	4	14	the	the	DET
ap-3493	4	15	tensor	tensor	NOUN
ap-3493	4	16	product	product	NOUN
ap-3493	4	17	of	of	ADP
ap-3493	4	18	four	four	NUM
ap-3493	4	19	representations	representation	NOUN
ap-3493	4	20	of	of	ADP
ap-3493	4	21	the	the	DET
ap-3493	4	22	superalgebra	superalgebra	NOUN
ap-3493	4	23	osp(1|2	osp(1|2	PROPN
ap-3493	4	24	)	)	PUNCT
ap-3493	4	25	and	and	CCONJ
ap-3493	4	26	that	that	SCONJ
ap-3493	4	27	the	the	DET
ap-3493	4	28	superintegrability	superintegrability	NOUN
ap-3493	4	29	is	be	AUX
ap-3493	4	30	naturally	naturally	ADV
ap-3493	4	31	understood	understand	VERB
ap-3493	4	32	in	in	ADP
ap-3493	4	33	that	that	DET
ap-3493	4	34	setting	setting	NOUN
ap-3493	4	35	.	.	PUNCT
ap-3493	5	1	the	the	DET
ap-3493	5	2	exact	exact	ADJ
ap-3493	5	3	separated	separate	VERB
ap-3493	5	4	solutions	solution	NOUN
ap-3493	5	5	are	be	AUX
ap-3493	5	6	obtained	obtain	VERB
ap-3493	5	7	through	through	ADP
ap-3493	5	8	the	the	DET
ap-3493	5	9	fischer	fischer	PROPN
ap-3493	5	10	decomposition	decomposition	NOUN
ap-3493	5	11	and	and	CCONJ
ap-3493	5	12	a	a	DET
ap-3493	5	13	cauchy	cauchy	PROPN
ap-3493	5	14	-	-	PUNCT
ap-3493	5	15	kovalevskaia	kovalevskaia	PROPN
ap-3493	5	16	extension	extension	NOUN
ap-3493	5	17	theorem	theorem	VERB
ap-3493	5	18	.	.	PUNCT
ap-3493	6	1	keywords	keyword	NOUN
ap-3493	6	2	:	:	PUNCT
ap-3493	6	3	bannai	bannai	PROPN
ap-3493	6	4	-	-	PUNCT
ap-3493	6	5	ito	ito	PROPN
ap-3493	6	6	algebra	algebra	PROPN
ap-3493	6	7	;	;	PUNCT
ap-3493	6	8	cauchy	cauchy	PROPN
ap-3493	6	9	-	-	PUNCT
ap-3493	6	10	kovalevskaia	kovalevskaia	PROPN
ap-3493	6	11	extension	extension	NOUN
ap-3493	6	12	;	;	PUNCT
ap-3493	6	13	quantum	quantum	ADJ
ap-3493	6	14	superintegrable	superintegrable	ADJ
ap-3493	6	15	model	model	NOUN
ap-3493	6	16	.	.	PUNCT
ap-3493	7	1	1	1	X
ap-3493	7	2	.	.	X
ap-3493	7	3	introduction	introduction	NOUN
ap-3493	7	4	superintegrability	superintegrability	NOUN
ap-3493	7	5	shares	share	VERB
ap-3493	7	6	an	an	DET
ap-3493	7	7	intimate	intimate	ADJ
ap-3493	7	8	connection	connection	NOUN
ap-3493	7	9	with	with	ADP
ap-3493	7	10	exact	exact	ADJ
ap-3493	7	11	solvability	solvability	NOUN
ap-3493	7	12	.	.	PUNCT
ap-3493	8	1	for	for	ADP
ap-3493	8	2	classical	classical	ADJ
ap-3493	8	3	systems	system	NOUN
ap-3493	8	4	,	,	PUNCT
ap-3493	8	5	this	this	DET
ap-3493	8	6	connection	connection	NOUN
ap-3493	8	7	is	be	AUX
ap-3493	8	8	fully	fully	ADV
ap-3493	8	9	understood	understand	VERB
ap-3493	8	10	while	while	SCONJ
ap-3493	8	11	it	it	PRON
ap-3493	8	12	remains	remain	VERB
ap-3493	8	13	an	an	DET
ap-3493	8	14	empirical	empirical	ADJ
ap-3493	8	15	observation	observation	NOUN
ap-3493	8	16	for	for	ADP
ap-3493	8	17	general	general	ADJ
ap-3493	8	18	quantum	quantum	NOUN
ap-3493	8	19	systems	system	NOUN
ap-3493	8	20	.	.	PUNCT
ap-3493	9	1	the	the	DET
ap-3493	9	2	study	study	NOUN
ap-3493	9	3	of	of	ADP
ap-3493	9	4	superintegrable	superintegrable	ADJ
ap-3493	9	5	models	model	NOUN
ap-3493	9	6	has	have	AUX
ap-3493	9	7	proved	prove	VERB
ap-3493	9	8	fruitful	fruitful	ADJ
ap-3493	9	9	in	in	ADP
ap-3493	9	10	understanding	understand	VERB
ap-3493	9	11	symmetries	symmetry	NOUN
ap-3493	9	12	and	and	CCONJ
ap-3493	9	13	their	their	PRON
ap-3493	9	14	algebraic	algebraic	ADJ
ap-3493	9	15	description	description	NOUN
ap-3493	9	16	,	,	PUNCT
ap-3493	9	17	and	and	CCONJ
ap-3493	9	18	has	have	AUX
ap-3493	9	19	also	also	ADV
ap-3493	9	20	contributed	contribute	VERB
ap-3493	9	21	to	to	ADP
ap-3493	9	22	the	the	DET
ap-3493	9	23	theory	theory	NOUN
ap-3493	9	24	of	of	ADP
ap-3493	9	25	special	special	ADJ
ap-3493	9	26	functions	function	NOUN
ap-3493	9	27	.	.	PUNCT
ap-3493	10	1	a	a	DET
ap-3493	10	2	quantum	quantum	ADJ
ap-3493	10	3	system	system	NOUN
ap-3493	10	4	in	in	ADP
ap-3493	10	5	n	n	ADP
ap-3493	10	6	dimensions	dimension	NOUN
ap-3493	10	7	with	with	ADP
ap-3493	10	8	hamiltonian	hamiltonian	ADJ
ap-3493	10	9	h	h	NOUN
ap-3493	10	10	is	be	AUX
ap-3493	10	11	said	say	VERB
ap-3493	10	12	to	to	PART
ap-3493	10	13	be	be	AUX
ap-3493	10	14	maximally	maximally	ADV
ap-3493	10	15	superintegrable	superintegrable	ADJ
ap-3493	10	16	if	if	SCONJ
ap-3493	10	17	it	it	PRON
ap-3493	10	18	possesses	possess	VERB
ap-3493	10	19	2n	2n	NUM
ap-3493	10	20	−	−	ADP
ap-3493	10	21	1	1	NUM
ap-3493	10	22	algebraically	algebraically	ADV
ap-3493	10	23	independent	independent	ADJ
ap-3493	10	24	constants	constant	NOUN
ap-3493	10	25	of	of	ADP
ap-3493	10	26	motion	motion	NOUN
ap-3493	10	27	c1	c1	PROPN
ap-3493	10	28	,	,	PUNCT
ap-3493	10	29	c2	c2	PROPN
ap-3493	10	30	,	,	PUNCT
ap-3493	10	31	.	.	PUNCT
ap-3493	10	32	.	.	PUNCT
ap-3493	10	33	.	.	PUNCT
ap-3493	11	1	,	,	PUNCT
ap-3493	11	2	c2n−1	c2n−1	PROPN
ap-3493	11	3	commuting	commute	VERB
ap-3493	11	4	with	with	ADP
ap-3493	11	5	h	h	NOUN
ap-3493	11	6	,	,	PUNCT
ap-3493	11	7	that	that	PRON
ap-3493	11	8	is	be	AUX
ap-3493	11	9	[	[	X
ap-3493	11	10	h	h	NOUN
ap-3493	11	11	,	,	PUNCT
ap-3493	11	12	ci	ci	NOUN
ap-3493	11	13	]	]	X
ap-3493	11	14	=	=	SYM
ap-3493	11	15	0	0	PUNCT
ap-3493	11	16	for	for	ADP
ap-3493	11	17	i	i	PRON
ap-3493	11	18	=	=	NOUN
ap-3493	11	19	1	1	NUM
ap-3493	11	20	,	,	PUNCT
ap-3493	11	21	.	.	PUNCT
ap-3493	11	22	.	.	PUNCT
ap-3493	12	1	.	.	PUNCT
ap-3493	13	1	,	,	PUNCT
ap-3493	13	2	2n	2n	NUM
ap-3493	13	3	−	−	NOUN
ap-3493	13	4	1	1	NUM
ap-3493	13	5	,	,	PUNCT
ap-3493	13	6	where	where	SCONJ
ap-3493	13	7	one	one	NUM
ap-3493	13	8	of	of	ADP
ap-3493	13	9	these	these	DET
ap-3493	13	10	constants	constant	NOUN
ap-3493	13	11	is	be	AUX
ap-3493	13	12	the	the	DET
ap-3493	13	13	hamiltonian	hamiltonian	NOUN
ap-3493	13	14	itself	itself	PRON
ap-3493	13	15	.	.	PUNCT
ap-3493	14	1	such	such	DET
ap-3493	14	2	a	a	DET
ap-3493	14	3	system	system	NOUN
ap-3493	14	4	is	be	AUX
ap-3493	14	5	further	far	ADV
ap-3493	14	6	said	say	VERB
ap-3493	14	7	to	to	PART
ap-3493	14	8	be	be	AUX
ap-3493	14	9	superintegrable	superintegrable	ADJ
ap-3493	14	10	of	of	ADP
ap-3493	14	11	order	order	NOUN
ap-3493	14	12	l	l	NOUN
ap-3493	14	13	if	if	SCONJ
ap-3493	14	14	the	the	DET
ap-3493	14	15	maximum	maximum	ADJ
ap-3493	14	16	order	order	NOUN
ap-3493	14	17	in	in	ADP
ap-3493	14	18	momenta	momenta	NOUN
ap-3493	14	19	of	of	ADP
ap-3493	14	20	the	the	DET
ap-3493	14	21	constants	constant	NOUN
ap-3493	14	22	of	of	ADP
ap-3493	14	23	motion	motion	NOUN
ap-3493	14	24	(	(	PUNCT
ap-3493	14	25	except	except	SCONJ
ap-3493	14	26	h	h	NOUN
ap-3493	14	27	)	)	PUNCT
ap-3493	14	28	is	be	AUX
ap-3493	14	29	l.	l.	PROPN
ap-3493	14	30	one	one	NUM
ap-3493	14	31	of	of	ADP
ap-3493	14	32	the	the	DET
ap-3493	14	33	important	important	ADJ
ap-3493	14	34	quantum	quantum	ADJ
ap-3493	14	35	superintegrable	superintegrable	ADJ
ap-3493	14	36	models	model	NOUN
ap-3493	14	37	is	be	AUX
ap-3493	14	38	the	the	DET
ap-3493	14	39	so	so	ADV
ap-3493	14	40	-	-	PUNCT
ap-3493	14	41	called	call	VERB
ap-3493	14	42	generic	generic	ADJ
ap-3493	14	43	three	three	NUM
ap-3493	14	44	-	-	PUNCT
ap-3493	14	45	parameter	parameter	NOUN
ap-3493	14	46	system	system	NOUN
ap-3493	14	47	on	on	ADP
ap-3493	14	48	the	the	DET
ap-3493	14	49	two	two	NUM
ap-3493	14	50	-	-	PUNCT
ap-3493	14	51	sphere	sphere	NOUN
ap-3493	14	52	[	[	X
ap-3493	14	53	12	12	NUM
ap-3493	14	54	]	]	PUNCT
ap-3493	14	55	,	,	PUNCT
ap-3493	14	56	whose	whose	DET
ap-3493	14	57	symmetries	symmetry	NOUN
ap-3493	14	58	generate	generate	VERB
ap-3493	14	59	the	the	DET
ap-3493	14	60	racah	racah	NOUN
ap-3493	14	61	algebra	algebra	NOUN
ap-3493	14	62	which	which	PRON
ap-3493	14	63	characterizes	characterize	VERB
ap-3493	14	64	the	the	DET
ap-3493	14	65	wilson	wilson	PROPN
ap-3493	14	66	and	and	CCONJ
ap-3493	14	67	racah	racah	VERB
ap-3493	14	68	polynomials	polynomial	NOUN
ap-3493	14	69	sitting	sit	VERB
ap-3493	14	70	atop	atop	ADP
ap-3493	14	71	the	the	DET
ap-3493	14	72	askey	askey	ADJ
ap-3493	14	73	scheme	scheme	NOUN
ap-3493	14	74	[	[	X
ap-3493	14	75	1	1	NUM
ap-3493	14	76	]	]	PUNCT
ap-3493	14	77	.	.	PUNCT
ap-3493	15	1	all	all	DET
ap-3493	15	2	two	two	NUM
ap-3493	15	3	-	-	PUNCT
ap-3493	15	4	dimensional	dimensional	ADJ
ap-3493	15	5	second	second	ADJ
ap-3493	15	6	order	order	NOUN
ap-3493	15	7	superintegrable	superintegrable	ADJ
ap-3493	15	8	models	model	NOUN
ap-3493	15	9	of	of	ADP
ap-3493	15	10	the	the	DET
ap-3493	15	11	form	form	NOUN
ap-3493	15	12	h	h	NOUN
ap-3493	15	13	=	=	PUNCT
ap-3493	15	14	∆	∆	PROPN
ap-3493	16	1	+	+	CCONJ
ap-3493	16	2	v	v	NOUN
ap-3493	16	3	where	where	SCONJ
ap-3493	16	4	∆	∆	PROPN
ap-3493	16	5	denotes	denote	VERB
ap-3493	16	6	the	the	DET
ap-3493	16	7	laplace	laplace	NOUN
ap-3493	16	8	-	-	PUNCT
ap-3493	16	9	beltrami	beltrami	NOUN
ap-3493	16	10	operator	operator	NOUN
ap-3493	16	11	have	have	AUX
ap-3493	16	12	been	be	AUX
ap-3493	16	13	classified	classify	VERB
ap-3493	16	14	[	[	PUNCT
ap-3493	16	15	12	12	NUM
ap-3493	16	16	]	]	PUNCT
ap-3493	16	17	and	and	CCONJ
ap-3493	16	18	can	can	AUX
ap-3493	16	19	be	be	AUX
ap-3493	16	20	obtained	obtain	VERB
ap-3493	16	21	from	from	ADP
ap-3493	16	22	the	the	DET
ap-3493	16	23	generic	generic	ADJ
ap-3493	16	24	three	three	NUM
ap-3493	16	25	-	-	PUNCT
ap-3493	16	26	parameter	parameter	NOUN
ap-3493	16	27	model	model	NOUN
ap-3493	16	28	through	through	ADP
ap-3493	16	29	contractions	contraction	NOUN
ap-3493	16	30	and	and	CCONJ
ap-3493	16	31	specializations	specialization	NOUN
ap-3493	17	1	[	[	X
ap-3493	17	2	11	11	NUM
ap-3493	17	3	]	]	PUNCT
ap-3493	17	4	.	.	PUNCT
ap-3493	18	1	a	a	DET
ap-3493	18	2	similar	similar	ADJ
ap-3493	18	3	model	model	NOUN
ap-3493	18	4	with	with	ADP
ap-3493	18	5	four	four	NUM
ap-3493	18	6	parameters	parameter	NOUN
ap-3493	18	7	defined	define	VERB
ap-3493	18	8	on	on	ADP
ap-3493	18	9	the	the	DET
ap-3493	18	10	three	three	NUM
ap-3493	18	11	-	-	PUNCT
ap-3493	18	12	sphere	sphere	NOUN
ap-3493	18	13	has	have	AUX
ap-3493	18	14	also	also	ADV
ap-3493	18	15	been	be	AUX
ap-3493	18	16	introduced	introduce	VERB
ap-3493	18	17	and	and	CCONJ
ap-3493	18	18	its	its	PRON
ap-3493	18	19	connection	connection	NOUN
ap-3493	18	20	to	to	PART
ap-3493	18	21	bivariate	bivariate	VERB
ap-3493	18	22	wilson	wilson	PROPN
ap-3493	18	23	and	and	CCONJ
ap-3493	18	24	racah	racah	PROPN
ap-3493	18	25	polynomials	polynomial	NOUN
ap-3493	18	26	has	have	AUX
ap-3493	18	27	been	be	AUX
ap-3493	18	28	established	establish	VERB
ap-3493	18	29	[	[	PUNCT
ap-3493	18	30	10	10	NUM
ap-3493	18	31	]	]	PUNCT
ap-3493	18	32	.	.	PUNCT
ap-3493	19	1	recently	recently	ADV
ap-3493	19	2	,	,	PUNCT
ap-3493	19	3	superintegrable	superintegrable	ADJ
ap-3493	19	4	models	model	NOUN
ap-3493	19	5	defined	define	VERB
ap-3493	19	6	by	by	ADP
ap-3493	19	7	hamiltonians	hamiltonian	NOUN
ap-3493	19	8	involving	involve	VERB
ap-3493	19	9	reflection	reflection	NOUN
ap-3493	19	10	operators	operator	NOUN
ap-3493	19	11	have	have	AUX
ap-3493	19	12	been	be	AUX
ap-3493	19	13	the	the	DET
ap-3493	19	14	subject	subject	NOUN
ap-3493	19	15	of	of	ADP
ap-3493	19	16	several	several	ADJ
ap-3493	19	17	investigations	investigation	NOUN
ap-3493	19	18	[	[	X
ap-3493	19	19	2–5	2–5	NOUN
ap-3493	19	20	,	,	PUNCT
ap-3493	19	21	9	9	NUM
ap-3493	19	22	]	]	PUNCT
ap-3493	19	23	.	.	PUNCT
ap-3493	20	1	one	one	NUM
ap-3493	20	2	of	of	ADP
ap-3493	20	3	the	the	DET
ap-3493	20	4	interesting	interesting	ADJ
ap-3493	20	5	features	feature	NOUN
ap-3493	20	6	of	of	ADP
ap-3493	20	7	these	these	DET
ap-3493	20	8	models	model	NOUN
ap-3493	20	9	is	be	AUX
ap-3493	20	10	their	their	PRON
ap-3493	20	11	connection	connection	NOUN
ap-3493	20	12	to	to	ADP
ap-3493	20	13	less	less	ADV
ap-3493	20	14	known	know	VERB
ap-3493	20	15	bispectral	bispectral	ADJ
ap-3493	20	16	orthogonal	orthogonal	ADJ
ap-3493	20	17	polynomials	polynomial	NOUN
ap-3493	20	18	referred	refer	VERB
ap-3493	20	19	to	to	ADP
ap-3493	20	20	as	as	ADP
ap-3493	20	21	−1	−1	NOUN
ap-3493	20	22	polynomials	polynomial	NOUN
ap-3493	20	23	.	.	PUNCT
ap-3493	21	1	many	many	ADJ
ap-3493	21	2	efforts	effort	NOUN
ap-3493	21	3	have	have	AUX
ap-3493	21	4	been	be	AUX
ap-3493	21	5	deployed	deploy	VERB
ap-3493	21	6	to	to	PART
ap-3493	21	7	characterize	characterize	VERB
ap-3493	21	8	these	these	DET
ap-3493	21	9	polynomials	polynomial	NOUN
ap-3493	21	10	,	,	PUNCT
ap-3493	21	11	which	which	PRON
ap-3493	21	12	can	can	AUX
ap-3493	21	13	be	be	AUX
ap-3493	21	14	organized	organize	VERB
ap-3493	21	15	in	in	ADP
ap-3493	21	16	a	a	DET
ap-3493	21	17	tableau	tableau	NOUN
ap-3493	21	18	similar	similar	ADJ
ap-3493	21	19	to	to	ADP
ap-3493	21	20	the	the	DET
ap-3493	21	21	askey	askey	ADJ
ap-3493	21	22	one	one	NOUN
ap-3493	22	1	[	[	X
ap-3493	22	2	13–19	13–19	NUM
ap-3493	22	3	]	]	PUNCT
ap-3493	22	4	.	.	PUNCT
ap-3493	23	1	of	of	ADP
ap-3493	23	2	particular	particular	ADJ
ap-3493	23	3	relevance	relevance	NOUN
ap-3493	23	4	to	to	ADP
ap-3493	23	5	the	the	DET
ap-3493	23	6	present	present	ADJ
ap-3493	23	7	paper	paper	NOUN
ap-3493	23	8	is	be	AUX
ap-3493	23	9	the	the	DET
ap-3493	23	10	laplace	laplace	NOUN
ap-3493	23	11	-	-	PUNCT
ap-3493	23	12	dunkl	dunkl	NOUN
ap-3493	23	13	equation	equation	NOUN
ap-3493	23	14	on	on	ADP
ap-3493	23	15	the	the	DET
ap-3493	23	16	two	two	NUM
ap-3493	23	17	-	-	PUNCT
ap-3493	23	18	sphere	sphere	NOUN
ap-3493	23	19	studied	study	VERB
ap-3493	23	20	in	in	ADP
ap-3493	23	21	[	[	X
ap-3493	23	22	6	6	NUM
ap-3493	23	23	,	,	PUNCT
ap-3493	23	24	7	7	NUM
ap-3493	23	25	]	]	PUNCT
ap-3493	23	26	,	,	PUNCT
ap-3493	23	27	which	which	PRON
ap-3493	23	28	has	have	VERB
ap-3493	23	29	the	the	DET
ap-3493	23	30	rank	rank	NOUN
ap-3493	23	31	-	-	PUNCT
ap-3493	23	32	one	one	NUM
ap-3493	23	33	bannai	bannai	VERB
ap-3493	23	34	-	-	PUNCT
ap-3493	23	35	ito	ito	PROPN
ap-3493	23	36	algebra	algebra	PROPN
ap-3493	23	37	as	as	ADP
ap-3493	23	38	its	its	PRON
ap-3493	23	39	symmetry	symmetry	NOUN
ap-3493	23	40	algebra	algebra	NOUN
ap-3493	23	41	[	[	X
ap-3493	23	42	17	17	NUM
ap-3493	23	43	]	]	PUNCT
ap-3493	23	44	.	.	PUNCT
ap-3493	24	1	this	this	DET
ap-3493	24	2	bannai	bannai	PROPN
ap-3493	24	3	-	-	PUNCT
ap-3493	24	4	ito	ito	PROPN
ap-3493	24	5	algebra	algebra	NOUN
ap-3493	24	6	encodes	encode	VERB
ap-3493	24	7	the	the	DET
ap-3493	24	8	bispectrality	bispectrality	NOUN
ap-3493	24	9	of	of	ADP
ap-3493	24	10	the	the	DET
ap-3493	24	11	bannai	bannai	PROPN
ap-3493	24	12	-	-	PUNCT
ap-3493	24	13	ito	ito	PROPN
ap-3493	24	14	polynomials	polynomial	NOUN
ap-3493	24	15	which	which	PRON
ap-3493	24	16	depend	depend	VERB
ap-3493	24	17	on	on	ADP
ap-3493	24	18	four	four	NUM
ap-3493	24	19	parameters	parameter	NOUN
ap-3493	24	20	and	and	CCONJ
ap-3493	24	21	stand	stand	VERB
ap-3493	24	22	at	at	ADP
ap-3493	24	23	the	the	DET
ap-3493	24	24	highest	high	ADJ
ap-3493	24	25	level	level	NOUN
ap-3493	24	26	of	of	ADP
ap-3493	24	27	the	the	DET
ap-3493	24	28	hierarchy	hierarchy	NOUN
ap-3493	24	29	of	of	ADP
ap-3493	24	30	−1	−1	NOUN
ap-3493	24	31	orthogonal	orthogonal	ADJ
ap-3493	24	32	polynomials	polynomial	NOUN
ap-3493	24	33	.	.	PUNCT
ap-3493	25	1	as	as	ADP
ap-3493	25	2	such	such	ADJ
ap-3493	25	3	,	,	PUNCT
ap-3493	25	4	this	this	DET
ap-3493	25	5	laplace	laplace	NOUN
ap-3493	25	6	-	-	PUNCT
ap-3493	25	7	dunkl	dunkl	NOUN
ap-3493	25	8	system	system	NOUN
ap-3493	25	9	on	on	ADP
ap-3493	25	10	the	the	DET
ap-3493	25	11	two	two	NUM
ap-3493	25	12	sphere	sphere	NOUN
ap-3493	25	13	can	can	AUX
ap-3493	25	14	be	be	AUX
ap-3493	25	15	thought	think	VERB
ap-3493	25	16	of	of	ADP
ap-3493	25	17	as	as	ADP
ap-3493	25	18	a	a	DET
ap-3493	25	19	generalization	generalization	NOUN
ap-3493	25	20	with	with	ADP
ap-3493	25	21	reflection	reflection	NOUN
ap-3493	25	22	operators	operator	NOUN
ap-3493	25	23	of	of	ADP
ap-3493	25	24	the	the	DET
ap-3493	25	25	generic	generic	ADJ
ap-3493	25	26	three	three	NUM
ap-3493	25	27	-	-	PUNCT
ap-3493	25	28	parameter	parameter	NOUN
ap-3493	25	29	model	model	NOUN
ap-3493	25	30	(	(	PUNCT
ap-3493	25	31	without	without	ADP
ap-3493	25	32	reflections	reflection	NOUN
ap-3493	25	33	)	)	PUNCT
ap-3493	25	34	on	on	ADP
ap-3493	25	35	the	the	DET
ap-3493	25	36	two	two	NUM
ap-3493	25	37	-	-	PUNCT
ap-3493	25	38	sphere	sphere	NOUN
ap-3493	25	39	which	which	PRON
ap-3493	25	40	is	be	AUX
ap-3493	25	41	recovered	recover	VERB
ap-3493	25	42	when	when	SCONJ
ap-3493	25	43	wavefunctions	wavefunction	NOUN
ap-3493	25	44	with	with	ADP
ap-3493	25	45	definite	definite	ADJ
ap-3493	25	46	parities	parity	NOUN
ap-3493	25	47	are	be	AUX
ap-3493	25	48	considered	consider	VERB
ap-3493	25	49	.	.	PUNCT
ap-3493	26	1	the	the	DET
ap-3493	26	2	goal	goal	NOUN
ap-3493	26	3	of	of	ADP
ap-3493	26	4	this	this	DET
ap-3493	26	5	paper	paper	NOUN
ap-3493	26	6	is	be	AUX
ap-3493	26	7	to	to	PART
ap-3493	26	8	introduce	introduce	VERB
ap-3493	26	9	a	a	DET
ap-3493	26	10	novel	novel	ADJ
ap-3493	26	11	quantum	quantum	ADJ
ap-3493	26	12	superintegrable	superintegrable	ADJ
ap-3493	26	13	model	model	NOUN
ap-3493	26	14	with	with	ADP
ap-3493	26	15	reflections	reflection	NOUN
ap-3493	26	16	on	on	ADP
ap-3493	26	17	the	the	DET
ap-3493	26	18	three	three	NUM
ap-3493	26	19	-	-	PUNCT
ap-3493	26	20	sphere	sphere	NOUN
ap-3493	26	21	which	which	PRON
ap-3493	26	22	similarly	similarly	ADV
ap-3493	26	23	embodies	embody	VERB
ap-3493	26	24	the	the	DET
ap-3493	26	25	generic	generic	ADJ
ap-3493	26	26	four	four	NUM
ap-3493	26	27	-	-	PUNCT
ap-3493	26	28	parameter	parameter	NOUN
ap-3493	26	29	model	model	NOUN
ap-3493	26	30	introduced	introduce	VERB
ap-3493	26	31	and	and	CCONJ
ap-3493	26	32	studied	study	VERB
ap-3493	26	33	in	in	ADP
ap-3493	26	34	[	[	X
ap-3493	26	35	10	10	NUM
ap-3493	26	36	]	]	PUNCT
ap-3493	26	37	.	.	PUNCT
ap-3493	27	1	the	the	DET
ap-3493	27	2	paper	paper	NOUN
ap-3493	27	3	is	be	AUX
ap-3493	27	4	divided	divide	VERB
ap-3493	27	5	as	as	SCONJ
ap-3493	27	6	follows	follow	VERB
ap-3493	27	7	.	.	PUNCT
ap-3493	28	1	in	in	ADP
ap-3493	28	2	section	section	NOUN
ap-3493	28	3	2	2	NUM
ap-3493	28	4	,	,	PUNCT
ap-3493	28	5	we	we	PRON
ap-3493	28	6	introduce	introduce	VERB
ap-3493	28	7	a	a	DET
ap-3493	28	8	superintegrable	superintegrable	ADJ
ap-3493	28	9	model	model	NOUN
ap-3493	28	10	with	with	ADP
ap-3493	28	11	four	four	NUM
ap-3493	28	12	-	-	PUNCT
ap-3493	28	13	parameters	parameter	NOUN
ap-3493	28	14	on	on	ADP
ap-3493	28	15	the	the	DET
ap-3493	28	16	three	three	NUM
ap-3493	28	17	-	-	PUNCT
ap-3493	28	18	sphere	sphere	NOUN
ap-3493	28	19	and	and	CCONJ
ap-3493	28	20	exhibit	exhibit	VERB
ap-3493	28	21	its	its	PRON
ap-3493	28	22	symmetries	symmetry	NOUN
ap-3493	28	23	explicitly	explicitly	ADV
ap-3493	28	24	.	.	PUNCT
ap-3493	29	1	in	in	ADP
ap-3493	29	2	section	section	NOUN
ap-3493	29	3	3	3	NUM
ap-3493	29	4	,	,	PUNCT
ap-3493	29	5	it	it	PRON
ap-3493	29	6	is	be	AUX
ap-3493	29	7	shown	show	VERB
ap-3493	29	8	how	how	SCONJ
ap-3493	29	9	the	the	DET
ap-3493	29	10	hamiltonian	hamiltonian	NOUN
ap-3493	29	11	of	of	ADP
ap-3493	29	12	the	the	DET
ap-3493	29	13	model	model	NOUN
ap-3493	29	14	can	can	AUX
ap-3493	29	15	be	be	AUX
ap-3493	29	16	constructed	construct	VERB
ap-3493	29	17	from	from	ADP
ap-3493	29	18	four	four	NUM
ap-3493	29	19	realizations	realization	NOUN
ap-3493	29	20	of	of	ADP
ap-3493	29	21	the	the	DET
ap-3493	29	22	superalgebra	superalgebra	NOUN
ap-3493	29	23	osp(1|2	osp(1|2	PROPN
ap-3493	29	24	)	)	PUNCT
ap-3493	29	25	.	.	PUNCT
ap-3493	30	1	moreover	moreover	ADV
ap-3493	30	2	,	,	PUNCT
ap-3493	30	3	the	the	DET
ap-3493	30	4	symmetry	symmetry	NOUN
ap-3493	30	5	algebra	algebra	NOUN
ap-3493	30	6	is	be	AUX
ap-3493	30	7	characterized	characterize	VERB
ap-3493	30	8	and	and	CCONJ
ap-3493	30	9	is	be	AUX
ap-3493	30	10	seen	see	VERB
ap-3493	30	11	to	to	PART
ap-3493	30	12	correspond	correspond	VERB
ap-3493	30	13	to	to	ADP
ap-3493	30	14	a	a	DET
ap-3493	30	15	rank	rank	NOUN
ap-3493	30	16	-	-	PUNCT
ap-3493	30	17	two	two	NUM
ap-3493	30	18	generalization	generalization	NOUN
ap-3493	30	19	of	of	ADP
ap-3493	30	20	the	the	DET
ap-3493	30	21	bannai	bannai	PROPN
ap-3493	30	22	-	-	PUNCT
ap-3493	30	23	ito	ito	PROPN
ap-3493	30	24	algebra	algebra	NOUN
ap-3493	30	25	.	.	PUNCT
ap-3493	31	1	in	in	ADP
ap-3493	31	2	section	section	NOUN
ap-3493	31	3	4	4	NUM
ap-3493	31	4	,	,	PUNCT
ap-3493	31	5	the	the	DET
ap-3493	31	6	structure	structure	NOUN
ap-3493	31	7	of	of	ADP
ap-3493	31	8	the	the	DET
ap-3493	31	9	space	space	NOUN
ap-3493	31	10	of	of	ADP
ap-3493	31	11	polynomial	polynomial	ADJ
ap-3493	31	12	solutions	solution	NOUN
ap-3493	31	13	is	be	AUX
ap-3493	31	14	exhibited	exhibit	VERB
ap-3493	31	15	using	use	VERB
ap-3493	31	16	a	a	DET
ap-3493	31	17	fischer	fischer	NOUN
ap-3493	31	18	decomposition	decomposition	NOUN
ap-3493	31	19	and	and	CCONJ
ap-3493	31	20	an	an	DET
ap-3493	31	21	explicit	explicit	ADJ
ap-3493	31	22	166	166	NUM
ap-3493	31	23	http://dx.doi.org/10.14311/ap.2016.56.0166	http://dx.doi.org/10.14311/ap.2016.56.0166	NOUN
ap-3493	31	24	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-3493	31	25	vol	vol	NOUN
ap-3493	31	26	.	.	PUNCT
ap-3493	32	1	56	56	NUM
ap-3493	32	2	no	no	NOUN
ap-3493	32	3	.	.	PUNCT
ap-3493	33	1	3/2016	3/2016	NUM
ap-3493	33	2	a	a	DET
ap-3493	33	3	superintegrable	superintegrable	ADJ
ap-3493	33	4	model	model	NOUN
ap-3493	33	5	with	with	ADP
ap-3493	33	6	reflections	reflection	NOUN
ap-3493	33	7	on	on	ADP
ap-3493	33	8	s3	s3	ADJ
ap-3493	33	9	basis	basis	NOUN
ap-3493	33	10	for	for	ADP
ap-3493	33	11	the	the	DET
ap-3493	33	12	eigenfunctions	eigenfunction	NOUN
ap-3493	33	13	is	be	AUX
ap-3493	33	14	constructed	construct	VERB
ap-3493	33	15	with	with	ADP
ap-3493	33	16	the	the	DET
ap-3493	33	17	help	help	NOUN
ap-3493	33	18	of	of	ADP
ap-3493	33	19	a	a	DET
ap-3493	33	20	cauchy	cauchy	PROPN
ap-3493	33	21	-	-	PUNCT
ap-3493	33	22	kovalevskaia	kovalevskaia	PROPN
ap-3493	33	23	extension	extension	NOUN
ap-3493	33	24	theorem	theorem	VERB
ap-3493	33	25	.	.	PUNCT
ap-3493	34	1	some	some	DET
ap-3493	34	2	concluding	conclude	VERB
ap-3493	34	3	remarks	remark	NOUN
ap-3493	34	4	are	be	AUX
ap-3493	34	5	offered	offer	VERB
ap-3493	34	6	in	in	ADP
ap-3493	34	7	section	section	NOUN
ap-3493	34	8	5	5	NUM
ap-3493	34	9	.	.	NOUN
ap-3493	35	1	2	2	NUM
ap-3493	35	2	.	.	X
ap-3493	35	3	a	a	DET
ap-3493	35	4	superintegrable	superintegrable	ADJ
ap-3493	35	5	model	model	NOUN
ap-3493	35	6	on	on	ADP
ap-3493	35	7	s3	s3	PROPN
ap-3493	35	8	let	let	VERB
ap-3493	35	9	s1	s1	NOUN
ap-3493	35	10	,	,	PUNCT
ap-3493	35	11	s2	s2	PROPN
ap-3493	35	12	,	,	PUNCT
ap-3493	35	13	s3	s3	PROPN
ap-3493	35	14	,	,	PUNCT
ap-3493	35	15	s4	s4	PROPN
ap-3493	35	16	be	be	VERB
ap-3493	35	17	the	the	DET
ap-3493	35	18	cartesian	cartesian	ADJ
ap-3493	35	19	coordinates	coordinate	NOUN
ap-3493	35	20	of	of	ADP
ap-3493	35	21	a	a	DET
ap-3493	35	22	four	four	NUM
ap-3493	35	23	-	-	PUNCT
ap-3493	35	24	dimensional	dimensional	ADJ
ap-3493	35	25	euclidian	euclidian	ADJ
ap-3493	35	26	space	space	NOUN
ap-3493	35	27	and	and	CCONJ
ap-3493	35	28	take	take	VERB
ap-3493	35	29	the	the	DET
ap-3493	35	30	restriction	restriction	NOUN
ap-3493	35	31	to	to	ADP
ap-3493	35	32	the	the	DET
ap-3493	35	33	embedded	embed	VERB
ap-3493	35	34	three	three	NUM
ap-3493	35	35	-	-	PUNCT
ap-3493	35	36	sphere	sphere	NOUN
ap-3493	36	1	:	:	PUNCT
ap-3493	36	2	s2	s2	VERB
ap-3493	36	3	1	1	NUM
ap-3493	36	4	+	+	NOUN
ap-3493	36	5	s2	s2	VERB
ap-3493	36	6	2	2	NUM
ap-3493	36	7	+	+	CCONJ
ap-3493	36	8	s2	s2	VERB
ap-3493	36	9	3	3	NUM
ap-3493	36	10	+	+	CCONJ
ap-3493	36	11	s2	s2	VERB
ap-3493	36	12	4	4	NUM
ap-3493	36	13	=	=	SYM
ap-3493	36	14	1	1	X
ap-3493	36	15	.	.	PUNCT
ap-3493	36	16	consider	consider	VERB
ap-3493	36	17	the	the	DET
ap-3493	36	18	system	system	NOUN
ap-3493	36	19	with	with	ADP
ap-3493	36	20	four	four	NUM
ap-3493	36	21	parameters	parameter	NOUN
ap-3493	36	22	µ1	µ1	ADJ
ap-3493	36	23	,	,	PUNCT
ap-3493	36	24	µ2	µ2	PROPN
ap-3493	36	25	,	,	PUNCT
ap-3493	36	26	µ3	µ3	NOUN
ap-3493	36	27	,	,	PUNCT
ap-3493	36	28	µ4	µ4	PROPN
ap-3493	36	29	with	with	ADP
ap-3493	36	30	µi	µi	PROPN
ap-3493	36	31	≥	≥	NOUN
ap-3493	36	32	0	0	NUM
ap-3493	36	33	for	for	ADP
ap-3493	36	34	i	i	PRON
ap-3493	36	35	=	=	NOUN
ap-3493	36	36	1	1	NUM
ap-3493	36	37	,	,	PUNCT
ap-3493	36	38	2	2	NUM
ap-3493	36	39	,	,	PUNCT
ap-3493	36	40	3	3	NUM
ap-3493	36	41	,	,	PUNCT
ap-3493	36	42	4	4	NUM
ap-3493	36	43	governed	govern	VERB
ap-3493	36	44	by	by	ADP
ap-3493	36	45	the	the	DET
ap-3493	36	46	hamiltonian	hamiltonian	ADJ
ap-3493	36	47	h	h	NOUN
ap-3493	36	48	=	=	PUNCT
ap-3493	36	49	∑	∑	PUNCT
ap-3493	37	1	1≤i	1≤i	NUM
ap-3493	37	2	<	<	X
ap-3493	37	3	j≤4	j≤4	PROPN
ap-3493	37	4	j2	j2	PROPN
ap-3493	37	5	ij	ij	NOUN
ap-3493	37	6	+	+	CCONJ
ap-3493	37	7	4∑	4∑	NOUN
ap-3493	37	8	i=1	i=1	PROPN
ap-3493	37	9	µi	µi	PROPN
ap-3493	37	10	s2	s2	PROPN
ap-3493	37	11	i	i	PRON
ap-3493	37	12	(	(	PUNCT
ap-3493	37	13	µi	µi	PROPN
ap-3493	37	14	−ri	−ri	PROPN
ap-3493	37	15	)	)	PUNCT
ap-3493	37	16	,	,	PUNCT
ap-3493	37	17	(	(	PUNCT
ap-3493	37	18	2.1	2.1	NUM
ap-3493	37	19	)	)	PUNCT
ap-3493	37	20	where	where	SCONJ
ap-3493	37	21	jij	jij	PROPN
ap-3493	37	22	=	=	NOUN
ap-3493	37	23	1	1	NUM
ap-3493	37	24	i	i	NOUN
ap-3493	37	25	(	(	PUNCT
ap-3493	37	26	si∂sj	si∂sj	PROPN
ap-3493	37	27	−	−	PROPN
ap-3493	37	28	sj∂si	sj∂si	NUM
ap-3493	37	29	)	)	PUNCT
ap-3493	37	30	,	,	PUNCT
ap-3493	37	31	rif(si	rif(si	X
ap-3493	37	32	)	)	PUNCT
ap-3493	37	33	=	=	SYM
ap-3493	37	34	f(−si	f(−si	NOUN
ap-3493	37	35	)	)	PUNCT
ap-3493	37	36	,	,	PUNCT
ap-3493	37	37	(	(	PUNCT
ap-3493	37	38	2.2	2.2	NUM
ap-3493	37	39	)	)	PUNCT
ap-3493	37	40	are	be	AUX
ap-3493	37	41	the	the	DET
ap-3493	37	42	angular	angular	ADJ
ap-3493	37	43	momentum	momentum	NOUN
ap-3493	37	44	operators	operator	NOUN
ap-3493	37	45	and	and	CCONJ
ap-3493	37	46	reflection	reflection	NOUN
ap-3493	37	47	operators	operator	NOUN
ap-3493	37	48	,	,	PUNCT
ap-3493	37	49	respectively	respectively	ADV
ap-3493	37	50	.	.	PUNCT
ap-3493	38	1	the	the	DET
ap-3493	38	2	six	six	NUM
ap-3493	38	3	quantities	quantity	NOUN
ap-3493	38	4	ljk	ljk	PROPN
ap-3493	38	5	=	=	PUNCT
ap-3493	38	6	(	(	PUNCT
ap-3493	38	7	1	1	NUM
ap-3493	38	8	2	2	NUM
ap-3493	38	9	+	+	NUM
ap-3493	38	10	µjrj	µjrj	NOUN
ap-3493	38	11	+	+	NOUN
ap-3493	38	12	µkrk	µkrk	NOUN
ap-3493	38	13	+	+	CCONJ
ap-3493	38	14	(	(	PUNCT
ap-3493	38	15	ijjk	ijjk	NOUN
ap-3493	39	1	+	+	X
ap-3493	39	2	µj	µj	INTJ
ap-3493	39	3	sk	sk	INTJ
ap-3493	39	4	sj	sj	PROPN
ap-3493	39	5	rj	rj	PROPN
ap-3493	39	6	−	−	PROPN
ap-3493	40	1	µk	µk	INTJ
ap-3493	41	1	sj	sj	INTJ
ap-3493	41	2	sk	sk	ADP
ap-3493	41	3	rk	rk	NOUN
ap-3493	41	4	)	)	PUNCT
ap-3493	42	1	k∏	k∏	PROPN
ap-3493	42	2	l	l	NOUN
ap-3493	42	3	=	=	SYM
ap-3493	42	4	j+1	j+1	ADJ
ap-3493	42	5	rl	rl	X
ap-3493	42	6	)	)	PUNCT
ap-3493	42	7	rjrk	rjrk	PROPN
ap-3493	42	8	,	,	PUNCT
ap-3493	42	9	1	1	NUM
ap-3493	42	10	≤	≤	NUM
ap-3493	42	11	j	j	NOUN
ap-3493	42	12	<	<	X
ap-3493	42	13	k	k	X
ap-3493	42	14	≤	≤	NUM
ap-3493	42	15	4	4	NUM
ap-3493	42	16	,	,	PUNCT
ap-3493	42	17	(	(	PUNCT
ap-3493	42	18	2.3	2.3	NUM
ap-3493	42	19	)	)	PUNCT
ap-3493	42	20	can	can	AUX
ap-3493	42	21	easily	easily	ADV
ap-3493	42	22	be	be	AUX
ap-3493	42	23	verified	verify	VERB
ap-3493	42	24	to	to	PART
ap-3493	42	25	commute	commute	VERB
ap-3493	42	26	with	with	ADP
ap-3493	42	27	h	h	NOUN
ap-3493	42	28	on	on	ADP
ap-3493	42	29	the	the	DET
ap-3493	42	30	3	3	NUM
ap-3493	42	31	-	-	PUNCT
ap-3493	42	32	sphere	sphere	NOUN
ap-3493	42	33	and	and	CCONJ
ap-3493	42	34	are	be	AUX
ap-3493	42	35	thus	thus	ADV
ap-3493	42	36	conserved	conserve	VERB
ap-3493	42	37	.	.	PUNCT
ap-3493	43	1	it	it	PRON
ap-3493	43	2	can	can	AUX
ap-3493	43	3	be	be	AUX
ap-3493	43	4	shown	show	VERB
ap-3493	43	5	that	that	SCONJ
ap-3493	43	6	any	any	DET
ap-3493	43	7	four	four	NUM
ap-3493	43	8	of	of	ADP
ap-3493	43	9	the	the	DET
ap-3493	43	10	ljk	ljk	NOUN
ap-3493	43	11	are	be	AUX
ap-3493	43	12	algebraically	algebraically	ADV
ap-3493	43	13	independent	independent	ADJ
ap-3493	43	14	.	.	PUNCT
ap-3493	44	1	hence	hence	ADV
ap-3493	44	2	h	h	NOUN
ap-3493	44	3	defines	define	VERB
ap-3493	44	4	a	a	DET
ap-3493	44	5	maximally	maximally	ADV
ap-3493	44	6	superintegrable	superintegrable	ADJ
ap-3493	44	7	system	system	NOUN
ap-3493	44	8	of	of	ADP
ap-3493	44	9	first	first	ADJ
ap-3493	44	10	order	order	NOUN
ap-3493	44	11	.	.	PUNCT
ap-3493	45	1	there	there	PRON
ap-3493	45	2	are	be	VERB
ap-3493	45	3	also	also	ADV
ap-3493	45	4	four	four	NUM
ap-3493	45	5	more	more	ADJ
ap-3493	45	6	conserved	conserved	ADJ
ap-3493	45	7	quantities	quantity	NOUN
ap-3493	45	8	of	of	ADP
ap-3493	45	9	the	the	DET
ap-3493	45	10	form	form	NOUN
ap-3493	45	11	ma	ma	PROPN
ap-3493	45	12	=	=	PUNCT
ap-3493	45	13	(	(	PUNCT
ap-3493	45	14	1	1	NUM
ap-3493	45	15	+	+	CCONJ
ap-3493	45	16	∑	∑	ADV
ap-3493	45	17	i∈a	i∈a	ADJ
ap-3493	45	18	µiri	µiri	NOUN
ap-3493	45	19	+	+	CCONJ
ap-3493	45	20	∑	∑	PROPN
ap-3493	45	21	j	j	PROPN
ap-3493	45	22	<	<	PROPN
ap-3493	45	23	k	k	PROPN
ap-3493	45	24	j	j	PROPN
ap-3493	45	25	,	,	PUNCT
ap-3493	45	26	k∈a	k∈a	X
ap-3493	45	27	(	(	PUNCT
ap-3493	45	28	ijjk	ijjk	NOUN
ap-3493	45	29	+	+	CCONJ
ap-3493	45	30	sk	sk	INTJ
ap-3493	45	31	µj	µj	INTJ
ap-3493	45	32	sj	sj	PROPN
ap-3493	45	33	rj	rj	PROPN
ap-3493	46	1	−	−	PROPN
ap-3493	46	2	sj	sj	INTJ
ap-3493	46	3	µk	µk	INTJ
ap-3493	46	4	sk	sk	INTJ
ap-3493	46	5	rk	rk	NOUN
ap-3493	46	6	)	)	PUNCT
ap-3493	47	1	k∏	k∏	PROPN
ap-3493	47	2	l	l	NOUN
ap-3493	47	3	=	=	SYM
ap-3493	47	4	j+1	j+1	ADJ
ap-3493	47	5	rl	rl	X
ap-3493	47	6	)	)	PUNCT
ap-3493	47	7	∏	∏	PROPN
ap-3493	47	8	i∈a	i∈a	PROPN
ap-3493	47	9	ri	ri	PROPN
ap-3493	47	10	,	,	PUNCT
ap-3493	47	11	(	(	PUNCT
ap-3493	47	12	2.4	2.4	NUM
ap-3493	47	13	)	)	PUNCT
ap-3493	47	14	where	where	SCONJ
ap-3493	47	15	a	a	PRON
ap-3493	47	16	=	=	X
ap-3493	47	17	{	{	PUNCT
ap-3493	47	18	1	1	NUM
ap-3493	47	19	,	,	PUNCT
ap-3493	47	20	2	2	NUM
ap-3493	47	21	,	,	PUNCT
ap-3493	47	22	3	3	NUM
ap-3493	47	23	}	}	PUNCT
ap-3493	47	24	,	,	PUNCT
ap-3493	47	25	{	{	PUNCT
ap-3493	47	26	1	1	NUM
ap-3493	47	27	,	,	PUNCT
ap-3493	47	28	2	2	NUM
ap-3493	47	29	,	,	PUNCT
ap-3493	47	30	4	4	NUM
ap-3493	47	31	}	}	PUNCT
ap-3493	47	32	,	,	PUNCT
ap-3493	47	33	{	{	PUNCT
ap-3493	47	34	1	1	NUM
ap-3493	47	35	,	,	PUNCT
ap-3493	47	36	3	3	NUM
ap-3493	47	37	,	,	PUNCT
ap-3493	47	38	4	4	NUM
ap-3493	47	39	}	}	PUNCT
ap-3493	47	40	or	or	CCONJ
ap-3493	47	41	{	{	PUNCT
ap-3493	47	42	2	2	NUM
ap-3493	47	43	,	,	PUNCT
ap-3493	47	44	3	3	NUM
ap-3493	47	45	,	,	PUNCT
ap-3493	47	46	4	4	NUM
ap-3493	47	47	}	}	PUNCT
ap-3493	47	48	.	.	PUNCT
ap-3493	48	1	furthermore	furthermore	ADV
ap-3493	48	2	,	,	PUNCT
ap-3493	48	3	a	a	DET
ap-3493	48	4	direct	direct	ADJ
ap-3493	48	5	computation	computation	NOUN
ap-3493	48	6	yields	yield	NOUN
ap-3493	49	1	[	[	X
ap-3493	49	2	h	h	X
ap-3493	49	3	,	,	PUNCT
ap-3493	49	4	ri	ri	X
ap-3493	49	5	]	]	X
ap-3493	49	6	=	=	SYM
ap-3493	49	7	0	0	NUM
ap-3493	49	8	,	,	PUNCT
ap-3493	49	9	i	i	PRON
ap-3493	49	10	=	=	NOUN
ap-3493	49	11	1	1	NUM
ap-3493	49	12	,	,	PUNCT
ap-3493	49	13	2	2	NUM
ap-3493	49	14	,	,	PUNCT
ap-3493	49	15	3	3	NUM
ap-3493	49	16	,	,	PUNCT
ap-3493	49	17	4	4	NUM
ap-3493	49	18	.	.	PUNCT
ap-3493	50	1	(	(	PUNCT
ap-3493	50	2	2.5	2.5	NUM
ap-3493	50	3	)	)	PUNCT
ap-3493	50	4	the	the	DET
ap-3493	50	5	reflections	reflection	NOUN
ap-3493	50	6	are	be	AUX
ap-3493	50	7	thus	thus	ADV
ap-3493	50	8	discrete	discrete	ADJ
ap-3493	50	9	symmetries	symmetry	NOUN
ap-3493	50	10	of	of	ADP
ap-3493	50	11	the	the	DET
ap-3493	50	12	system	system	NOUN
ap-3493	50	13	.	.	PUNCT
ap-3493	51	1	3	3	X
ap-3493	51	2	.	.	X
ap-3493	51	3	algebraic	algebraic	ADJ
ap-3493	51	4	construction	construction	NOUN
ap-3493	51	5	from	from	ADP
ap-3493	51	6	osp(1|2	osp(1|2	PROPN
ap-3493	51	7	)	)	PUNCT
ap-3493	51	8	the	the	DET
ap-3493	51	9	superalgebra	superalgebra	NOUN
ap-3493	51	10	osp(1|2	osp(1|2	PROPN
ap-3493	51	11	)	)	PUNCT
ap-3493	51	12	can	can	AUX
ap-3493	51	13	be	be	AUX
ap-3493	51	14	presented	present	VERB
ap-3493	51	15	with	with	ADP
ap-3493	51	16	five	five	NUM
ap-3493	51	17	generators	generator	NOUN
ap-3493	51	18	x	x	X
ap-3493	51	19	,	,	PUNCT
ap-3493	51	20	d	d	NOUN
ap-3493	51	21	,	,	PUNCT
ap-3493	51	22	e	e	NOUN
ap-3493	51	23	,	,	PUNCT
ap-3493	51	24	|x|2	|x|2	NOUN
ap-3493	51	25	and	and	CCONJ
ap-3493	51	26	d2	d2	VERB
ap-3493	51	27	with	with	ADP
ap-3493	51	28	the	the	DET
ap-3493	51	29	following	follow	VERB
ap-3493	51	30	defining	define	VERB
ap-3493	51	31	relations	relation	NOUN
ap-3493	51	32	:	:	PUNCT
ap-3493	51	33	{	{	PUNCT
ap-3493	51	34	x	x	NOUN
ap-3493	51	35	,	,	PUNCT
ap-3493	51	36	x	x	NOUN
ap-3493	51	37	}	}	PUNCT
ap-3493	51	38	=	=	SYM
ap-3493	51	39	2|x|2	2|x|2	NUM
ap-3493	51	40	,	,	PUNCT
ap-3493	51	41	{	{	PUNCT
ap-3493	51	42	d	d	X
ap-3493	51	43	,	,	PUNCT
ap-3493	51	44	d	d	NOUN
ap-3493	51	45	}	}	PUNCT
ap-3493	51	46	=	=	SYM
ap-3493	51	47	2d2	2d2	NUM
ap-3493	51	48	,	,	PUNCT
ap-3493	51	49	{	{	PUNCT
ap-3493	51	50	x	x	NOUN
ap-3493	51	51	,	,	PUNCT
ap-3493	51	52	d	d	NOUN
ap-3493	51	53	}	}	PUNCT
ap-3493	51	54	=	=	SYM
ap-3493	51	55	2e	2e	NOUN
ap-3493	51	56	,	,	PUNCT
ap-3493	51	57	[	[	X
ap-3493	51	58	d	d	X
ap-3493	51	59	,	,	PUNCT
ap-3493	51	60	e	e	X
ap-3493	51	61	]	]	PUNCT
ap-3493	51	62	=	=	SYM
ap-3493	51	63	d	d	NOUN
ap-3493	51	64	,	,	PUNCT
ap-3493	51	65	[	[	X
ap-3493	51	66	d	d	NOUN
ap-3493	51	67	,	,	PUNCT
ap-3493	51	68	|x|2	|x|2	PROPN
ap-3493	51	69	]	]	X
ap-3493	51	70	=	=	SYM
ap-3493	51	71	2x	2x	NUM
ap-3493	51	72	,	,	PUNCT
ap-3493	51	73	[	[	X
ap-3493	51	74	e	e	NOUN
ap-3493	51	75	,	,	PUNCT
ap-3493	51	76	x	x	X
ap-3493	51	77	]	]	X
ap-3493	51	78	=	=	SYM
ap-3493	51	79	x	x	SYM
ap-3493	51	80	,	,	PUNCT
ap-3493	51	81	[	[	X
ap-3493	51	82	d2	d2	NOUN
ap-3493	51	83	,	,	PUNCT
ap-3493	51	84	x	x	X
ap-3493	51	85	]	]	X
ap-3493	51	86	=	=	SYM
ap-3493	51	87	2d	2d	NOUN
ap-3493	51	88	,	,	PUNCT
ap-3493	51	89	[	[	X
ap-3493	51	90	d2	d2	NOUN
ap-3493	51	91	,	,	PUNCT
ap-3493	51	92	e	e	X
ap-3493	51	93	]	]	X
ap-3493	51	94	=	=	SYM
ap-3493	51	95	2d2	2d2	NUM
ap-3493	51	96	,	,	PUNCT
ap-3493	51	97	[	[	X
ap-3493	51	98	d2	d2	NOUN
ap-3493	51	99	,	,	PUNCT
ap-3493	51	100	|x|2	|x|2	PROPN
ap-3493	51	101	]	]	X
ap-3493	51	102	=	=	SYM
ap-3493	51	103	4e	4e	NOUN
ap-3493	51	104	,	,	PUNCT
ap-3493	51	105	[	[	X
ap-3493	51	106	e	e	NOUN
ap-3493	51	107	,	,	PUNCT
ap-3493	51	108	|x|2	|x|2	PROPN
ap-3493	51	109	]	]	X
ap-3493	51	110	=	=	SYM
ap-3493	51	111	2|x|2	2|x|2	NUM
ap-3493	51	112	,	,	PUNCT
ap-3493	51	113	(	(	PUNCT
ap-3493	51	114	3.1	3.1	NUM
ap-3493	51	115	)	)	PUNCT
ap-3493	51	116	where	where	SCONJ
ap-3493	51	117	[	[	X
ap-3493	51	118	a	a	X
ap-3493	51	119	,	,	PUNCT
ap-3493	51	120	b	b	NOUN
ap-3493	51	121	]	]	X
ap-3493	51	122	=	=	SYM
ap-3493	51	123	ab	ab	PROPN
ap-3493	52	1	−	−	PROPN
ap-3493	52	2	ba	ba	PROPN
ap-3493	52	3	is	be	AUX
ap-3493	52	4	the	the	DET
ap-3493	52	5	commutator	commutator	NOUN
ap-3493	52	6	and	and	CCONJ
ap-3493	52	7	{	{	PUNCT
ap-3493	52	8	a	a	DET
ap-3493	52	9	,	,	PUNCT
ap-3493	52	10	b	b	NOUN
ap-3493	52	11	}	}	PUNCT
ap-3493	52	12	=	=	SYM
ap-3493	52	13	ab	ab	PROPN
ap-3493	53	1	+	+	CCONJ
ap-3493	53	2	ba	ba	PROPN
ap-3493	53	3	is	be	AUX
ap-3493	53	4	the	the	DET
ap-3493	53	5	anti	anti	ADJ
ap-3493	53	6	-	-	NOUN
ap-3493	53	7	commutator	commutator	NOUN
ap-3493	53	8	.	.	PUNCT
ap-3493	54	1	one	one	PRON
ap-3493	54	2	can	can	AUX
ap-3493	54	3	realize	realize	VERB
ap-3493	54	4	four	four	NUM
ap-3493	54	5	mutually	mutually	ADV
ap-3493	54	6	commuting	commute	VERB
ap-3493	54	7	copies	copy	NOUN
ap-3493	54	8	of	of	ADP
ap-3493	54	9	this	this	DET
ap-3493	54	10	superalgebra	superalgebra	NOUN
ap-3493	54	11	by	by	ADP
ap-3493	54	12	taking	take	VERB
ap-3493	54	13	di	di	NOUN
ap-3493	54	14	=	=	PUNCT
ap-3493	54	15	∂si	∂si	PROPN
ap-3493	54	16	−	−	PROPN
ap-3493	54	17	µi	µi	INTJ
ap-3493	54	18	si	si	PROPN
ap-3493	54	19	ri	ri	PROPN
ap-3493	54	20	,	,	PUNCT
ap-3493	54	21	d2	d2	PROPN
ap-3493	55	1	i	i	PRON
ap-3493	55	2	=	=	PUNCT
ap-3493	55	3	didi	didi	PROPN
ap-3493	55	4	,	,	PUNCT
ap-3493	55	5	xi	xi	X
ap-3493	55	6	=	=	SYM
ap-3493	55	7	si	si	X
ap-3493	55	8	,	,	PUNCT
ap-3493	55	9	|xi|2	|xi|2	PUNCT
ap-3493	55	10	=	=	SYM
ap-3493	56	1	s2	s2	VERB
ap-3493	56	2	i	i	PRON
ap-3493	56	3	,	,	PUNCT
ap-3493	56	4	ei	ei	X
ap-3493	56	5	=	=	SYM
ap-3493	56	6	si∂si	si∂si	PROPN
ap-3493	57	1	+	+	CCONJ
ap-3493	57	2	1	1	NUM
ap-3493	57	3	2	2	NUM
ap-3493	57	4	,	,	PUNCT
ap-3493	57	5	(	(	PUNCT
ap-3493	57	6	3.2	3.2	NUM
ap-3493	57	7	)	)	PUNCT
ap-3493	57	8	where	where	SCONJ
ap-3493	57	9	i	i	PRON
ap-3493	57	10	=	=	NOUN
ap-3493	57	11	1	1	NUM
ap-3493	57	12	,	,	PUNCT
ap-3493	57	13	2	2	NUM
ap-3493	57	14	,	,	PUNCT
ap-3493	57	15	3	3	NUM
ap-3493	57	16	,	,	PUNCT
ap-3493	57	17	4	4	NUM
ap-3493	57	18	.	.	PUNCT
ap-3493	58	1	each	each	DET
ap-3493	58	2	superalgebra	superalgebra	NOUN
ap-3493	58	3	possesses	possess	VERB
ap-3493	58	4	a	a	DET
ap-3493	58	5	scasimir	scasimir	NOUN
ap-3493	58	6	element	element	NOUN
ap-3493	58	7	given	give	VERB
ap-3493	58	8	by	by	ADP
ap-3493	58	9	si	si	X
ap-3493	58	10	=	=	SYM
ap-3493	58	11	1	1	NUM
ap-3493	58	12	2	2	NUM
ap-3493	58	13	(	(	PUNCT
ap-3493	58	14	[	[	X
ap-3493	58	15	di	di	X
ap-3493	58	16	,	,	PUNCT
ap-3493	58	17	xi]−	xi]−	PROPN
ap-3493	58	18	1	1	NUM
ap-3493	58	19	)	)	PUNCT
ap-3493	58	20	,	,	PUNCT
ap-3493	58	21	(	(	PUNCT
ap-3493	58	22	3.3	3.3	NUM
ap-3493	58	23	)	)	PUNCT
ap-3493	58	24	which	which	PRON
ap-3493	58	25	anticommutes	anticommute	VERB
ap-3493	58	26	with	with	ADP
ap-3493	58	27	the	the	DET
ap-3493	58	28	odd	odd	ADJ
ap-3493	58	29	generators	generator	NOUN
ap-3493	58	30	{	{	PUNCT
ap-3493	58	31	si	si	X
ap-3493	58	32	,	,	PUNCT
ap-3493	58	33	di	di	NOUN
ap-3493	58	34	}	}	PUNCT
ap-3493	58	35	=	=	SYM
ap-3493	58	36	{	{	PUNCT
ap-3493	58	37	si	si	X
ap-3493	58	38	,	,	PUNCT
ap-3493	58	39	xi	xi	ADJ
ap-3493	58	40	}	}	PUNCT
ap-3493	58	41	=	=	SYM
ap-3493	58	42	0	0	NUM
ap-3493	58	43	,	,	PUNCT
ap-3493	58	44	(	(	PUNCT
ap-3493	58	45	3.4	3.4	NUM
ap-3493	58	46	)	)	PUNCT
ap-3493	58	47	and	and	CCONJ
ap-3493	58	48	thus	thus	ADV
ap-3493	58	49	commutes	commute	NOUN
ap-3493	58	50	with	with	ADP
ap-3493	58	51	the	the	DET
ap-3493	58	52	even	even	ADJ
ap-3493	58	53	generators	generator	NOUN
ap-3493	58	54	[	[	X
ap-3493	58	55	si	si	X
ap-3493	58	56	,	,	PUNCT
ap-3493	58	57	ei	ei	X
ap-3493	58	58	]	]	X
ap-3493	58	59	=	=	PUNCT
ap-3493	59	1	[	[	X
ap-3493	59	2	si	si	X
ap-3493	59	3	,	,	PUNCT
ap-3493	59	4	|xi|2	|xi|2	PUNCT
ap-3493	59	5	]	]	PUNCT
ap-3493	59	6	=	=	PUNCT
ap-3493	60	1	[	[	X
ap-3493	60	2	si	si	X
ap-3493	60	3	,	,	PUNCT
ap-3493	60	4	d2	d2	NOUN
ap-3493	60	5	i	i	PRON
ap-3493	60	6	]	]	PUNCT
ap-3493	61	1	=	=	PUNCT
ap-3493	61	2	0	0	X
ap-3493	61	3	.	.	PUNCT
ap-3493	62	1	(	(	PUNCT
ap-3493	62	2	3.5	3.5	NUM
ap-3493	62	3	)	)	PUNCT
ap-3493	62	4	167	167	NUM
ap-3493	62	5	hendrik	hendrik	PROPN
ap-3493	62	6	de	de	X
ap-3493	62	7	bie	bie	PROPN
ap-3493	62	8	,	,	PUNCT
ap-3493	62	9	vincent	vincent	PROPN
ap-3493	62	10	x.	x.	PROPN
ap-3493	62	11	genest	genest	PROPN
ap-3493	62	12	,	,	PUNCT
ap-3493	62	13	jean	jean	PROPN
ap-3493	62	14	-	-	PUNCT
ap-3493	62	15	michel	michel	PROPN
ap-3493	62	16	lemay	lemay	PROPN
ap-3493	62	17	,	,	PUNCT
ap-3493	62	18	luc	luc	PROPN
ap-3493	62	19	vinet	vinet	PROPN
ap-3493	62	20	acta	acta	PROPN
ap-3493	62	21	polytechnica	polytechnica	PROPN
ap-3493	62	22	it	it	PRON
ap-3493	62	23	is	be	AUX
ap-3493	62	24	immediate	immediate	ADJ
ap-3493	62	25	to	to	PART
ap-3493	62	26	verify	verify	VERB
ap-3493	62	27	that	that	SCONJ
ap-3493	62	28	in	in	ADP
ap-3493	62	29	the	the	DET
ap-3493	62	30	realization	realization	NOUN
ap-3493	62	31	(	(	PUNCT
ap-3493	62	32	3.2	3.2	NUM
ap-3493	62	33	)	)	PUNCT
ap-3493	62	34	,	,	PUNCT
ap-3493	62	35	the	the	DET
ap-3493	62	36	reflection	reflection	NOUN
ap-3493	62	37	ri	ri	NOUN
ap-3493	62	38	verifies	verifie	NOUN
ap-3493	62	39	the	the	DET
ap-3493	62	40	same	same	ADJ
ap-3493	62	41	commutation	commutation	NOUN
ap-3493	62	42	relations	relation	NOUN
ap-3493	62	43	as	as	ADP
ap-3493	62	44	the	the	DET
ap-3493	62	45	scasimir	scasimir	NOUN
ap-3493	62	46	[	[	X
ap-3493	62	47	ri	ri	PROPN
ap-3493	62	48	,	,	PUNCT
ap-3493	62	49	ei	ei	X
ap-3493	62	50	]	]	X
ap-3493	62	51	=	=	PUNCT
ap-3493	63	1	[	[	X
ap-3493	63	2	ri	ri	NOUN
ap-3493	63	3	,	,	PUNCT
ap-3493	63	4	|xi|2	|xi|2	PUNCT
ap-3493	63	5	]	]	PUNCT
ap-3493	63	6	=	=	SYM
ap-3493	64	1	[	[	X
ap-3493	64	2	ri	ri	PROPN
ap-3493	64	3	,	,	PUNCT
ap-3493	64	4	d2	d2	PROPN
ap-3493	64	5	i	i	PRON
ap-3493	64	6	]	]	X
ap-3493	65	1	=	=	PRON
ap-3493	65	2	{	{	PUNCT
ap-3493	65	3	ri	ri	PROPN
ap-3493	65	4	,	,	PUNCT
ap-3493	65	5	di	di	NOUN
ap-3493	65	6	}	}	PUNCT
ap-3493	65	7	=	=	SYM
ap-3493	65	8	{	{	PUNCT
ap-3493	65	9	ri	ri	PROPN
ap-3493	65	10	,	,	PUNCT
ap-3493	65	11	xi	xi	ADJ
ap-3493	65	12	}	}	PUNCT
ap-3493	65	13	=	=	SYM
ap-3493	65	14	0	0	X
ap-3493	65	15	.	.	PUNCT
ap-3493	66	1	(	(	PUNCT
ap-3493	66	2	3.6	3.6	NUM
ap-3493	66	3	)	)	PUNCT
ap-3493	66	4	this	this	PRON
ap-3493	66	5	implies	imply	VERB
ap-3493	66	6	that	that	SCONJ
ap-3493	66	7	one	one	PRON
ap-3493	66	8	can	can	AUX
ap-3493	66	9	construct	construct	VERB
ap-3493	66	10	a	a	DET
ap-3493	66	11	casimir	casimir	NOUN
ap-3493	66	12	operator	operator	NOUN
ap-3493	66	13	of	of	ADP
ap-3493	66	14	the	the	DET
ap-3493	66	15	form	form	NOUN
ap-3493	66	16	qi	qi	NOUN
ap-3493	66	17	=	=	SYM
ap-3493	66	18	siri	siri	NOUN
ap-3493	66	19	.	.	PUNCT
ap-3493	67	1	(	(	PUNCT
ap-3493	67	2	3.7	3.7	NUM
ap-3493	67	3	)	)	PUNCT
ap-3493	67	4	it	it	PRON
ap-3493	67	5	is	be	AUX
ap-3493	67	6	straightforward	straightforward	ADJ
ap-3493	67	7	to	to	PART
ap-3493	67	8	verify	verify	VERB
ap-3493	67	9	that	that	SCONJ
ap-3493	67	10	qi	qi	PROPN
ap-3493	67	11	indeed	indeed	ADV
ap-3493	67	12	commutes	commute	VERB
ap-3493	67	13	with	with	ADP
ap-3493	67	14	every	every	DET
ap-3493	67	15	generator	generator	NOUN
ap-3493	67	16	.	.	PUNCT
ap-3493	68	1	these	these	DET
ap-3493	68	2	four	four	NUM
ap-3493	68	3	realizations	realization	NOUN
ap-3493	68	4	of	of	ADP
ap-3493	68	5	osp(1|2	osp(1|2	PROPN
ap-3493	68	6	)	)	PUNCT
ap-3493	68	7	can	can	AUX
ap-3493	68	8	act	act	VERB
ap-3493	68	9	as	as	ADP
ap-3493	68	10	building	build	VERB
ap-3493	68	11	blocks	block	NOUN
ap-3493	68	12	for	for	ADP
ap-3493	68	13	many	many	ADJ
ap-3493	68	14	other	other	ADJ
ap-3493	68	15	realizations	realization	NOUN
ap-3493	68	16	.	.	PUNCT
ap-3493	69	1	let	let	VERB
ap-3493	69	2	[	[	X
ap-3493	69	3	n	n	X
ap-3493	69	4	]	]	X
ap-3493	69	5	=	=	PUNCT
ap-3493	69	6	{	{	PUNCT
ap-3493	69	7	1	1	NUM
ap-3493	69	8	,	,	PUNCT
ap-3493	69	9	2	2	NUM
ap-3493	69	10	,	,	PUNCT
ap-3493	69	11	.	.	PUNCT
ap-3493	69	12	.	.	PUNCT
ap-3493	70	1	.	.	PUNCT
ap-3493	71	1	,	,	PUNCT
ap-3493	71	2	n	n	CCONJ
ap-3493	71	3	}	}	PUNCT
ap-3493	72	1	and	and	CCONJ
ap-3493	72	2	a	a	DET
ap-3493	72	3	⊂	⊂	PROPN
ap-3493	73	1	[	[	X
ap-3493	73	2	4	4	NUM
ap-3493	73	3	]	]	PUNCT
ap-3493	73	4	.	.	PUNCT
ap-3493	74	1	the	the	DET
ap-3493	74	2	operators	operator	NOUN
ap-3493	74	3	given	give	VERB
ap-3493	74	4	by	by	ADP
ap-3493	74	5	da	da	PROPN
ap-3493	74	6	=	=	PUNCT
ap-3493	74	7	∑	∑	PUNCT
ap-3493	74	8	i∈a	i∈a	ADJ
ap-3493	74	9	(	(	PUNCT
ap-3493	74	10	di	di	INTJ
ap-3493	74	11	supa∏	supa∏	PROPN
ap-3493	74	12	j	j	PROPN
ap-3493	74	13	=	=	PROPN
ap-3493	74	14	i+1	i+1	PROPN
ap-3493	74	15	rj	rj	PROPN
ap-3493	74	16	)	)	PUNCT
ap-3493	74	17	,	,	PUNCT
ap-3493	74	18	d2	d2	VERB
ap-3493	74	19	a	a	DET
ap-3493	74	20	=	=	X
ap-3493	74	21	dada	dada	PROPN
ap-3493	74	22	,	,	PUNCT
ap-3493	74	23	xa	xa	PROPN
ap-3493	74	24	=	=	PUNCT
ap-3493	74	25	∑	∑	PUNCT
ap-3493	74	26	i∈a	i∈a	ADJ
ap-3493	74	27	(	(	PUNCT
ap-3493	74	28	si	si	PROPN
ap-3493	74	29	supa∏	supa∏	PROPN
ap-3493	74	30	j	j	PROPN
ap-3493	74	31	=	=	PROPN
ap-3493	74	32	i+1	i+1	PROPN
ap-3493	74	33	rj	rj	PROPN
ap-3493	74	34	)	)	PUNCT
ap-3493	74	35	,	,	PUNCT
ap-3493	74	36	|xa|2	|xa|2	PUNCT
ap-3493	74	37	=	=	SYM
ap-3493	74	38	∑	∑	PUNCT
ap-3493	74	39	i∈a	i∈a	ADJ
ap-3493	74	40	s2	s2	PROPN
ap-3493	74	41	i	i	PRON
ap-3493	74	42	,	,	PUNCT
ap-3493	74	43	ea	ea	X
ap-3493	74	44	=	=	PUNCT
ap-3493	74	45	∑	∑	PUNCT
ap-3493	74	46	i∈a	i∈a	ADJ
ap-3493	74	47	ei	ei	PROPN
ap-3493	74	48	,	,	PUNCT
ap-3493	74	49	(	(	PUNCT
ap-3493	74	50	3.8	3.8	NUM
ap-3493	74	51	)	)	PUNCT
ap-3493	74	52	verify	verify	VERB
ap-3493	74	53	the	the	DET
ap-3493	74	54	commutation	commutation	NOUN
ap-3493	74	55	relations	relation	NOUN
ap-3493	74	56	(	(	PUNCT
ap-3493	74	57	3.1	3.1	NUM
ap-3493	74	58	)	)	PUNCT
ap-3493	74	59	for	for	ADP
ap-3493	74	60	any	any	DET
ap-3493	74	61	a	a	DET
ap-3493	74	62	⊂	⊂	PROPN
ap-3493	75	1	[	[	X
ap-3493	75	2	4	4	NUM
ap-3493	75	3	]	]	PUNCT
ap-3493	75	4	and	and	CCONJ
ap-3493	75	5	thus	thus	ADV
ap-3493	75	6	form	form	VERB
ap-3493	75	7	new	new	ADJ
ap-3493	75	8	realizations	realization	NOUN
ap-3493	75	9	of	of	ADP
ap-3493	75	10	osp(1|2	osp(1|2	PROPN
ap-3493	75	11	)	)	PUNCT
ap-3493	75	12	.	.	PUNCT
ap-3493	76	1	these	these	DET
ap-3493	76	2	result	result	VERB
ap-3493	76	3	from	from	ADP
ap-3493	76	4	the	the	DET
ap-3493	76	5	repeated	repeat	VERB
ap-3493	76	6	application	application	NOUN
ap-3493	76	7	of	of	ADP
ap-3493	76	8	the	the	DET
ap-3493	76	9	coproduct	coproduct	NOUN
ap-3493	76	10	of	of	ADP
ap-3493	76	11	osp(1|2	osp(1|2	PROPN
ap-3493	76	12	)	)	PUNCT
ap-3493	76	13	(	(	PUNCT
ap-3493	76	14	see	see	VERB
ap-3493	76	15	[	[	X
ap-3493	76	16	20	20	NUM
ap-3493	76	17	]	]	NUM
ap-3493	76	18	)	)	PUNCT
ap-3493	76	19	.	.	PUNCT
ap-3493	77	1	moreover	moreover	ADV
ap-3493	77	2	,	,	PUNCT
ap-3493	77	3	for	for	ADP
ap-3493	77	4	any	any	DET
ap-3493	77	5	a	a	DET
ap-3493	77	6	the	the	DET
ap-3493	77	7	scasimir	scasimir	NOUN
ap-3493	77	8	and	and	CCONJ
ap-3493	77	9	the	the	DET
ap-3493	77	10	casimir	casimir	NOUN
ap-3493	77	11	operators	operator	NOUN
ap-3493	77	12	are	be	AUX
ap-3493	77	13	also	also	ADV
ap-3493	77	14	similarly	similarly	ADV
ap-3493	77	15	defined	define	VERB
ap-3493	77	16	:	:	PUNCT
ap-3493	77	17	sa	sa	X
ap-3493	77	18	=	=	SYM
ap-3493	77	19	1	1	NUM
ap-3493	77	20	2	2	NUM
ap-3493	77	21	(	(	PUNCT
ap-3493	77	22	[	[	X
ap-3493	77	23	da	da	X
ap-3493	77	24	,	,	PUNCT
ap-3493	77	25	xa]−	xa]−	PROPN
ap-3493	77	26	1	1	NUM
ap-3493	77	27	)	)	PUNCT
ap-3493	77	28	,	,	PUNCT
ap-3493	77	29	qa	qa	PROPN
ap-3493	77	30	=	=	SYM
ap-3493	77	31	sa	sa	PROPN
ap-3493	77	32	∏	∏	PROPN
ap-3493	77	33	i∈a	i∈a	PROPN
ap-3493	77	34	ri	ri	PROPN
ap-3493	77	35	.	.	PUNCT
ap-3493	78	1	(	(	PUNCT
ap-3493	78	2	3.9	3.9	NUM
ap-3493	78	3	)	)	PUNCT
ap-3493	78	4	one	one	NOUN
ap-3493	78	5	can	can	AUX
ap-3493	78	6	directly	directly	ADV
ap-3493	78	7	check	check	VERB
ap-3493	78	8	that	that	PRON
ap-3493	78	9	qi	qi	PRON
ap-3493	78	10	=	=	SYM
ap-3493	78	11	µi	µi	PROPN
ap-3493	78	12	,	,	PUNCT
ap-3493	78	13	qjk	qjk	PROPN
ap-3493	78	14	=	=	PUNCT
ap-3493	78	15	ljk	ljk	PROPN
ap-3493	78	16	,	,	PUNCT
ap-3493	78	17	qb	qb	PROPN
ap-3493	78	18	=	=	PUNCT
ap-3493	78	19	mb	mb	PROPN
ap-3493	78	20	,	,	PUNCT
ap-3493	78	21	(	(	PUNCT
ap-3493	78	22	3.10	3.10	NUM
ap-3493	78	23	)	)	PUNCT
ap-3493	78	24	where	where	SCONJ
ap-3493	78	25	qjk	qjk	PROPN
ap-3493	78	26	denotes	denote	VERB
ap-3493	78	27	qa	qa	PROPN
ap-3493	78	28	with	with	ADP
ap-3493	78	29	a	a	DET
ap-3493	78	30	=	=	SYM
ap-3493	78	31	{	{	PUNCT
ap-3493	78	32	j	j	PROPN
ap-3493	78	33	,	,	PUNCT
ap-3493	78	34	k	k	NOUN
ap-3493	78	35	}	}	PUNCT
ap-3493	78	36	and	and	CCONJ
ap-3493	78	37	b	b	NOUN
ap-3493	78	38	is	be	AUX
ap-3493	78	39	any	any	DET
ap-3493	78	40	3	3	NUM
ap-3493	78	41	-	-	PUNCT
ap-3493	78	42	subset	subset	NOUN
ap-3493	78	43	of	of	ADP
ap-3493	78	44	[	[	X
ap-3493	78	45	4	4	NUM
ap-3493	78	46	]	]	PUNCT
ap-3493	78	47	.	.	PUNCT
ap-3493	79	1	another	another	DET
ap-3493	79	2	explicit	explicit	ADJ
ap-3493	79	3	computation	computation	NOUN
ap-3493	79	4	gives	give	VERB
ap-3493	79	5	s2	s2	PROPN
ap-3493	80	1	[	[	X
ap-3493	80	2	4	4	NUM
ap-3493	80	3	]	]	PUNCT
ap-3493	80	4	−	−	PROPN
ap-3493	81	1	s[4	s[4	SYM
ap-3493	81	2	]	]	X
ap-3493	81	3	−	−	PROPN
ap-3493	81	4	3	3	NUM
ap-3493	81	5	4	4	NUM
ap-3493	81	6	=	=	SYM
ap-3493	81	7	∑	∑	PUNCT
ap-3493	81	8	1≤i	1≤i	PROPN
ap-3493	81	9	<	<	X
ap-3493	82	1	j≤4	j≤4	PROPN
ap-3493	82	2	j2	j2	PROPN
ap-3493	82	3	ij	ij	INTJ
ap-3493	82	4	+	+	CCONJ
ap-3493	82	5	(	(	PUNCT
ap-3493	82	6	s2	s2	VERB
ap-3493	82	7	1	1	NUM
ap-3493	82	8	+	+	NOUN
ap-3493	82	9	s2	s2	VERB
ap-3493	82	10	2	2	NUM
ap-3493	82	11	+	+	CCONJ
ap-3493	82	12	s2	s2	VERB
ap-3493	82	13	3	3	NUM
ap-3493	82	14	+	+	CCONJ
ap-3493	82	15	s2	s2	VERB
ap-3493	82	16	4	4	NUM
ap-3493	82	17	)	)	PUNCT
ap-3493	82	18	4∑	4∑	NOUN
ap-3493	82	19	i=1	i=1	PROPN
ap-3493	82	20	µi	µi	PROPN
ap-3493	82	21	s2	s2	PROPN
ap-3493	82	22	i	i	PRON
ap-3493	82	23	(	(	PUNCT
ap-3493	82	24	µi	µi	PROPN
ap-3493	82	25	−ri	−ri	PROPN
ap-3493	82	26	)	)	PUNCT
ap-3493	82	27	.	.	PUNCT
ap-3493	83	1	(	(	PUNCT
ap-3493	83	2	3.11	3.11	NUM
ap-3493	83	3	)	)	PUNCT
ap-3493	83	4	however	however	ADV
ap-3493	83	5	,	,	PUNCT
ap-3493	83	6	since	since	SCONJ
ap-3493	83	7	|x[4]|2	|x[4]|2	PUNCT
ap-3493	83	8	=	=	SYM
ap-3493	83	9	s2	s2	NOUN
ap-3493	83	10	1	1	NUM
ap-3493	83	11	+	+	CCONJ
ap-3493	83	12	s2	s2	VERB
ap-3493	83	13	2	2	NUM
ap-3493	83	14	+	+	CCONJ
ap-3493	83	15	s2	s2	VERB
ap-3493	83	16	3	3	NUM
ap-3493	83	17	+	+	CCONJ
ap-3493	83	18	s2	s2	VERB
ap-3493	83	19	4	4	NUM
ap-3493	83	20	commutes	commute	NOUN
ap-3493	83	21	with	with	ADP
ap-3493	83	22	s[4	s[4	NOUN
ap-3493	83	23	]	]	PUNCT
ap-3493	83	24	and	and	CCONJ
ap-3493	83	25	all	all	DET
ap-3493	83	26	the	the	DET
ap-3493	83	27	casimirs	casimir	NOUN
ap-3493	83	28	,	,	PUNCT
ap-3493	83	29	it	it	PRON
ap-3493	83	30	is	be	AUX
ap-3493	83	31	central	central	ADJ
ap-3493	83	32	in	in	ADP
ap-3493	83	33	the	the	DET
ap-3493	83	34	algebra	algebra	NOUN
ap-3493	83	35	generated	generate	VERB
ap-3493	83	36	by	by	ADP
ap-3493	83	37	the	the	DET
ap-3493	83	38	casimirs	casimir	NOUN
ap-3493	83	39	and	and	CCONJ
ap-3493	83	40	can	can	AUX
ap-3493	83	41	thus	thus	ADV
ap-3493	83	42	be	be	AUX
ap-3493	83	43	treated	treat	VERB
ap-3493	83	44	as	as	ADP
ap-3493	83	45	a	a	DET
ap-3493	83	46	constant	constant	ADJ
ap-3493	83	47	.	.	PUNCT
ap-3493	84	1	taking	take	VERB
ap-3493	84	2	|x[4]|2	|x[4]|2	PRON
ap-3493	84	3	=	=	SYM
ap-3493	84	4	1	1	NUM
ap-3493	84	5	,	,	PUNCT
ap-3493	84	6	it	it	PRON
ap-3493	84	7	is	be	AUX
ap-3493	84	8	straightforward	straightforward	ADJ
ap-3493	84	9	by	by	ADP
ap-3493	84	10	comparing	compare	VERB
ap-3493	84	11	(	(	PUNCT
ap-3493	84	12	3.11	3.11	NUM
ap-3493	84	13	)	)	PUNCT
ap-3493	84	14	and	and	CCONJ
ap-3493	84	15	(	(	PUNCT
ap-3493	84	16	2.1	2.1	NUM
ap-3493	84	17	)	)	PUNCT
ap-3493	84	18	that	that	PRON
ap-3493	84	19	s2	s2	NOUN
ap-3493	85	1	[	[	X
ap-3493	85	2	4	4	NUM
ap-3493	85	3	]	]	PUNCT
ap-3493	85	4	−	−	PROPN
ap-3493	86	1	s[4	s[4	SYM
ap-3493	86	2	]	]	X
ap-3493	86	3	−	−	PROPN
ap-3493	86	4	3	3	NUM
ap-3493	86	5	4	4	NUM
ap-3493	86	6	=	=	SYM
ap-3493	86	7	h.	h.	NOUN
ap-3493	86	8	(	(	PUNCT
ap-3493	86	9	3.12	3.12	NUM
ap-3493	86	10	)	)	PUNCT
ap-3493	86	11	hence	hence	ADV
ap-3493	86	12	,	,	PUNCT
ap-3493	86	13	a	a	DET
ap-3493	86	14	quadratic	quadratic	ADJ
ap-3493	86	15	combination	combination	NOUN
ap-3493	86	16	of	of	ADP
ap-3493	86	17	the	the	DET
ap-3493	86	18	scasimir	scasimir	NOUN
ap-3493	86	19	of	of	ADP
ap-3493	86	20	four	four	NUM
ap-3493	86	21	copies	copy	NOUN
ap-3493	86	22	of	of	ADP
ap-3493	86	23	osp(1|2	osp(1|2	PROPN
ap-3493	86	24	)	)	PUNCT
ap-3493	86	25	yields	yield	VERB
ap-3493	86	26	the	the	DET
ap-3493	86	27	hamiltonian	hamiltonian	NOUN
ap-3493	86	28	of	of	ADP
ap-3493	86	29	the	the	DET
ap-3493	86	30	superintegrable	superintegrable	ADJ
ap-3493	86	31	model	model	NOUN
ap-3493	86	32	presented	present	VERB
ap-3493	86	33	in	in	ADP
ap-3493	86	34	section	section	NOUN
ap-3493	86	35	1	1	NUM
ap-3493	86	36	and	and	CCONJ
ap-3493	86	37	the	the	DET
ap-3493	86	38	intermediate	intermediate	ADJ
ap-3493	86	39	casimirs	casimir	NOUN
ap-3493	86	40	are	be	AUX
ap-3493	86	41	its	its	PRON
ap-3493	86	42	symmetries	symmetry	NOUN
ap-3493	86	43	.	.	PUNCT
ap-3493	87	1	indeed	indeed	ADV
ap-3493	87	2	,	,	PUNCT
ap-3493	87	3	it	it	PRON
ap-3493	87	4	can	can	AUX
ap-3493	87	5	be	be	AUX
ap-3493	87	6	checked	check	VERB
ap-3493	87	7	that	that	SCONJ
ap-3493	88	1	[	[	X
ap-3493	88	2	qa	qa	X
ap-3493	88	3	,	,	PUNCT
ap-3493	88	4	h	h	NOUN
ap-3493	88	5	]	]	X
ap-3493	88	6	=	=	SYM
ap-3493	88	7	0	0	NUM
ap-3493	88	8	for	for	ADP
ap-3493	88	9	a	a	DET
ap-3493	88	10	⊂	⊂	PROPN
ap-3493	88	11	[	[	X
ap-3493	88	12	4	4	NUM
ap-3493	88	13	]	]	PUNCT
ap-3493	88	14	.	.	PUNCT
ap-3493	89	1	the	the	DET
ap-3493	89	2	symmetry	symmetry	NOUN
ap-3493	89	3	algebra	algebra	NOUN
ap-3493	89	4	has	have	VERB
ap-3493	89	5	the	the	DET
ap-3493	89	6	following	follow	VERB
ap-3493	89	7	structure	structure	NOUN
ap-3493	89	8	relations	relation	NOUN
ap-3493	89	9	{	{	PUNCT
ap-3493	89	10	qa	qa	PROPN
ap-3493	89	11	,	,	PUNCT
ap-3493	89	12	qb	qb	PROPN
ap-3493	89	13	}	}	PUNCT
ap-3493	89	14	=	=	PUNCT
ap-3493	89	15	q(a∪b)\(a∩b	q(a∪b)\(a∩b	PROPN
ap-3493	89	16	)	)	PUNCT
ap-3493	90	1	+	+	NUM
ap-3493	90	2	2qa∩bqa∪b	2qa∩bqa∪b	NUM
ap-3493	90	3	+	+	NUM
ap-3493	90	4	2qa\(a∩b)qb\(a∩b	2qa\(a∩b)qb\(a∩b	NUM
ap-3493	90	5	)	)	PUNCT
ap-3493	90	6	,	,	PUNCT
ap-3493	90	7	(	(	PUNCT
ap-3493	90	8	3.13	3.13	NUM
ap-3493	90	9	)	)	PUNCT
ap-3493	90	10	where	where	SCONJ
ap-3493	90	11	a	a	PRON
ap-3493	90	12	,	,	PUNCT
ap-3493	90	13	b	b	X
ap-3493	90	14	⊂	⊂	PROPN
ap-3493	90	15	[	[	X
ap-3493	90	16	4	4	X
ap-3493	90	17	]	]	PUNCT
ap-3493	90	18	and	and	CCONJ
ap-3493	90	19	q∅	q∅	ADV
ap-3493	90	20	=	=	SYM
ap-3493	90	21	−1/2	−1/2	VERB
ap-3493	90	22	as	as	SCONJ
ap-3493	90	23	prescribed	prescribe	VERB
ap-3493	90	24	by	by	ADP
ap-3493	90	25	the	the	DET
ap-3493	90	26	definitions	definition	NOUN
ap-3493	90	27	(	(	PUNCT
ap-3493	90	28	3.8	3.8	NUM
ap-3493	90	29	)	)	PUNCT
ap-3493	90	30	and	and	CCONJ
ap-3493	90	31	(	(	PUNCT
ap-3493	90	32	3.9	3.9	NUM
ap-3493	90	33	)	)	PUNCT
ap-3493	90	34	.	.	PUNCT
ap-3493	91	1	this	this	DET
ap-3493	91	2	algebra	algebra	NOUN
ap-3493	91	3	has	have	AUX
ap-3493	91	4	already	already	ADV
ap-3493	91	5	been	be	AUX
ap-3493	91	6	studied	study	VERB
ap-3493	91	7	in	in	ADP
ap-3493	91	8	[	[	X
ap-3493	91	9	8	8	NUM
ap-3493	91	10	]	]	PUNCT
ap-3493	91	11	and	and	CCONJ
ap-3493	91	12	is	be	AUX
ap-3493	91	13	interpreted	interpret	VERB
ap-3493	91	14	as	as	ADP
ap-3493	91	15	a	a	DET
ap-3493	91	16	rank	rank	NOUN
ap-3493	91	17	2	2	NUM
ap-3493	91	18	bannai	bannai	PROPN
ap-3493	91	19	-	-	PUNCT
ap-3493	91	20	ito	ito	PROPN
ap-3493	91	21	algebra	algebra	NOUN
ap-3493	91	22	.	.	PUNCT
ap-3493	92	1	to	to	PART
ap-3493	92	2	see	see	VERB
ap-3493	92	3	this	this	PRON
ap-3493	92	4	,	,	PUNCT
ap-3493	92	5	we	we	PRON
ap-3493	92	6	remark	remark	VERB
ap-3493	92	7	that	that	SCONJ
ap-3493	92	8	the	the	DET
ap-3493	92	9	casimirs	casimir	NOUN
ap-3493	92	10	with	with	ADP
ap-3493	92	11	a	a	DET
ap-3493	92	12	⊂	⊂	PROPN
ap-3493	92	13	[	[	X
ap-3493	92	14	3	3	NUM
ap-3493	92	15	]	]	PUNCT
ap-3493	92	16	generate	generate	VERB
ap-3493	92	17	the	the	DET
ap-3493	92	18	(	(	PUNCT
ap-3493	92	19	rank	rank	NOUN
ap-3493	92	20	1	1	NUM
ap-3493	92	21	)	)	PUNCT
ap-3493	92	22	bannai	bannai	PROPN
ap-3493	92	23	-	-	PUNCT
ap-3493	92	24	ito	ito	PROPN
ap-3493	92	25	algebra	algebra	PROPN
ap-3493	92	26	.	.	PUNCT
ap-3493	93	1	let	let	VERB
ap-3493	93	2	k1	k1	NOUN
ap-3493	93	3	=	=	SYM
ap-3493	93	4	q12,k2	q12,k2	PROPN
ap-3493	93	5	=	=	NOUN
ap-3493	93	6	q23	q23	NOUN
ap-3493	93	7	and	and	CCONJ
ap-3493	93	8	k3	k3	X
ap-3493	93	9	=	=	NOUN
ap-3493	93	10	q13	q13	NOUN
ap-3493	93	11	.	.	PUNCT
ap-3493	94	1	the	the	DET
ap-3493	94	2	recurrence	recurrence	NOUN
ap-3493	94	3	relations	relation	NOUN
ap-3493	94	4	(	(	PUNCT
ap-3493	94	5	3.13	3.13	NUM
ap-3493	94	6	)	)	PUNCT
ap-3493	94	7	can	can	AUX
ap-3493	94	8	then	then	ADV
ap-3493	94	9	be	be	AUX
ap-3493	94	10	rewritten	rewrite	VERB
ap-3493	94	11	as	as	ADP
ap-3493	94	12	{	{	PUNCT
ap-3493	94	13	k1,k2	k1,k2	PROPN
ap-3493	94	14	}	}	PUNCT
ap-3493	94	15	=	=	PUNCT
ap-3493	95	1	k3	k3	PROPN
ap-3493	95	2	+	+	CCONJ
ap-3493	95	3	ω3	ω3	ADJ
ap-3493	95	4	,	,	PUNCT
ap-3493	95	5	{	{	PUNCT
ap-3493	95	6	k2,k3	k2,k3	PROPN
ap-3493	95	7	}	}	PUNCT
ap-3493	95	8	=	=	SYM
ap-3493	95	9	k1	k1	PROPN
ap-3493	95	10	+	+	X
ap-3493	95	11	ω1	ω1	PROPN
ap-3493	95	12	,	,	PUNCT
ap-3493	95	13	{	{	PUNCT
ap-3493	95	14	k3,k1	k3,k1	PROPN
ap-3493	95	15	}	}	PUNCT
ap-3493	95	16	=	=	SYM
ap-3493	95	17	k2	k2	PROPN
ap-3493	95	18	+	+	CCONJ
ap-3493	95	19	ω2	ω2	ADJ
ap-3493	95	20	,	,	PUNCT
ap-3493	95	21	(	(	PUNCT
ap-3493	95	22	3.14	3.14	NUM
ap-3493	95	23	)	)	PUNCT
ap-3493	95	24	where	where	SCONJ
ap-3493	95	25	ω1	ω1	PROPN
ap-3493	95	26	,	,	PUNCT
ap-3493	95	27	ω2	ω2	ADJ
ap-3493	95	28	,	,	PUNCT
ap-3493	95	29	ω3	ω3	PROPN
ap-3493	95	30	are	be	AUX
ap-3493	95	31	central	central	ADJ
ap-3493	95	32	elements	element	NOUN
ap-3493	95	33	given	give	VERB
ap-3493	95	34	by	by	ADP
ap-3493	95	35	ω1	ω1	PROPN
ap-3493	95	36	=	=	SYM
ap-3493	95	37	2q3q123	2q3q123	NUM
ap-3493	95	38	+	+	CCONJ
ap-3493	95	39	2q1q2	2q1q2	NUM
ap-3493	95	40	,	,	PUNCT
ap-3493	95	41	ω2	ω2	NOUN
ap-3493	95	42	=	=	SYM
ap-3493	95	43	2q1q123	2q1q123	NUM
ap-3493	95	44	+	+	CCONJ
ap-3493	95	45	2q2q3	2q2q3	NOUN
ap-3493	95	46	,	,	PUNCT
ap-3493	95	47	ω3	ω3	NOUN
ap-3493	95	48	=	=	SYM
ap-3493	95	49	2q2q123	2q2q123	NUM
ap-3493	95	50	+	+	CCONJ
ap-3493	95	51	2q1q3	2q1q3	NUM
ap-3493	95	52	.	.	PUNCT
ap-3493	96	1	(	(	PUNCT
ap-3493	96	2	3.15	3.15	NUM
ap-3493	96	3	)	)	PUNCT
ap-3493	96	4	this	this	PRON
ap-3493	96	5	corresponds	correspond	VERB
ap-3493	96	6	to	to	ADP
ap-3493	96	7	the	the	DET
ap-3493	96	8	bannai	bannai	PROPN
ap-3493	96	9	-	-	PUNCT
ap-3493	96	10	ito	ito	PROPN
ap-3493	96	11	algebra	algebra	PROPN
ap-3493	96	12	introduced	introduce	VERB
ap-3493	96	13	in	in	ADP
ap-3493	96	14	[	[	X
ap-3493	96	15	17	17	NUM
ap-3493	96	16	]	]	PUNCT
ap-3493	96	17	which	which	PRON
ap-3493	96	18	appears	appear	VERB
ap-3493	96	19	in	in	ADP
ap-3493	96	20	a	a	DET
ap-3493	96	21	corresponding	corresponding	ADJ
ap-3493	96	22	superintegrable	superintegrable	ADJ
ap-3493	96	23	model	model	NOUN
ap-3493	96	24	with	with	ADP
ap-3493	96	25	reflections	reflection	NOUN
ap-3493	96	26	on	on	ADP
ap-3493	96	27	s2	s2	NOUN
ap-3493	96	28	as	as	ADP
ap-3493	96	29	its	its	PRON
ap-3493	96	30	symmetry	symmetry	NOUN
ap-3493	96	31	algebra	algebra	NOUN
ap-3493	96	32	[	[	X
ap-3493	96	33	6	6	NUM
ap-3493	96	34	]	]	PUNCT
ap-3493	96	35	.	.	PUNCT
ap-3493	97	1	168	168	NUM
ap-3493	97	2	vol	vol	NOUN
ap-3493	97	3	.	.	PUNCT
ap-3493	98	1	56	56	NUM
ap-3493	98	2	no	no	NOUN
ap-3493	98	3	.	.	PUNCT
ap-3493	99	1	3/2016	3/2016	NUM
ap-3493	99	2	a	a	DET
ap-3493	99	3	superintegrable	superintegrable	ADJ
ap-3493	99	4	model	model	NOUN
ap-3493	99	5	with	with	ADP
ap-3493	99	6	reflections	reflection	NOUN
ap-3493	99	7	on	on	ADP
ap-3493	99	8	s3	s3	PROPN
ap-3493	99	9	4	4	NUM
ap-3493	99	10	.	.	PUNCT
ap-3493	99	11	wavefunctions	wavefunction	NOUN
ap-3493	99	12	to	to	PART
ap-3493	99	13	obtain	obtain	VERB
ap-3493	99	14	the	the	DET
ap-3493	99	15	solutions	solution	NOUN
ap-3493	99	16	to	to	ADP
ap-3493	99	17	the	the	DET
ap-3493	99	18	equation	equation	NOUN
ap-3493	99	19	hψ	hψ	X
ap-3493	99	20	=	=	PUNCT
ap-3493	99	21	λψ	λψ	SCONJ
ap-3493	99	22	let	let	VERB
ap-3493	99	23	us	we	PRON
ap-3493	99	24	first	first	ADV
ap-3493	99	25	introduce	introduce	VERB
ap-3493	99	26	the	the	DET
ap-3493	99	27	gauge	gauge	ADJ
ap-3493	99	28	transformation	transformation	NOUN
ap-3493	99	29	z	z	PROPN
ap-3493	99	30	→	→	SYM
ap-3493	99	31	z̃	z̃	PROPN
ap-3493	99	32	≡	≡	PROPN
ap-3493	99	33	g(~s)−1zg(~s	g(~s)−1zg(~s	NOUN
ap-3493	99	34	)	)	PUNCT
ap-3493	99	35	,	,	PUNCT
ap-3493	99	36	g(~s	g(~s	X
ap-3493	99	37	)	)	PUNCT
ap-3493	100	1	=	=	SYM
ap-3493	100	2	4∏	4∏	NUM
ap-3493	101	1	i=1	i=1	NUM
ap-3493	101	2	|si|µi	|si|µi	NOUN
ap-3493	101	3	,	,	PUNCT
ap-3493	101	4	(	(	PUNCT
ap-3493	101	5	4.1	4.1	NUM
ap-3493	101	6	)	)	PUNCT
ap-3493	101	7	where	where	SCONJ
ap-3493	101	8	z	z	NOUN
ap-3493	101	9	is	be	AUX
ap-3493	101	10	any	any	DET
ap-3493	101	11	operator	operator	NOUN
ap-3493	101	12	and	and	CCONJ
ap-3493	101	13	~s	~s	NUM
ap-3493	101	14	≡	≡	PROPN
ap-3493	101	15	(	(	PUNCT
ap-3493	101	16	s1	s1	PROPN
ap-3493	101	17	,	,	PUNCT
ap-3493	101	18	s2	s2	PROPN
ap-3493	101	19	,	,	PUNCT
ap-3493	101	20	s3	s3	PROPN
ap-3493	101	21	,	,	PUNCT
ap-3493	101	22	s4	s4	PROPN
ap-3493	101	23	)	)	PUNCT
ap-3493	101	24	.	.	PUNCT
ap-3493	102	1	under	under	ADP
ap-3493	102	2	this	this	DET
ap-3493	102	3	transformation	transformation	NOUN
ap-3493	102	4	,	,	PUNCT
ap-3493	102	5	the	the	DET
ap-3493	102	6	generators	generator	NOUN
ap-3493	102	7	of	of	ADP
ap-3493	102	8	osp(1|2	osp(1|2	PROPN
ap-3493	102	9	)	)	PUNCT
ap-3493	102	10	in	in	ADP
ap-3493	102	11	the	the	DET
ap-3493	102	12	realization	realization	NOUN
ap-3493	102	13	(	(	PUNCT
ap-3493	102	14	3.2	3.2	NUM
ap-3493	102	15	)	)	PUNCT
ap-3493	102	16	become	become	VERB
ap-3493	102	17	d̃i	d̃i	ADJ
ap-3493	102	18	=	=	PUNCT
ap-3493	102	19	∂si	∂si	PROPN
ap-3493	103	1	+	+	CCONJ
ap-3493	103	2	µi	µi	PROPN
ap-3493	103	3	si	si	PROPN
ap-3493	103	4	(	(	PUNCT
ap-3493	103	5	1−ri	1−ri	NUM
ap-3493	103	6	)	)	PUNCT
ap-3493	103	7	,	,	PUNCT
ap-3493	103	8	d̃2	d̃2	PROPN
ap-3493	103	9	i	i	PRON
ap-3493	103	10	=	=	NOUN
ap-3493	103	11	d̃id̃i	d̃id̃i	PROPN
ap-3493	103	12	,	,	PUNCT
ap-3493	103	13	x̃i	x̃i	PUNCT
ap-3493	104	1	=	=	PUNCT
ap-3493	104	2	xi	xi	PROPN
ap-3493	104	3	=	=	SYM
ap-3493	104	4	si	si	X
ap-3493	104	5	,	,	PUNCT
ap-3493	104	6	|x̃i|2	|x̃i|2	NOUN
ap-3493	104	7	=	=	SYM
ap-3493	104	8	s2	s2	PROPN
ap-3493	104	9	i	i	PRON
ap-3493	104	10	,	,	PUNCT
ap-3493	104	11	ẽi	ẽi	X
ap-3493	104	12	=	=	PUNCT
ap-3493	104	13	si∂si	si∂si	PROPN
ap-3493	104	14	+	+	CCONJ
ap-3493	104	15	γi	γi	NOUN
ap-3493	104	16	,	,	PUNCT
ap-3493	104	17	r̃i	r̃i	NOUN
ap-3493	104	18	=	=	SYM
ap-3493	104	19	ri	ri	PROPN
ap-3493	104	20	,	,	PUNCT
ap-3493	104	21	s̃i	s̃i	X
ap-3493	104	22	=	=	SYM
ap-3493	104	23	−µiri	−µiri	PROPN
ap-3493	104	24	,	,	PUNCT
ap-3493	104	25	q̃i	q̃i	VERB
ap-3493	104	26	=	=	PUNCT
ap-3493	104	27	µi	µi	PROPN
ap-3493	104	28	,	,	PUNCT
ap-3493	104	29	(	(	PUNCT
ap-3493	104	30	4.2	4.2	NUM
ap-3493	104	31	)	)	PUNCT
ap-3493	104	32	where	where	SCONJ
ap-3493	104	33	γa	γa	NOUN
ap-3493	104	34	=	=	SYM
ap-3493	104	35	∑	∑	AUX
ap-3493	104	36	i∈a	i∈a	ADJ
ap-3493	104	37	(	(	PUNCT
ap-3493	104	38	µi	µi	PROPN
ap-3493	104	39	+	+	NOUN
ap-3493	104	40	1	1	NUM
ap-3493	104	41	2	2	NUM
ap-3493	104	42	)	)	PUNCT
ap-3493	104	43	.	.	PUNCT
ap-3493	105	1	(	(	PUNCT
ap-3493	105	2	4.3	4.3	NUM
ap-3493	105	3	)	)	PUNCT
ap-3493	105	4	these	these	DET
ap-3493	105	5	operators	operator	NOUN
ap-3493	105	6	also	also	ADV
ap-3493	105	7	verify	verify	VERB
ap-3493	105	8	(	(	PUNCT
ap-3493	105	9	3.1	3.1	NUM
ap-3493	105	10	)	)	PUNCT
ap-3493	105	11	and	and	CCONJ
ap-3493	105	12	correspond	correspond	VERB
ap-3493	105	13	to	to	ADP
ap-3493	105	14	the	the	DET
ap-3493	105	15	realization	realization	NOUN
ap-3493	105	16	of	of	ADP
ap-3493	105	17	osp(1|2	osp(1|2	PROPN
ap-3493	105	18	)	)	PUNCT
ap-3493	105	19	(	(	PUNCT
ap-3493	105	20	or	or	CCONJ
ap-3493	105	21	equivalently	equivalently	ADV
ap-3493	105	22	sl−1(2	sl−1(2	NOUN
ap-3493	105	23	)	)	PUNCT
ap-3493	105	24	)	)	PUNCT
ap-3493	105	25	arising	arise	VERB
ap-3493	105	26	in	in	ADP
ap-3493	105	27	the	the	DET
ap-3493	105	28	one	one	NUM
ap-3493	105	29	-	-	PUNCT
ap-3493	105	30	dimensional	dimensional	ADJ
ap-3493	105	31	parabose	parabose	NOUN
ap-3493	105	32	oscillator	oscillator	NOUN
ap-3493	105	33	[	[	X
ap-3493	105	34	2	2	NUM
ap-3493	105	35	]	]	PUNCT
ap-3493	105	36	.	.	PUNCT
ap-3493	106	1	furthermore	furthermore	ADV
ap-3493	106	2	,	,	PUNCT
ap-3493	106	3	the	the	DET
ap-3493	106	4	construction	construction	NOUN
ap-3493	106	5	(	(	PUNCT
ap-3493	106	6	3.8	3.8	NUM
ap-3493	106	7	)	)	PUNCT
ap-3493	106	8	can	can	AUX
ap-3493	106	9	be	be	AUX
ap-3493	106	10	reproduced	reproduce	VERB
ap-3493	106	11	with	with	ADP
ap-3493	106	12	this	this	DET
ap-3493	106	13	transformed	transform	VERB
ap-3493	106	14	realization	realization	NOUN
ap-3493	106	15	to	to	PART
ap-3493	106	16	obtain	obtain	VERB
ap-3493	106	17	operators	operator	NOUN
ap-3493	106	18	of	of	ADP
ap-3493	106	19	the	the	DET
ap-3493	106	20	form	form	NOUN
ap-3493	106	21	d̃a	d̃a	NOUN
ap-3493	106	22	,	,	PUNCT
ap-3493	106	23	x̃a	x̃a	PROPN
ap-3493	106	24	,	,	PUNCT
ap-3493	106	25	ẽa	ẽa	PROPN
ap-3493	106	26	,	,	PUNCT
ap-3493	106	27	s̃a	s̃a	PROPN
ap-3493	106	28	and	and	CCONJ
ap-3493	106	29	q̃a	q̃a	PROPN
ap-3493	106	30	and	and	CCONJ
ap-3493	106	31	is	be	AUX
ap-3493	106	32	trivially	trivially	ADV
ap-3493	106	33	seen	see	VERB
ap-3493	106	34	to	to	PART
ap-3493	106	35	be	be	AUX
ap-3493	106	36	equivalent	equivalent	ADJ
ap-3493	106	37	to	to	ADP
ap-3493	106	38	the	the	DET
ap-3493	106	39	gauge	gauge	ADJ
ap-3493	106	40	transformation	transformation	NOUN
ap-3493	106	41	of	of	ADP
ap-3493	106	42	the	the	DET
ap-3493	106	43	corresponding	correspond	VERB
ap-3493	106	44	operators	operator	NOUN
ap-3493	106	45	.	.	PUNCT
ap-3493	107	1	hence	hence	ADV
ap-3493	107	2	,	,	PUNCT
ap-3493	107	3	we	we	PRON
ap-3493	107	4	can	can	AUX
ap-3493	107	5	obtain	obtain	VERB
ap-3493	107	6	eigenvalues	eigenvalue	NOUN
ap-3493	107	7	and	and	CCONJ
ap-3493	107	8	eigenfunctions	eigenfunction	NOUN
ap-3493	107	9	of	of	ADP
ap-3493	107	10	h	h	NOUN
ap-3493	107	11	by	by	ADP
ap-3493	107	12	finding	find	VERB
ap-3493	107	13	eigenfunctions	eigenfunction	NOUN
ap-3493	107	14	of	of	ADP
ap-3493	107	15	s̃[4	s̃[4	PROPN
ap-3493	107	16	]	]	PUNCT
ap-3493	107	17	.	.	PUNCT
ap-3493	108	1	note	note	VERB
ap-3493	108	2	that	that	SCONJ
ap-3493	108	3	since	since	SCONJ
ap-3493	108	4	s̃[4	s̃[4	PROPN
ap-3493	108	5	]	]	PUNCT
ap-3493	108	6	commutes	commute	NOUN
ap-3493	108	7	with	with	ADP
ap-3493	108	8	p	p	NOUN
ap-3493	108	9	=	=	PUNCT
ap-3493	108	10	r1r2r3r4	r1r2r3r4	PROPN
ap-3493	108	11	,	,	PUNCT
ap-3493	108	12	this	this	PRON
ap-3493	108	13	is	be	AUX
ap-3493	108	14	equivalent	equivalent	ADJ
ap-3493	108	15	to	to	ADP
ap-3493	108	16	finding	find	VERB
ap-3493	108	17	eigenfunctions	eigenfunction	NOUN
ap-3493	108	18	of	of	ADP
ap-3493	108	19	q̃[4	q̃[4	NUM
ap-3493	108	20	]	]	PUNCT
ap-3493	108	21	.	.	PUNCT
ap-3493	109	1	we	we	PRON
ap-3493	109	2	thus	thus	ADV
ap-3493	109	3	aim	aim	VERB
ap-3493	109	4	to	to	PART
ap-3493	109	5	obtain	obtain	VERB
ap-3493	109	6	polynomial	polynomial	ADJ
ap-3493	109	7	eigenfunctions	eigenfunction	NOUN
ap-3493	109	8	of	of	ADP
ap-3493	109	9	s̃[4	s̃[4	PROPN
ap-3493	109	10	]	]	PUNCT
ap-3493	109	11	.	.	PUNCT
ap-3493	110	1	to	to	PART
ap-3493	110	2	do	do	VERB
ap-3493	110	3	so	so	ADV
ap-3493	110	4	,	,	PUNCT
ap-3493	110	5	let	let	VERB
ap-3493	110	6	us	we	PRON
ap-3493	110	7	first	first	ADJ
ap-3493	110	8	introduce	introduce	VERB
ap-3493	110	9	pm(rn	pm(rn	PROPN
ap-3493	110	10	)	)	PUNCT
ap-3493	110	11	,	,	PUNCT
ap-3493	110	12	the	the	DET
ap-3493	110	13	space	space	NOUN
ap-3493	110	14	of	of	ADP
ap-3493	110	15	homogeneous	homogeneous	ADJ
ap-3493	110	16	polynomials	polynomial	NOUN
ap-3493	110	17	of	of	ADP
ap-3493	110	18	degree	degree	NOUN
ap-3493	110	19	m	m	NOUN
ap-3493	110	20	in	in	ADP
ap-3493	110	21	the	the	DET
ap-3493	110	22	variables	variable	NOUN
ap-3493	110	23	s1	s1	NOUN
ap-3493	110	24	,	,	PUNCT
ap-3493	110	25	s2	s2	PROPN
ap-3493	110	26	,	,	PUNCT
ap-3493	110	27	.	.	PUNCT
ap-3493	110	28	.	.	PUNCT
ap-3493	111	1	.	.	PUNCT
ap-3493	112	1	,	,	PUNCT
ap-3493	112	2	sn	sn	INTJ
ap-3493	112	3	.	.	PUNCT
ap-3493	113	1	we	we	PRON
ap-3493	113	2	define	define	VERB
ap-3493	113	3	km(rn	km(rn	PROPN
ap-3493	113	4	)	)	PUNCT
ap-3493	113	5	the	the	DET
ap-3493	113	6	kernel	kernel	PROPN
ap-3493	113	7	space	space	NOUN
ap-3493	113	8	of	of	ADP
ap-3493	113	9	degree	degree	NOUN
ap-3493	113	10	m	m	PROPN
ap-3493	113	11	as	as	ADP
ap-3493	113	12	km(rn	km(rn	PROPN
ap-3493	113	13	)	)	PUNCT
ap-3493	114	1	=	=	SYM
ap-3493	115	1	ker	ker	NOUN
ap-3493	115	2	d̃[n	d̃[n	X
ap-3493	115	3	]	]	X
ap-3493	115	4	∩	∩	NOUN
ap-3493	115	5	pm(rn	pm(rn	PROPN
ap-3493	115	6	)	)	PUNCT
ap-3493	115	7	.	.	PUNCT
ap-3493	116	1	(	(	PUNCT
ap-3493	116	2	4.4	4.4	NUM
ap-3493	116	3	)	)	PUNCT
ap-3493	116	4	when	when	SCONJ
ap-3493	116	5	n	n	X
ap-3493	116	6	=	=	SYM
ap-3493	116	7	4	4	NUM
ap-3493	116	8	,	,	PUNCT
ap-3493	116	9	this	this	PRON
ap-3493	116	10	is	be	AUX
ap-3493	116	11	an	an	DET
ap-3493	116	12	eigenspace	eigenspace	NOUN
ap-3493	116	13	of	of	ADP
ap-3493	116	14	s̃[4	s̃[4	PROPN
ap-3493	116	15	]	]	PUNCT
ap-3493	116	16	.	.	PUNCT
ap-3493	117	1	indeed	indeed	ADV
ap-3493	117	2	,	,	PUNCT
ap-3493	117	3	take	take	VERB
ap-3493	117	4	ψm	ψm	ADV
ap-3493	117	5	∈	∈	PROPN
ap-3493	117	6	km(r4	km(r4	NOUN
ap-3493	117	7	)	)	PUNCT
ap-3493	117	8	and	and	CCONJ
ap-3493	117	9	compute	compute	NOUN
ap-3493	117	10	s̃[4]ψ̃m	s̃[4]ψ̃m	NOUN
ap-3493	117	11	=	=	PROPN
ap-3493	117	12	1	1	NUM
ap-3493	117	13	2(d̃[4]x̃[4	2(d̃[4]x̃[4	NUM
ap-3493	117	14	]	]	PUNCT
ap-3493	118	1	−	−	PROPN
ap-3493	119	1	x̃[4]d̃[4	x̃[4]d̃[4	PROPN
ap-3493	119	2	]	]	PUNCT
ap-3493	119	3	−	−	PUNCT
ap-3493	119	4	1)ψ̃m	1)ψ̃m	NOUN
ap-3493	119	5	=	=	NOUN
ap-3493	119	6	1	1	NUM
ap-3493	119	7	2(d̃[4]x̃[4	2(d̃[4]x̃[4	NUM
ap-3493	119	8	]	]	PUNCT
ap-3493	119	9	−	−	NUM
ap-3493	119	10	1)ψ̃m	1)ψ̃m	NOUN
ap-3493	119	11	=	=	NOUN
ap-3493	119	12	1	1	NUM
ap-3493	119	13	2(d̃[4]x̃[4	2(d̃[4]x̃[4	NUM
ap-3493	119	14	]	]	PUNCT
ap-3493	120	1	+	+	CCONJ
ap-3493	120	2	x̃[4]d̃[4	x̃[4]d̃[4	NUM
ap-3493	120	3	]	]	X
ap-3493	120	4	−	−	PUNCT
ap-3493	120	5	1)ψ̃m	1)ψ̃m	NUM
ap-3493	120	6	=	=	NOUN
ap-3493	120	7	1	1	NUM
ap-3493	120	8	2	2	NUM
ap-3493	120	9	(	(	PUNCT
ap-3493	120	10	{	{	PUNCT
ap-3493	120	11	x̃[4	x̃[4	X
ap-3493	120	12	]	]	X
ap-3493	120	13	,	,	PUNCT
ap-3493	120	14	d̃[4	d̃[4	PROPN
ap-3493	120	15	]	]	X
ap-3493	120	16	}	}	PUNCT
ap-3493	120	17	−	−	PROPN
ap-3493	120	18	1	1	X
ap-3493	120	19	)	)	PUNCT
ap-3493	120	20	ψ̃m	ψ̃m	NOUN
ap-3493	120	21	=	=	NOUN
ap-3493	120	22	1	1	NUM
ap-3493	120	23	2(2ẽ[4	2(2ẽ[4	NUM
ap-3493	120	24	]	]	SYM
ap-3493	120	25	−	−	PROPN
ap-3493	120	26	1)ψ̃m	1)ψ̃m	NUM
ap-3493	120	27	=	=	SYM
ap-3493	120	28	(	(	PUNCT
ap-3493	120	29	4∑	4∑	NOUN
ap-3493	120	30	i=1	i=1	PROPN
ap-3493	120	31	si∂si	si∂si	PROPN
ap-3493	120	32	+	+	NUM
ap-3493	120	33	γ[4	γ[4	X
ap-3493	120	34	]	]	PUNCT
ap-3493	120	35	−	−	PROPN
ap-3493	120	36	1	1	NUM
ap-3493	120	37	2	2	NUM
ap-3493	120	38	)	)	PUNCT
ap-3493	120	39	ψ̃m	ψ̃m	NOUN
ap-3493	120	40	,	,	PUNCT
ap-3493	120	41	(	(	PUNCT
ap-3493	120	42	4.5	4.5	NUM
ap-3493	120	43	)	)	PUNCT
ap-3493	120	44	where	where	SCONJ
ap-3493	120	45	we	we	PRON
ap-3493	120	46	used	use	VERB
ap-3493	120	47	the	the	DET
ap-3493	120	48	property	property	NOUN
ap-3493	120	49	d̃[4]ψ̃m	d̃[4]ψ̃m	NOUN
ap-3493	120	50	=	=	SYM
ap-3493	120	51	0	0	PUNCT
ap-3493	120	52	and	and	CCONJ
ap-3493	120	53	the	the	DET
ap-3493	120	54	commutation	commutation	NOUN
ap-3493	120	55	relations	relation	NOUN
ap-3493	120	56	(	(	PUNCT
ap-3493	120	57	3.1	3.1	NUM
ap-3493	120	58	)	)	PUNCT
ap-3493	120	59	.	.	PUNCT
ap-3493	121	1	since	since	SCONJ
ap-3493	121	2	ψ̃m	ψ̃m	NOUN
ap-3493	121	3	is	be	AUX
ap-3493	121	4	a	a	DET
ap-3493	121	5	homogeneous	homogeneous	ADJ
ap-3493	121	6	polynomial	polynomial	NOUN
ap-3493	121	7	of	of	ADP
ap-3493	121	8	degree	degree	NOUN
ap-3493	121	9	m	m	NOUN
ap-3493	121	10	,	,	PUNCT
ap-3493	121	11	it	it	PRON
ap-3493	121	12	is	be	AUX
ap-3493	121	13	an	an	DET
ap-3493	121	14	eigenfunction	eigenfunction	NOUN
ap-3493	121	15	of	of	ADP
ap-3493	121	16	the	the	DET
ap-3493	121	17	euler	euler	NOUN
ap-3493	121	18	operator	operator	NOUN
ap-3493	121	19	:	:	PUNCT
ap-3493	121	20	∑4	∑4	PROPN
ap-3493	122	1	i=1	i=1	PROPN
ap-3493	122	2	si∂si	si∂si	PROPN
ap-3493	122	3	ψ̃m	ψ̃m	X
ap-3493	122	4	=	=	PUNCT
ap-3493	122	5	mψ̃m	mψ̃m	PROPN
ap-3493	122	6	.	.	PUNCT
ap-3493	123	1	this	this	PRON
ap-3493	123	2	implies	imply	VERB
ap-3493	123	3	s̃[4]ψ̃m	s̃[4]ψ̃m	NOUN
ap-3493	123	4	=	=	SYM
ap-3493	123	5	(	(	PUNCT
ap-3493	123	6	m+	m+	NUM
ap-3493	123	7	γ[4	γ[4	NOUN
ap-3493	123	8	]	]	PUNCT
ap-3493	123	9	−	−	PROPN
ap-3493	123	10	1	1	NUM
ap-3493	123	11	2	2	NUM
ap-3493	123	12	)	)	PUNCT
ap-3493	123	13	ψ̃m	ψ̃m	NOUN
ap-3493	123	14	(	(	PUNCT
ap-3493	123	15	4.6	4.6	NUM
ap-3493	123	16	)	)	PUNCT
ap-3493	123	17	and	and	CCONJ
ap-3493	123	18	shows	show	VERB
ap-3493	123	19	that	that	SCONJ
ap-3493	123	20	km(r4	km(r4	NOUN
ap-3493	123	21	)	)	PUNCT
ap-3493	123	22	is	be	AUX
ap-3493	123	23	an	an	DET
ap-3493	123	24	eigenspace	eigenspace	NOUN
ap-3493	123	25	of	of	ADP
ap-3493	123	26	s̃[4	s̃[4	PROPN
ap-3493	123	27	]	]	PUNCT
ap-3493	123	28	.	.	PUNCT
ap-3493	124	1	we	we	PRON
ap-3493	124	2	use	use	VERB
ap-3493	124	3	two	two	NUM
ap-3493	124	4	results	result	NOUN
ap-3493	124	5	in	in	ADP
ap-3493	124	6	order	order	NOUN
ap-3493	124	7	to	to	PART
ap-3493	124	8	construct	construct	VERB
ap-3493	124	9	explicitly	explicitly	ADV
ap-3493	124	10	the	the	DET
ap-3493	124	11	eigenfunctions	eigenfunction	NOUN
ap-3493	124	12	.	.	PUNCT
ap-3493	125	1	first	first	ADV
ap-3493	125	2	,	,	PUNCT
ap-3493	125	3	the	the	DET
ap-3493	125	4	space	space	NOUN
ap-3493	125	5	of	of	ADP
ap-3493	125	6	homogeneous	homogeneous	ADJ
ap-3493	125	7	polynomials	polynomial	NOUN
ap-3493	125	8	pm(rn	pm(rn	PROPN
ap-3493	125	9	)	)	PUNCT
ap-3493	125	10	admits	admit	VERB
ap-3493	125	11	a	a	DET
ap-3493	125	12	decomposition	decomposition	NOUN
ap-3493	125	13	in	in	ADP
ap-3493	125	14	terms	term	NOUN
ap-3493	125	15	of	of	ADP
ap-3493	125	16	the	the	DET
ap-3493	125	17	kernel	kernel	NOUN
ap-3493	125	18	spaces	space	VERB
ap-3493	125	19	.	.	PUNCT
ap-3493	126	1	this	this	PRON
ap-3493	126	2	is	be	AUX
ap-3493	126	3	called	call	VERB
ap-3493	126	4	the	the	DET
ap-3493	126	5	fischer	fischer	NOUN
ap-3493	126	6	decomposition	decomposition	NOUN
ap-3493	126	7	and	and	CCONJ
ap-3493	126	8	can	can	AUX
ap-3493	126	9	be	be	AUX
ap-3493	126	10	cast	cast	VERB
ap-3493	126	11	as	as	ADP
ap-3493	126	12	pm(rn	pm(rn	PROPN
ap-3493	126	13	)	)	PUNCT
ap-3493	127	1	=	=	PUNCT
ap-3493	127	2	m⊕	m⊕	X
ap-3493	127	3	j=0	j=0	VERB
ap-3493	127	4	x̃j[n]km−j(r	x̃j[n]km−j(r	PROPN
ap-3493	127	5	n	n	CCONJ
ap-3493	127	6	)	)	PUNCT
ap-3493	127	7	.	.	PUNCT
ap-3493	128	1	(	(	PUNCT
ap-3493	128	2	4.7	4.7	NUM
ap-3493	128	3	)	)	PUNCT
ap-3493	128	4	second	second	ADJ
ap-3493	128	5	,	,	PUNCT
ap-3493	128	6	we	we	PRON
ap-3493	128	7	use	use	VERB
ap-3493	128	8	the	the	DET
ap-3493	128	9	cauchy	cauchy	PROPN
ap-3493	128	10	-	-	PUNCT
ap-3493	128	11	kovalevskaia	kovalevskaia	PROPN
ap-3493	128	12	isomorphism	isomorphism	PROPN
ap-3493	128	13	(	(	PUNCT
ap-3493	128	14	ck	ck	NOUN
ap-3493	128	15	-	-	PUNCT
ap-3493	128	16	map	map	NOUN
ap-3493	128	17	)	)	PUNCT
ap-3493	128	18	between	between	ADP
ap-3493	128	19	the	the	DET
ap-3493	128	20	space	space	NOUN
ap-3493	128	21	of	of	ADP
ap-3493	128	22	m	m	PROPN
ap-3493	128	23	-	-	ADJ
ap-3493	128	24	homogeneous	homogeneous	ADJ
ap-3493	128	25	polynomials	polynomial	NOUN
ap-3493	128	26	in	in	ADP
ap-3493	128	27	n−	n−	NOUN
ap-3493	128	28	1	1	NUM
ap-3493	128	29	variables	variable	NOUN
ap-3493	128	30	and	and	CCONJ
ap-3493	128	31	the	the	DET
ap-3493	128	32	kernel	kernel	PROPN
ap-3493	128	33	space	space	NOUN
ap-3493	128	34	of	of	ADP
ap-3493	128	35	degree	degree	NOUN
ap-3493	128	36	m	m	NOUN
ap-3493	128	37	in	in	ADP
ap-3493	128	38	n	n	PRON
ap-3493	128	39	variables	variable	NOUN
ap-3493	128	40	:	:	PUNCT
ap-3493	128	41	ckµn	ckµn	PROPN
ap-3493	128	42	sn	sn	NOUN
ap-3493	128	43	:	:	PUNCT
ap-3493	128	44	pm(rn−1)→	pm(rn−1)→	NOUN
ap-3493	128	45	km(rn	km(rn	PROPN
ap-3493	128	46	)	)	PUNCT
ap-3493	128	47	.	.	PUNCT
ap-3493	129	1	(	(	PUNCT
ap-3493	129	2	4.8	4.8	NUM
ap-3493	129	3	)	)	PUNCT
ap-3493	129	4	one	one	NOUN
ap-3493	129	5	can	can	AUX
ap-3493	129	6	compute	compute	VERB
ap-3493	129	7	the	the	DET
ap-3493	129	8	ck	ck	NOUN
ap-3493	129	9	-	-	PUNCT
ap-3493	129	10	map	map	NOUN
ap-3493	129	11	explicitly	explicitly	ADV
ap-3493	129	12	.	.	PUNCT
ap-3493	130	1	to	to	PART
ap-3493	130	2	compute	compute	VERB
ap-3493	130	3	ckµ4	ckµ4	PROPN
ap-3493	130	4	s4	s4	PROPN
ap-3493	130	5	,	,	PUNCT
ap-3493	130	6	take	take	VERB
ap-3493	130	7	p(s1	p(s1	NOUN
ap-3493	130	8	,	,	PUNCT
ap-3493	130	9	s2	s2	PROPN
ap-3493	130	10	,	,	PUNCT
ap-3493	130	11	s3	s3	PROPN
ap-3493	130	12	)	)	PUNCT
ap-3493	130	13	∈	∈	PROPN
ap-3493	130	14	pm(r3	pm(r3	NOUN
ap-3493	130	15	)	)	PUNCT
ap-3493	130	16	and	and	CCONJ
ap-3493	130	17	let	let	VERB
ap-3493	130	18	ckµ4	ckµ4	PROPN
ap-3493	130	19	s4	s4	PROPN
ap-3493	130	20	[	[	PUNCT
ap-3493	130	21	p(s1	p(s1	NOUN
ap-3493	130	22	,	,	PUNCT
ap-3493	130	23	s2	s2	NOUN
ap-3493	130	24	,	,	PUNCT
ap-3493	130	25	s3	s3	PROPN
ap-3493	130	26	)	)	PUNCT
ap-3493	130	27	]	]	PUNCT
ap-3493	131	1	=	=	PUNCT
ap-3493	131	2	m∑	m∑	NOUN
ap-3493	131	3	α=0	α=0	PROPN
ap-3493	131	4	sα4	sα4	VERB
ap-3493	131	5	pα(s1	pα(s1	PROPN
ap-3493	131	6	,	,	PUNCT
ap-3493	131	7	s2	s2	PROPN
ap-3493	131	8	,	,	PUNCT
ap-3493	131	9	s3	s3	PROPN
ap-3493	131	10	)	)	PUNCT
ap-3493	131	11	,	,	PUNCT
ap-3493	131	12	(	(	PUNCT
ap-3493	131	13	4.9	4.9	NUM
ap-3493	131	14	)	)	PUNCT
ap-3493	131	15	169	169	NUM
ap-3493	131	16	hendrik	hendrik	PROPN
ap-3493	131	17	de	de	X
ap-3493	131	18	bie	bie	PROPN
ap-3493	131	19	,	,	PUNCT
ap-3493	131	20	vincent	vincent	PROPN
ap-3493	131	21	x.	x.	PROPN
ap-3493	131	22	genest	genest	PROPN
ap-3493	131	23	,	,	PUNCT
ap-3493	131	24	jean	jean	PROPN
ap-3493	131	25	-	-	PUNCT
ap-3493	131	26	michel	michel	PROPN
ap-3493	131	27	lemay	lemay	PROPN
ap-3493	131	28	,	,	PUNCT
ap-3493	131	29	luc	luc	PROPN
ap-3493	131	30	vinet	vinet	PROPN
ap-3493	131	31	acta	acta	PROPN
ap-3493	131	32	polytechnica	polytechnica	PROPN
ap-3493	131	33	where	where	SCONJ
ap-3493	131	34	pα(s1	pα(s1	PROPN
ap-3493	131	35	,	,	PUNCT
ap-3493	131	36	s2	s2	PROPN
ap-3493	131	37	,	,	PUNCT
ap-3493	131	38	s3	s3	PROPN
ap-3493	131	39	)	)	PUNCT
ap-3493	131	40	∈	∈	PROPN
ap-3493	131	41	pm−α(r3	pm−α(r3	NOUN
ap-3493	131	42	)	)	PUNCT
ap-3493	131	43	and	and	CCONJ
ap-3493	131	44	p0(s1	p0(s1	PRON
ap-3493	131	45	,	,	PUNCT
ap-3493	131	46	s2	s2	PROPN
ap-3493	131	47	,	,	PUNCT
ap-3493	131	48	s3	s3	PROPN
ap-3493	131	49	)	)	PUNCT
ap-3493	131	50	≡	≡	PROPN
ap-3493	131	51	p(s1	p(s1	NOUN
ap-3493	131	52	,	,	PUNCT
ap-3493	131	53	s2	s2	PROPN
ap-3493	131	54	,	,	PUNCT
ap-3493	131	55	s3	s3	PROPN
ap-3493	131	56	)	)	PUNCT
ap-3493	131	57	.	.	PUNCT
ap-3493	132	1	demand	demand	NOUN
ap-3493	132	2	that	that	PRON
ap-3493	132	3	d̃[4	d̃[4	PROPN
ap-3493	132	4	]	]	PUNCT
ap-3493	132	5	m∑	m∑	CCONJ
ap-3493	132	6	α=0	α=0	PRON
ap-3493	132	7	sα4	sα4	VERB
ap-3493	132	8	pα(s1	pα(s1	PROPN
ap-3493	132	9	,	,	PUNCT
ap-3493	132	10	s2	s2	PROPN
ap-3493	132	11	,	,	PUNCT
ap-3493	132	12	s3	s3	PROPN
ap-3493	132	13	)	)	PUNCT
ap-3493	132	14	=	=	SYM
ap-3493	132	15	0	0	PUNCT
ap-3493	133	1	(	(	PUNCT
ap-3493	133	2	4.10	4.10	NUM
ap-3493	133	3	)	)	PUNCT
ap-3493	133	4	to	to	PART
ap-3493	133	5	fix	fix	VERB
ap-3493	133	6	and	and	CCONJ
ap-3493	133	7	compute	compute	VERB
ap-3493	133	8	the	the	DET
ap-3493	133	9	coefficients	coefficient	NOUN
ap-3493	133	10	pα(s1	pα(s1	PROPN
ap-3493	133	11	,	,	PUNCT
ap-3493	133	12	s2	s2	PROPN
ap-3493	133	13	,	,	PUNCT
ap-3493	133	14	s3	s3	PROPN
ap-3493	133	15	)	)	PUNCT
ap-3493	133	16	.	.	PUNCT
ap-3493	134	1	a	a	DET
ap-3493	134	2	straightforward	straightforward	ADJ
ap-3493	134	3	calculation	calculation	NOUN
ap-3493	134	4	yields	yield	VERB
ap-3493	134	5	ckµ4	ckµ4	PROPN
ap-3493	134	6	s4	s4	PROPN
ap-3493	134	7	=	=	PUNCT
ap-3493	135	1	∞∑	∞∑	NUM
ap-3493	135	2	i=0	i=0	PROPN
ap-3493	135	3	(	(	PUNCT
ap-3493	135	4	−1)i(s4)2i	−1)i(s4)2i	NOUN
ap-3493	135	5	i!(γ4)i(2)2i	i!(γ4)i(2)2i	PROPN
ap-3493	135	6	d̃	d̃	PROPN
ap-3493	135	7	2i	2i	NOUN
ap-3493	135	8	[	[	X
ap-3493	135	9	4	4	X
ap-3493	135	10	]	]	X
ap-3493	135	11	+	+	CCONJ
ap-3493	135	12	∞∑	∞∑	PROPN
ap-3493	135	13	i=0	i=0	PROPN
ap-3493	135	14	(	(	PUNCT
ap-3493	135	15	−1)i+1(s4)2i+1	−1)i+1(s4)2i+1	INTJ
ap-3493	135	16	i!(γ4)i+1(2)2i+1	i!(γ4)i+1(2)2i+1	PROPN
ap-3493	135	17	d̃	d̃	PROPN
ap-3493	135	18	2i+1	2i+1	PROPN
ap-3493	136	1	[	[	X
ap-3493	136	2	4	4	X
ap-3493	136	3	]	]	PUNCT
ap-3493	136	4	,	,	PUNCT
ap-3493	136	5	(	(	PUNCT
ap-3493	136	6	4.11	4.11	NUM
ap-3493	136	7	)	)	PUNCT
ap-3493	136	8	where	where	SCONJ
ap-3493	136	9	(	(	PUNCT
ap-3493	136	10	a)i	a)i	X
ap-3493	136	11	=	=	SYM
ap-3493	136	12	a(a+	a(a+	NOUN
ap-3493	136	13	1	1	NUM
ap-3493	136	14	)	)	PUNCT
ap-3493	136	15	.	.	PUNCT
ap-3493	136	16	.	.	PUNCT
ap-3493	136	17	.	.	PUNCT
ap-3493	137	1	(	(	PUNCT
ap-3493	137	2	a+	a+	PUNCT
ap-3493	137	3	n−	n−	NOUN
ap-3493	137	4	1	1	NUM
ap-3493	137	5	)	)	PUNCT
ap-3493	137	6	denotes	denote	VERB
ap-3493	137	7	the	the	DET
ap-3493	137	8	pochhammer	pochhammer	NOUN
ap-3493	137	9	symbol	symbol	NOUN
ap-3493	137	10	.	.	PUNCT
ap-3493	138	1	similarly	similarly	ADV
ap-3493	138	2	,	,	PUNCT
ap-3493	138	3	one	one	PRON
ap-3493	138	4	obtains	obtain	VERB
ap-3493	138	5	ckµn	ckµn	NOUN
ap-3493	138	6	sn	sn	NOUN
ap-3493	138	7	=	=	PUNCT
ap-3493	139	1	∞∑	∞∑	NUM
ap-3493	139	2	i=0	i=0	PROPN
ap-3493	139	3	(	(	PUNCT
ap-3493	139	4	−1)i(sn)2i	−1)i(sn)2i	PROPN
ap-3493	139	5	i!(γn)i(2)2i	i!(γn)i(2)2i	PROPN
ap-3493	139	6	d̃	d̃	PROPN
ap-3493	139	7	2i	2i	NOUN
ap-3493	139	8	[	[	X
ap-3493	139	9	n	n	X
ap-3493	139	10	]	]	X
ap-3493	139	11	+	+	CCONJ
ap-3493	139	12	∞∑	∞∑	PROPN
ap-3493	139	13	i=0	i=0	PROPN
ap-3493	139	14	(	(	PUNCT
ap-3493	139	15	−1)i+1(sn)2i+1	−1)i+1(sn)2i+1	NOUN
ap-3493	139	16	i!(γn)i+1(2)2i+1	i!(γn)i+1(2)2i+1	NOUN
ap-3493	140	1	d̃	d̃	PROPN
ap-3493	140	2	2i+1	2i+1	PROPN
ap-3493	141	1	[	[	X
ap-3493	141	2	n	n	X
ap-3493	141	3	]	]	PUNCT
ap-3493	141	4	,	,	PUNCT
ap-3493	141	5	(	(	PUNCT
ap-3493	141	6	4.12	4.12	NUM
ap-3493	141	7	)	)	PUNCT
ap-3493	141	8	for	for	ADP
ap-3493	141	9	n	n	NOUN
ap-3493	141	10	=	=	SYM
ap-3493	141	11	2	2	NUM
ap-3493	141	12	,	,	PUNCT
ap-3493	141	13	3	3	NUM
ap-3493	141	14	,	,	PUNCT
ap-3493	141	15	4	4	NUM
ap-3493	141	16	.	.	PUNCT
ap-3493	141	17	now	now	ADV
ap-3493	141	18	,	,	PUNCT
ap-3493	141	19	iterating	iterate	VERB
ap-3493	141	20	the	the	DET
ap-3493	141	21	fischer	fischer	NOUN
ap-3493	141	22	decomposition	decomposition	NOUN
ap-3493	141	23	(	(	PUNCT
ap-3493	141	24	4.7	4.7	NUM
ap-3493	141	25	)	)	PUNCT
ap-3493	141	26	and	and	CCONJ
ap-3493	141	27	the	the	DET
ap-3493	141	28	ck	ck	NOUN
ap-3493	141	29	-	-	PUNCT
ap-3493	141	30	map	map	NOUN
ap-3493	141	31	(	(	PUNCT
ap-3493	141	32	4.8	4.8	NUM
ap-3493	141	33	)	)	PUNCT
ap-3493	141	34	,	,	PUNCT
ap-3493	141	35	the	the	DET
ap-3493	141	36	eigenspace	eigenspace	PROPN
ap-3493	141	37	km(r4	km(r4	NOUN
ap-3493	141	38	)	)	PUNCT
ap-3493	141	39	can	can	AUX
ap-3493	141	40	be	be	AUX
ap-3493	141	41	expressed	express	VERB
ap-3493	141	42	as	as	ADP
ap-3493	141	43	km(r4	km(r4	NOUN
ap-3493	141	44	)	)	PUNCT
ap-3493	141	45	∼=	∼=	PART
ap-3493	141	46	ckµ4	ckµ4	NOUN
ap-3493	141	47	s4	s4	PROPN
ap-3493	141	48	[	[	PUNCT
ap-3493	141	49	m⊕	m⊕	PRON
ap-3493	141	50	j2=0	j2=0	PUNCT
ap-3493	141	51	x̃m−j2	x̃m−j2	PUNCT
ap-3493	142	1	[	[	X
ap-3493	142	2	3	3	X
ap-3493	142	3	]	]	X
ap-3493	142	4	ckµ3	ckµ3	PROPN
ap-3493	142	5	s3	s3	PROPN
ap-3493	142	6	[	[	PUNCT
ap-3493	142	7	j2⊕	j2⊕	PROPN
ap-3493	142	8	j1=0	j1=0	PROPN
ap-3493	142	9	x̃j2−j1	x̃j2−j1	PUNCT
ap-3493	143	1	[	[	X
ap-3493	143	2	2	2	X
ap-3493	143	3	]	]	PUNCT
ap-3493	143	4	ckµ2	ckµ2	PROPN
ap-3493	143	5	s2	s2	PROPN
ap-3493	143	6	[	[	PUNCT
ap-3493	143	7	pj1(r	pj1(r	NOUN
ap-3493	143	8	)	)	PUNCT
ap-3493	143	9	]	]	PUNCT
ap-3493	144	1	]	]	X
ap-3493	144	2	]	]	PUNCT
ap-3493	144	3	.	.	PUNCT
ap-3493	145	1	(	(	PUNCT
ap-3493	145	2	4.13	4.13	X
ap-3493	145	3	)	)	PUNCT
ap-3493	145	4	this	this	PRON
ap-3493	145	5	means	mean	VERB
ap-3493	145	6	that	that	SCONJ
ap-3493	145	7	we	we	PRON
ap-3493	145	8	can	can	AUX
ap-3493	145	9	explicitly	explicitly	ADV
ap-3493	145	10	construct	construct	VERB
ap-3493	145	11	a	a	DET
ap-3493	145	12	basis	basis	NOUN
ap-3493	145	13	of	of	ADP
ap-3493	145	14	eigenfunctions	eigenfunction	NOUN
ap-3493	145	15	{	{	PUNCT
ap-3493	145	16	ψ̃(m	ψ̃(m	PROPN
ap-3493	145	17	)	)	PUNCT
ap-3493	145	18	j1,j2,j3	j1,j2,j3	PROPN
ap-3493	145	19	(	(	PUNCT
ap-3493	145	20	~s)}j1+j2+j3	~s)}j1+j2+j3	NOUN
ap-3493	145	21	=	=	SYM
ap-3493	145	22	m	m	NOUN
ap-3493	145	23	of	of	ADP
ap-3493	145	24	km(r4	km(r4	NOUN
ap-3493	145	25	)	)	PUNCT
ap-3493	145	26	with	with	ADP
ap-3493	145	27	ψ̃	ψ̃	PROPN
ap-3493	145	28	(	(	PUNCT
ap-3493	145	29	m	m	NOUN
ap-3493	145	30	)	)	PUNCT
ap-3493	145	31	j1,j2,j3	j1,j2,j3	PROPN
ap-3493	145	32	(	(	PUNCT
ap-3493	145	33	~s	~s	NUM
ap-3493	145	34	)	)	PUNCT
ap-3493	145	35	=	=	SYM
ap-3493	145	36	ckµ4	ckµ4	PROPN
ap-3493	145	37	s4	s4	PROPN
ap-3493	145	38	[	[	PUNCT
ap-3493	145	39	x̃j3	x̃j3	PROPN
ap-3493	146	1	[	[	X
ap-3493	146	2	3]ckµ3	3]ckµ3	PROPN
ap-3493	146	3	s3	s3	PROPN
ap-3493	146	4	[	[	PUNCT
ap-3493	146	5	x̃j2	x̃j2	PROPN
ap-3493	147	1	[	[	X
ap-3493	147	2	2]ckµ2	2]ckµ2	NUM
ap-3493	147	3	s2	s2	NOUN
ap-3493	147	4	[	[	X
ap-3493	147	5	sj1	sj1	NOUN
ap-3493	147	6	1	1	NUM
ap-3493	147	7	]	]	PUNCT
ap-3493	147	8	]	]	X
ap-3493	147	9	]	]	PUNCT
ap-3493	147	10	.	.	PUNCT
ap-3493	148	1	(	(	PUNCT
ap-3493	148	2	4.14	4.14	NUM
ap-3493	148	3	)	)	PUNCT
ap-3493	148	4	this	this	DET
ap-3493	148	5	calculation	calculation	NOUN
ap-3493	148	6	can	can	AUX
ap-3493	148	7	be	be	AUX
ap-3493	148	8	carried	carry	VERB
ap-3493	148	9	straightforwardly	straightforwardly	ADV
ap-3493	148	10	with	with	ADP
ap-3493	148	11	the	the	DET
ap-3493	148	12	help	help	NOUN
ap-3493	148	13	of	of	ADP
ap-3493	148	14	the	the	DET
ap-3493	148	15	identities	identity	NOUN
ap-3493	148	16	with	with	ADP
ap-3493	148	17	ψ̃m	ψ̃m	PROPN
ap-3493	148	18	∈	∈	PROPN
ap-3493	148	19	km(rn	km(rn	PROPN
ap-3493	148	20	)	)	PUNCT
ap-3493	148	21	d̃2α	d̃2α	PROPN
ap-3493	149	1	[	[	X
ap-3493	149	2	n]x̃	n]x̃	NOUN
ap-3493	149	3	2β	2β	NOUN
ap-3493	149	4	[	[	PUNCT
ap-3493	149	5	n]ψ̃m	n]ψ̃m	NOUN
ap-3493	149	6	=	=	SYM
ap-3493	149	7	22α(−β)α(1−m−	22α(−β)α(1−m−	NUM
ap-3493	149	8	β	β	NOUN
ap-3493	149	9	−	−	X
ap-3493	149	10	γ[n])αx2β−2α	γ[n])αx2β−2α	INTJ
ap-3493	150	1	[	[	X
ap-3493	150	2	n	n	CCONJ
ap-3493	150	3	]	]	PUNCT
ap-3493	150	4	ψ̃m	ψ̃m	NOUN
ap-3493	150	5	,	,	PUNCT
ap-3493	150	6	d̃2α+1	d̃2α+1	VERB
ap-3493	150	7	[	[	X
ap-3493	150	8	n	n	X
ap-3493	150	9	]	]	X
ap-3493	150	10	x̃2β	x̃2β	PUNCT
ap-3493	151	1	[	[	PUNCT
ap-3493	151	2	n]ψ̃m	n]ψ̃m	NOUN
ap-3493	151	3	=	=	SYM
ap-3493	151	4	22αβ(1−	22αβ(1−	NUM
ap-3493	151	5	β)α(1−m−	β)α(1−m−	NOUN
ap-3493	151	6	β	β	NOUN
ap-3493	151	7	−	−	PROPN
ap-3493	151	8	γ[n])αx2β−2α−1	γ[n])αx2β−2α−1	X
ap-3493	151	9	[	[	X
ap-3493	151	10	n	n	X
ap-3493	151	11	]	]	PUNCT
ap-3493	151	12	ψ̃m	ψ̃m	NOUN
ap-3493	151	13	,	,	PUNCT
ap-3493	151	14	d̃2α	d̃2α	VERB
ap-3493	151	15	[	[	X
ap-3493	151	16	n]x̃	n]x̃	NOUN
ap-3493	151	17	2β+1	2β+1	PROPN
ap-3493	152	1	[	[	X
ap-3493	152	2	n	n	X
ap-3493	152	3	]	]	X
ap-3493	152	4	ψ̃m	ψ̃m	X
ap-3493	153	1	=	=	SYM
ap-3493	153	2	22α(−β)α(−m−	22α(−β)α(−m−	NUM
ap-3493	153	3	β	β	SYM
ap-3493	154	1	−	−	NOUN
ap-3493	154	2	γ[n])αx2β+1−2α	γ[n])αx2β+1−2α	PROPN
ap-3493	155	1	[	[	X
ap-3493	155	2	n	n	CCONJ
ap-3493	155	3	]	]	PUNCT
ap-3493	155	4	ψ̃m	ψ̃m	NOUN
ap-3493	155	5	,	,	PUNCT
ap-3493	155	6	d̃2α+1	d̃2α+1	VERB
ap-3493	155	7	[	[	X
ap-3493	155	8	n	n	X
ap-3493	155	9	]	]	X
ap-3493	155	10	x̃2β+1	x̃2β+1	PROPN
ap-3493	156	1	[	[	X
ap-3493	156	2	n	n	X
ap-3493	156	3	]	]	X
ap-3493	156	4	ψ̃m	ψ̃m	X
ap-3493	157	1	=	=	NOUN
ap-3493	157	2	22α+1(−β)α(m+	22α+1(−β)α(m+	NUM
ap-3493	157	3	β	β	NOUN
ap-3493	157	4	+	+	CCONJ
ap-3493	157	5	γ[n])(1−m−	γ[n])(1−m−	NOUN
ap-3493	158	1	β	β	NOUN
ap-3493	158	2	−	−	X
ap-3493	159	1	γ[n])αx2β−2α	γ[n])αx2β−2α	INTJ
ap-3493	160	1	[	[	X
ap-3493	160	2	n	n	CCONJ
ap-3493	160	3	]	]	PUNCT
ap-3493	160	4	ψ̃	ψ̃	NOUN
ap-3493	160	5	,	,	PUNCT
ap-3493	160	6	(	(	PUNCT
ap-3493	160	7	4.15	4.15	NUM
ap-3493	160	8	)	)	PUNCT
ap-3493	160	9	which	which	PRON
ap-3493	160	10	follows	follow	VERB
ap-3493	160	11	from	from	ADP
ap-3493	160	12	(	(	PUNCT
ap-3493	160	13	3.1	3.1	NUM
ap-3493	160	14	)	)	PUNCT
ap-3493	160	15	.	.	PUNCT
ap-3493	161	1	the	the	DET
ap-3493	161	2	result	result	NOUN
ap-3493	161	3	can	can	AUX
ap-3493	161	4	be	be	AUX
ap-3493	161	5	presented	present	VERB
ap-3493	161	6	in	in	ADP
ap-3493	161	7	terms	term	NOUN
ap-3493	161	8	of	of	ADP
ap-3493	161	9	the	the	DET
ap-3493	161	10	jacobi	jacobi	PROPN
ap-3493	161	11	polynomials	polynomials	PROPN
ap-3493	161	12	p	p	PROPN
ap-3493	161	13	(	(	PUNCT
ap-3493	161	14	α	α	X
ap-3493	161	15	,	,	PUNCT
ap-3493	161	16	β	β	NOUN
ap-3493	161	17	)	)	PUNCT
ap-3493	161	18	n	n	PROPN
ap-3493	161	19	(	(	PUNCT
ap-3493	161	20	x	x	NOUN
ap-3493	161	21	)	)	PUNCT
ap-3493	161	22	,	,	PUNCT
ap-3493	161	23	defined	define	VERB
ap-3493	161	24	as	as	ADP
ap-3493	161	25	[	[	X
ap-3493	161	26	1	1	NUM
ap-3493	161	27	]	]	X
ap-3493	161	28	p	p	X
ap-3493	161	29	(	(	PUNCT
ap-3493	161	30	α	α	X
ap-3493	161	31	,	,	PUNCT
ap-3493	161	32	β	β	NOUN
ap-3493	161	33	)	)	PUNCT
ap-3493	161	34	n	n	PROPN
ap-3493	161	35	(	(	PUNCT
ap-3493	161	36	x	x	X
ap-3493	161	37	)	)	PUNCT
ap-3493	161	38	=	=	SYM
ap-3493	161	39	(	(	PUNCT
ap-3493	161	40	α+	α+	X
ap-3493	161	41	1)n	1)n	NUM
ap-3493	161	42	n	n	CCONJ
ap-3493	161	43	!	!	NOUN
ap-3493	161	44	2f1	2f1	NUM
ap-3493	161	45	(	(	PUNCT
ap-3493	161	46	−n	−n	PROPN
ap-3493	161	47	,	,	PUNCT
ap-3493	161	48	n+	n+	NUM
ap-3493	161	49	α+	α+	X
ap-3493	161	50	β	β	X
ap-3493	161	51	+	+	NOUN
ap-3493	161	52	1	1	NUM
ap-3493	161	53	α+	α+	SYM
ap-3493	161	54	1	1	NUM
ap-3493	161	55	∣∣∣1−	∣∣∣1−	NUM
ap-3493	161	56	x2	x2	PROPN
ap-3493	161	57	)	)	PUNCT
ap-3493	161	58	,	,	PUNCT
ap-3493	161	59	(	(	PUNCT
ap-3493	161	60	4.16	4.16	NUM
ap-3493	161	61	)	)	PUNCT
ap-3493	161	62	with	with	ADP
ap-3493	161	63	the	the	DET
ap-3493	161	64	help	help	NOUN
ap-3493	161	65	of	of	ADP
ap-3493	161	66	the	the	DET
ap-3493	161	67	identity	identity	NOUN
ap-3493	161	68	:	:	PUNCT
ap-3493	161	69	(	(	PUNCT
ap-3493	161	70	x+	x+	X
ap-3493	161	71	y)np	y)np	PROPN
ap-3493	161	72	(	(	PUNCT
ap-3493	161	73	α	α	NOUN
ap-3493	161	74	,	,	PUNCT
ap-3493	161	75	β	β	NOUN
ap-3493	161	76	)	)	PUNCT
ap-3493	161	77	n	n	PROPN
ap-3493	161	78	(	(	PUNCT
ap-3493	161	79	x−	x−	PROPN
ap-3493	161	80	y	y	PROPN
ap-3493	161	81	x+	x+	PROPN
ap-3493	161	82	y	y	PROPN
ap-3493	161	83	)	)	PUNCT
ap-3493	161	84	=	=	PUNCT
ap-3493	161	85	(	(	PUNCT
ap-3493	161	86	α+	α+	X
ap-3493	161	87	1)n	1)n	NUM
ap-3493	161	88	n	n	CCONJ
ap-3493	161	89	!	!	PUNCT
ap-3493	161	90	xn2f1	xn2f1	PUNCT
ap-3493	162	1	(	(	PUNCT
ap-3493	162	2	−n	−n	PROPN
ap-3493	162	3	,	,	PUNCT
ap-3493	162	4	−n−	−n−	NOUN
ap-3493	162	5	β	β	NOUN
ap-3493	162	6	α+	α+	PUNCT
ap-3493	162	7	1	1	NUM
ap-3493	162	8	∣∣∣−	∣∣∣−	PROPN
ap-3493	162	9	y	y	NOUN
ap-3493	162	10	x	x	PROPN
ap-3493	162	11	)	)	PUNCT
ap-3493	162	12	.	.	PUNCT
ap-3493	163	1	(	(	PUNCT
ap-3493	163	2	4.17	4.17	NUM
ap-3493	163	3	)	)	PUNCT
ap-3493	163	4	one	one	NOUN
ap-3493	163	5	obtains	obtain	VERB
ap-3493	163	6	ψ̃	ψ̃	PROPN
ap-3493	163	7	(	(	PUNCT
ap-3493	163	8	m	m	NOUN
ap-3493	163	9	)	)	PUNCT
ap-3493	163	10	j1,j2,j3	j1,j2,j3	PROPN
ap-3493	163	11	(	(	PUNCT
ap-3493	163	12	~s	~s	NUM
ap-3493	163	13	)	)	PUNCT
ap-3493	163	14	=	=	SYM
ap-3493	163	15	pj1,j2,j3(~s)qj1,j2(s1	pj1,j2,j3(~s)qj1,j2(s1	NOUN
ap-3493	163	16	,	,	PUNCT
ap-3493	163	17	s2	s2	PROPN
ap-3493	163	18	,	,	PUNCT
ap-3493	163	19	s3)rj1(s1	s3)rj1(s1	PROPN
ap-3493	163	20	,	,	PUNCT
ap-3493	163	21	s2	s2	PROPN
ap-3493	163	22	)	)	PUNCT
ap-3493	163	23	,	,	PUNCT
ap-3493	163	24	(	(	PUNCT
ap-3493	163	25	4.18	4.18	NUM
ap-3493	163	26	)	)	PUNCT
ap-3493	163	27	where	where	SCONJ
ap-3493	163	28	pj1,j2,j3(~s	pj1,j2,j3(~s	NOUN
ap-3493	163	29	)	)	PUNCT
ap-3493	163	30	=	=	SYM
ap-3493	164	1	c	c	X
ap-3493	164	2	!	!	PUNCT
ap-3493	165	1	(	(	PUNCT
ap-3493	165	2	γ4)c	γ4)c	NOUN
ap-3493	165	3	(	(	PUNCT
ap-3493	165	4	s2	s2	NOUN
ap-3493	165	5	1	1	NUM
ap-3493	165	6	+	+	NOUN
ap-3493	165	7	s2	s2	VERB
ap-3493	165	8	2	2	NUM
ap-3493	165	9	+	+	CCONJ
ap-3493	165	10	s2	s2	VERB
ap-3493	165	11	3	3	NUM
ap-3493	165	12	+	+	NOUN
ap-3493	165	13	s2	s2	VERB
ap-3493	165	14	4)c	4)c	NUM
ap-3493	165	15	×	×	NOUN
ap-3493	165	16	p	p	PROPN
ap-3493	165	17	(	(	PUNCT
ap-3493	165	18	γ4−1,j1+j2+γ[3]−1	γ4−1,j1+j2+γ[3]−1	PROPN
ap-3493	165	19	)	)	PUNCT
ap-3493	165	20	c	c	NOUN
ap-3493	165	21	(	(	PUNCT
ap-3493	165	22	s2	s2	PROPN
ap-3493	165	23	1+s2	1+s2	NUM
ap-3493	165	24	2+s2	2+s2	NUM
ap-3493	165	25	3−s	3−s	NUM
ap-3493	165	26	2	2	NUM
ap-3493	165	27	4	4	NUM
ap-3493	165	28	s2	s2	NOUN
ap-3493	165	29	1+s2	1+s2	NUM
ap-3493	165	30	2+s2	2+s2	NUM
ap-3493	165	31	3+s2	3+s2	NUM
ap-3493	165	32	4	4	NUM
ap-3493	165	33	)	)	PUNCT
ap-3493	165	34	−	−	PRON
ap-3493	165	35	s4x̃[3	s4x̃[3	NOUN
ap-3493	165	36	]	]	X
ap-3493	165	37	s2	s2	NOUN
ap-3493	165	38	1+s2	1+s2	NUM
ap-3493	165	39	2+s2	2+s2	NUM
ap-3493	165	40	3+s2	3+s2	NUM
ap-3493	165	41	4	4	NUM
ap-3493	165	42	p	p	NOUN
ap-3493	165	43	(	(	PUNCT
ap-3493	165	44	γ4,j1+j2+γ[3	γ4,j1+j2+γ[3	NOUN
ap-3493	165	45	]	]	PUNCT
ap-3493	165	46	)	)	PUNCT
ap-3493	165	47	c−1	c−1	PROPN
ap-3493	165	48	(	(	PUNCT
ap-3493	165	49	s2	s2	PROPN
ap-3493	165	50	1+s2	1+s2	NUM
ap-3493	165	51	2+s2	2+s2	NUM
ap-3493	165	52	3−s	3−s	NUM
ap-3493	165	53	2	2	NUM
ap-3493	165	54	4	4	NUM
ap-3493	165	55	s2	s2	NOUN
ap-3493	165	56	1+s2	1+s2	NUM
ap-3493	165	57	2+s2	2+s2	NUM
ap-3493	165	58	3+s2	3+s2	NUM
ap-3493	165	59	4	4	NUM
ap-3493	165	60	)	)	PUNCT
ap-3493	165	61	if	if	SCONJ
ap-3493	165	62	j3	j3	PROPN
ap-3493	165	63	=	=	SYM
ap-3493	165	64	2c	2c	NUM
ap-3493	165	65	,	,	PUNCT
ap-3493	165	66	x̃[3]p	x̃[3]p	PROPN
ap-3493	165	67	(	(	PUNCT
ap-3493	165	68	γ4−1,j1+j2+γ[3	γ4−1,j1+j2+γ[3	PROPN
ap-3493	165	69	]	]	X
ap-3493	165	70	)	)	PUNCT
ap-3493	165	71	c	c	NOUN
ap-3493	166	1	(	(	PUNCT
ap-3493	166	2	s2	s2	PROPN
ap-3493	166	3	1+s2	1+s2	NUM
ap-3493	166	4	2+s2	2+s2	NUM
ap-3493	166	5	3−s	3−s	NUM
ap-3493	166	6	2	2	NUM
ap-3493	166	7	4	4	NUM
ap-3493	166	8	s2	s2	NOUN
ap-3493	166	9	1+s2	1+s2	NUM
ap-3493	166	10	2+s2	2+s2	NUM
ap-3493	166	11	3+s2	3+s2	NUM
ap-3493	166	12	4	4	NUM
ap-3493	166	13	)	)	PUNCT
ap-3493	166	14	−	−	PROPN
ap-3493	166	15	s3	s3	PROPN
ap-3493	166	16	j1+j2+c+γ[3	j1+j2+c+γ[3	PROPN
ap-3493	166	17	]	]	X
ap-3493	167	1	c+γ4	c+γ4	PROPN
ap-3493	167	2	p	p	PROPN
ap-3493	167	3	(	(	PUNCT
ap-3493	167	4	γ4,j1+j2+γ[3]−1	γ4,j1+j2+γ[3]−1	X
ap-3493	167	5	)	)	PUNCT
ap-3493	167	6	c	c	PROPN
ap-3493	168	1	(	(	PUNCT
ap-3493	168	2	s2	s2	PROPN
ap-3493	168	3	1+s2	1+s2	NUM
ap-3493	168	4	2+s2	2+s2	NUM
ap-3493	168	5	3−s	3−s	NUM
ap-3493	168	6	2	2	NUM
ap-3493	168	7	4	4	NUM
ap-3493	168	8	s2	s2	NOUN
ap-3493	168	9	1+s2	1+s2	NUM
ap-3493	168	10	2+s2	2+s2	NUM
ap-3493	168	11	3+s2	3+s2	NUM
ap-3493	168	12	4	4	NUM
ap-3493	168	13	)	)	PUNCT
ap-3493	168	14	if	if	SCONJ
ap-3493	168	15	j3	j3	PROPN
ap-3493	168	16	=	=	PUNCT
ap-3493	168	17	2c+	2c+	NUM
ap-3493	168	18	1	1	NUM
ap-3493	168	19	,	,	PUNCT
ap-3493	168	20	qj1,j2(s1	qj1,j2(s1	PROPN
ap-3493	168	21	,	,	PUNCT
ap-3493	168	22	s2	s2	PROPN
ap-3493	168	23	,	,	PUNCT
ap-3493	168	24	s3	s3	PROPN
ap-3493	168	25	)	)	PUNCT
ap-3493	168	26	=	=	SYM
ap-3493	169	1	b	b	X
ap-3493	169	2	!	!	PUNCT
ap-3493	169	3	(	(	PUNCT
ap-3493	169	4	γ3)b	γ3)b	PROPN
ap-3493	169	5	(	(	PUNCT
ap-3493	169	6	s2	s2	NOUN
ap-3493	169	7	1	1	NUM
ap-3493	169	8	+	+	CCONJ
ap-3493	169	9	s2	s2	VERB
ap-3493	169	10	2	2	NUM
ap-3493	169	11	+	+	CCONJ
ap-3493	169	12	s2	s2	VERB
ap-3493	169	13	3)b	3)b	NUM
ap-3493	169	14	×	×	NOUN
ap-3493	169	15	p	p	PROPN
ap-3493	169	16	(	(	PUNCT
ap-3493	169	17	γ3−1,j1+γ[2]−1	γ3−1,j1+γ[2]−1	PROPN
ap-3493	169	18	)	)	PUNCT
ap-3493	169	19	b	b	PROPN
ap-3493	169	20	(	(	PUNCT
ap-3493	169	21	s2	s2	PROPN
ap-3493	169	22	1+s2	1+s2	NUM
ap-3493	169	23	2−s	2−s	NUM
ap-3493	169	24	2	2	NUM
ap-3493	169	25	3	3	NUM
ap-3493	169	26	s2	s2	NOUN
ap-3493	169	27	1+s2	1+s2	NUM
ap-3493	169	28	2+s2	2+s2	NUM
ap-3493	169	29	3	3	NUM
ap-3493	169	30	)	)	PUNCT
ap-3493	169	31	−	−	PROPN
ap-3493	170	1	s3x̃[2	s3x̃[2	PROPN
ap-3493	170	2	]	]	PUNCT
ap-3493	170	3	s2	s2	NOUN
ap-3493	170	4	1+s2	1+s2	NUM
ap-3493	170	5	2+s2	2+s2	NUM
ap-3493	170	6	3	3	NUM
ap-3493	170	7	p	p	NOUN
ap-3493	170	8	(	(	PUNCT
ap-3493	170	9	γ3,j1+γ[2	γ3,j1+γ[2	NOUN
ap-3493	170	10	]	]	X
ap-3493	170	11	)	)	PUNCT
ap-3493	170	12	b−1	b−1	PROPN
ap-3493	170	13	(	(	PUNCT
ap-3493	170	14	s2	s2	PROPN
ap-3493	170	15	1+s2	1+s2	NUM
ap-3493	170	16	2−s	2−s	NUM
ap-3493	170	17	2	2	NUM
ap-3493	170	18	3	3	NUM
ap-3493	170	19	s2	s2	NOUN
ap-3493	170	20	1+s2	1+s2	NUM
ap-3493	170	21	2+s2	2+s2	NUM
ap-3493	170	22	3	3	NUM
ap-3493	170	23	)	)	PUNCT
ap-3493	171	1	if	if	SCONJ
ap-3493	171	2	j2	j2	PROPN
ap-3493	171	3	=	=	SYM
ap-3493	171	4	2b	2b	NUM
ap-3493	171	5	,	,	PUNCT
ap-3493	171	6	x̃[2]p	x̃[2]p	X
ap-3493	171	7	(	(	PUNCT
ap-3493	171	8	γ3−1,j1+γ[2	γ3−1,j1+γ[2	PROPN
ap-3493	171	9	]	]	PUNCT
ap-3493	171	10	)	)	PUNCT
ap-3493	171	11	b	b	PROPN
ap-3493	171	12	(	(	PUNCT
ap-3493	171	13	s2	s2	PROPN
ap-3493	171	14	1+s2	1+s2	NUM
ap-3493	171	15	2−s	2−s	NUM
ap-3493	171	16	2	2	NUM
ap-3493	171	17	3	3	NUM
ap-3493	171	18	s2	s2	NOUN
ap-3493	171	19	1+s2	1+s2	NUM
ap-3493	171	20	2+s2	2+s2	NUM
ap-3493	171	21	3	3	NUM
ap-3493	171	22	)	)	PUNCT
ap-3493	171	23	−	−	PROPN
ap-3493	171	24	s2	s2	PROPN
ap-3493	171	25	j1+b+γ[2	j1+b+γ[2	NOUN
ap-3493	171	26	]	]	X
ap-3493	171	27	b+γ3	b+γ3	PROPN
ap-3493	171	28	p	p	X
ap-3493	171	29	(	(	PUNCT
ap-3493	171	30	γ3,j1+γ[2]−1	γ3,j1+γ[2]−1	PROPN
ap-3493	171	31	)	)	PUNCT
ap-3493	171	32	b	b	PROPN
ap-3493	171	33	(	(	PUNCT
ap-3493	171	34	s2	s2	PROPN
ap-3493	171	35	1+s2	1+s2	NUM
ap-3493	171	36	2−s	2−s	NUM
ap-3493	171	37	2	2	NUM
ap-3493	171	38	3	3	NUM
ap-3493	171	39	s2	s2	NOUN
ap-3493	171	40	1+s2	1+s2	NUM
ap-3493	171	41	2+s2	2+s2	NUM
ap-3493	171	42	3	3	NUM
ap-3493	171	43	)	)	PUNCT
ap-3493	171	44	if	if	SCONJ
ap-3493	171	45	j2	j2	PROPN
ap-3493	171	46	=	=	SYM
ap-3493	171	47	2b+	2b+	NUM
ap-3493	171	48	1	1	NUM
ap-3493	171	49	,	,	PUNCT
ap-3493	171	50	170	170	NUM
ap-3493	171	51	vol	vol	NOUN
ap-3493	171	52	.	.	PUNCT
ap-3493	172	1	56	56	NUM
ap-3493	172	2	no	no	NOUN
ap-3493	172	3	.	.	PUNCT
ap-3493	173	1	3/2016	3/2016	NUM
ap-3493	173	2	a	a	DET
ap-3493	173	3	superintegrable	superintegrable	ADJ
ap-3493	173	4	model	model	NOUN
ap-3493	173	5	with	with	ADP
ap-3493	173	6	reflections	reflection	NOUN
ap-3493	173	7	on	on	ADP
ap-3493	173	8	s3	s3	PROPN
ap-3493	173	9	rj1(s1	rj1(s1	SYM
ap-3493	173	10	,	,	PUNCT
ap-3493	173	11	s2	s2	PROPN
ap-3493	173	12	)	)	PUNCT
ap-3493	173	13	=	=	SYM
ap-3493	174	1	a	a	PRON
ap-3493	174	2	!	!	PUNCT
ap-3493	175	1	(	(	PUNCT
ap-3493	175	2	γ2)a	γ2)a	PROPN
ap-3493	175	3	(	(	PUNCT
ap-3493	175	4	s2	s2	NOUN
ap-3493	175	5	1	1	NUM
ap-3493	175	6	+	+	NUM
ap-3493	175	7	s2	s2	VERB
ap-3493	175	8	2)a	2)a	NUM
ap-3493	175	9	×	×	NOUN
ap-3493	176	1			ADJ
ap-3493	176	2	p	p	X
ap-3493	176	3	(	(	PUNCT
ap-3493	176	4	γ2−1,γ1−1	γ2−1,γ1−1	PROPN
ap-3493	176	5	)	)	PUNCT
ap-3493	176	6	a	a	DET
ap-3493	176	7	(	(	PUNCT
ap-3493	176	8	s2	s2	PROPN
ap-3493	176	9	1−s	1−s	NUM
ap-3493	176	10	2	2	NUM
ap-3493	176	11	2	2	NUM
ap-3493	176	12	s2	s2	NOUN
ap-3493	176	13	1+s2	1+s2	NUM
ap-3493	176	14	2	2	NUM
ap-3493	176	15	)	)	PUNCT
ap-3493	176	16	−	−	NOUN
ap-3493	177	1	s1s2	s1s2	PROPN
ap-3493	177	2	s2	s2	PROPN
ap-3493	177	3	1+s2	1+s2	NUM
ap-3493	177	4	2	2	NUM
ap-3493	177	5	p	p	NOUN
ap-3493	177	6	(	(	PUNCT
ap-3493	177	7	γ2,γ1	γ2,γ1	PROPN
ap-3493	177	8	)	)	PUNCT
ap-3493	177	9	a−1	a−1	PROPN
ap-3493	177	10	(	(	PUNCT
ap-3493	177	11	s2	s2	PROPN
ap-3493	177	12	1−s	1−s	NUM
ap-3493	177	13	2	2	NUM
ap-3493	177	14	2	2	NUM
ap-3493	177	15	s2	s2	NOUN
ap-3493	177	16	1+s2	1+s2	NUM
ap-3493	177	17	2	2	NUM
ap-3493	177	18	)	)	PUNCT
ap-3493	177	19	if	if	SCONJ
ap-3493	177	20	j1	j1	PROPN
ap-3493	177	21	=	=	SYM
ap-3493	177	22	2a	2a	NUM
ap-3493	177	23	,	,	PUNCT
ap-3493	177	24	s1p	s1p	PROPN
ap-3493	177	25	(	(	PUNCT
ap-3493	177	26	γ2−1,γ1	γ2−1,γ1	NOUN
ap-3493	177	27	)	)	PUNCT
ap-3493	177	28	a	a	PRON
ap-3493	177	29	(	(	PUNCT
ap-3493	177	30	s2	s2	PROPN
ap-3493	177	31	1−s	1−s	NUM
ap-3493	177	32	2	2	NUM
ap-3493	177	33	2	2	NUM
ap-3493	177	34	s2	s2	NOUN
ap-3493	177	35	1+s2	1+s2	NUM
ap-3493	177	36	2	2	NUM
ap-3493	177	37	)	)	PUNCT
ap-3493	177	38	−	−	PROPN
ap-3493	178	1	s2	s2	PROPN
ap-3493	178	2	a+γ1	a+γ1	VERB
ap-3493	178	3	a+γ2	a+γ2	PROPN
ap-3493	178	4	p	p	NOUN
ap-3493	178	5	(	(	PUNCT
ap-3493	178	6	γ2,γ1−1	γ2,γ1−1	PROPN
ap-3493	178	7	)	)	PUNCT
ap-3493	178	8	a	a	PRON
ap-3493	178	9	(	(	PUNCT
ap-3493	178	10	s2	s2	PROPN
ap-3493	178	11	1−s	1−s	NUM
ap-3493	178	12	2	2	NUM
ap-3493	178	13	2	2	NUM
ap-3493	178	14	s2	s2	NOUN
ap-3493	178	15	1+s2	1+s2	NUM
ap-3493	178	16	2	2	NUM
ap-3493	178	17	)	)	PUNCT
ap-3493	178	18	if	if	SCONJ
ap-3493	178	19	j1	j1	PROPN
ap-3493	178	20	=	=	SYM
ap-3493	178	21	2a+	2a+	NUM
ap-3493	178	22	1	1	NUM
ap-3493	178	23	.	.	PUNCT
ap-3493	178	24	note	note	VERB
ap-3493	178	25	that	that	SCONJ
ap-3493	178	26	the	the	DET
ap-3493	178	27	expressions	expression	NOUN
ap-3493	178	28	for	for	ADP
ap-3493	178	29	pj1,j2,j3(s1	pj1,j2,j3(s1	ADJ
ap-3493	178	30	,	,	PUNCT
ap-3493	178	31	s2	s2	PROPN
ap-3493	178	32	,	,	PUNCT
ap-3493	178	33	s3	s3	PROPN
ap-3493	178	34	,	,	PUNCT
ap-3493	178	35	s4	s4	PROPN
ap-3493	178	36	)	)	PUNCT
ap-3493	178	37	and	and	CCONJ
ap-3493	178	38	qj1,j2(s1	qj1,j2(s1	PROPN
ap-3493	178	39	,	,	PUNCT
ap-3493	178	40	s2	s2	PROPN
ap-3493	178	41	,	,	PUNCT
ap-3493	178	42	s3	s3	PROPN
ap-3493	178	43	)	)	PUNCT
ap-3493	178	44	contain	contain	VERB
ap-3493	178	45	the	the	DET
ap-3493	178	46	operators	operator	NOUN
ap-3493	178	47	x̃[3	x̃[3	NOUN
ap-3493	178	48	]	]	PUNCT
ap-3493	178	49	and	and	CCONJ
ap-3493	178	50	x̃[2	x̃[2	NUM
ap-3493	178	51	]	]	PUNCT
ap-3493	178	52	respectively	respectively	ADV
ap-3493	178	53	.	.	PUNCT
ap-3493	179	1	recalling	recall	VERB
ap-3493	179	2	the	the	DET
ap-3493	179	3	expressions	expression	NOUN
ap-3493	179	4	(	(	PUNCT
ap-3493	179	5	4.2	4.2	NUM
ap-3493	179	6	)	)	PUNCT
ap-3493	179	7	and	and	CCONJ
ap-3493	179	8	(	(	PUNCT
ap-3493	179	9	3.8	3.8	NUM
ap-3493	179	10	)	)	PUNCT
ap-3493	179	11	,	,	PUNCT
ap-3493	179	12	it	it	PRON
ap-3493	179	13	can	can	AUX
ap-3493	179	14	be	be	AUX
ap-3493	179	15	seen	see	VERB
ap-3493	179	16	that	that	SCONJ
ap-3493	179	17	these	these	DET
ap-3493	179	18	operators	operator	NOUN
ap-3493	179	19	only	only	ADV
ap-3493	179	20	contain	contain	VERB
ap-3493	179	21	variables	variable	NOUN
ap-3493	179	22	si	si	X
ap-3493	179	23	and	and	CCONJ
ap-3493	179	24	reflection	reflection	PROPN
ap-3493	179	25	operators	operator	NOUN
ap-3493	179	26	ri	ri	PROPN
ap-3493	179	27	.	.	PUNCT
ap-3493	180	1	these	these	DET
ap-3493	180	2	reflections	reflection	NOUN
ap-3493	180	3	conveniently	conveniently	ADV
ap-3493	180	4	account	account	VERB
ap-3493	180	5	for	for	ADP
ap-3493	180	6	signs	sign	NOUN
ap-3493	180	7	occuring	occur	VERB
ap-3493	180	8	in	in	ADP
ap-3493	180	9	the	the	DET
ap-3493	180	10	solutions	solution	NOUN
ap-3493	180	11	without	without	ADP
ap-3493	180	12	having	have	VERB
ap-3493	180	13	to	to	PART
ap-3493	180	14	give	give	VERB
ap-3493	180	15	a	a	DET
ap-3493	180	16	different	different	ADJ
ap-3493	180	17	expression	expression	NOUN
ap-3493	180	18	for	for	ADP
ap-3493	180	19	every	every	DET
ap-3493	180	20	parity	parity	NOUN
ap-3493	180	21	combination	combination	NOUN
ap-3493	180	22	of	of	ADP
ap-3493	180	23	the	the	DET
ap-3493	180	24	parameters	parameter	NOUN
ap-3493	180	25	j1	j1	PROPN
ap-3493	180	26	,	,	PUNCT
ap-3493	180	27	j2	j2	PROPN
ap-3493	180	28	and	and	CCONJ
ap-3493	180	29	j3	j3	PROPN
ap-3493	180	30	.	.	PUNCT
ap-3493	181	1	by	by	ADP
ap-3493	181	2	effecting	effect	VERB
ap-3493	181	3	the	the	DET
ap-3493	181	4	reverse	reverse	ADJ
ap-3493	181	5	gauge	gauge	NOUN
ap-3493	181	6	transformation	transformation	NOUN
ap-3493	181	7	,	,	PUNCT
ap-3493	181	8	we	we	PRON
ap-3493	181	9	thus	thus	ADV
ap-3493	181	10	obtain	obtain	VERB
ap-3493	181	11	a	a	DET
ap-3493	181	12	basis	basis	NOUN
ap-3493	181	13	for	for	ADP
ap-3493	181	14	the	the	DET
ap-3493	181	15	eigenspace	eigenspace	NOUN
ap-3493	181	16	of	of	ADP
ap-3493	181	17	the	the	DET
ap-3493	181	18	operator	operator	NOUN
ap-3493	181	19	s[4	s[4	NOUN
ap-3493	181	20	]	]	PUNCT
ap-3493	181	21	given	give	VERB
ap-3493	181	22	by	by	ADP
ap-3493	181	23	ψ	ψ	X
ap-3493	181	24	(	(	PUNCT
ap-3493	181	25	m	m	NOUN
ap-3493	181	26	)	)	PUNCT
ap-3493	181	27	j1,j2,j3	j1,j2,j3	PROPN
ap-3493	181	28	(	(	PUNCT
ap-3493	181	29	~s	~s	NUM
ap-3493	181	30	)	)	PUNCT
ap-3493	181	31	=	=	SYM
ap-3493	181	32	ψ̃	ψ̃	PROPN
ap-3493	181	33	(	(	PUNCT
ap-3493	181	34	m	m	NOUN
ap-3493	181	35	)	)	PUNCT
ap-3493	181	36	j1,j2,j3	j1,j2,j3	PROPN
ap-3493	181	37	(	(	PUNCT
ap-3493	181	38	~s)g(~s	~s)g(~s	ADJ
ap-3493	181	39	)	)	PUNCT
ap-3493	181	40	,	,	PUNCT
ap-3493	181	41	(	(	PUNCT
ap-3493	181	42	4.19	4.19	NUM
ap-3493	181	43	)	)	PUNCT
ap-3493	181	44	where	where	SCONJ
ap-3493	181	45	m	m	VERB
ap-3493	181	46	=	=	SYM
ap-3493	181	47	0	0	NUM
ap-3493	181	48	,	,	PUNCT
ap-3493	181	49	1	1	NUM
ap-3493	181	50	,	,	PUNCT
ap-3493	181	51	.	.	PUNCT
ap-3493	181	52	.	.	PUNCT
ap-3493	181	53	.	.	PUNCT
ap-3493	182	1	and	and	CCONJ
ap-3493	182	2	j1	j1	PROPN
ap-3493	182	3	+	+	CCONJ
ap-3493	182	4	j2	j2	PROPN
ap-3493	182	5	+	+	CCONJ
ap-3493	182	6	j3	j3	PROPN
ap-3493	182	7	=	=	SYM
ap-3493	182	8	m.	m.	NOUN
ap-3493	182	9	with	with	ADP
ap-3493	182	10	the	the	DET
ap-3493	182	11	help	help	NOUN
ap-3493	182	12	of	of	ADP
ap-3493	182	13	(	(	PUNCT
ap-3493	182	14	4.6	4.6	NUM
ap-3493	182	15	)	)	PUNCT
ap-3493	182	16	,	,	PUNCT
ap-3493	182	17	they	they	PRON
ap-3493	182	18	obey	obey	VERB
ap-3493	182	19	the	the	DET
ap-3493	182	20	relation	relation	NOUN
ap-3493	182	21	s[4]ψ	s[4]ψ	PROPN
ap-3493	182	22	(	(	PUNCT
ap-3493	182	23	m	m	NOUN
ap-3493	182	24	)	)	PUNCT
ap-3493	182	25	j1,j2,j3	j1,j2,j3	PROPN
ap-3493	182	26	(	(	PUNCT
ap-3493	182	27	~s	~s	NUM
ap-3493	182	28	)	)	PUNCT
ap-3493	182	29	=	=	SYM
ap-3493	182	30	(	(	PUNCT
ap-3493	182	31	m+	m+	NUM
ap-3493	182	32	γ[4	γ[4	NOUN
ap-3493	182	33	]	]	PUNCT
ap-3493	182	34	−	−	PROPN
ap-3493	182	35	1	1	NUM
ap-3493	182	36	2	2	NUM
ap-3493	182	37	)	)	PUNCT
ap-3493	182	38	ψ	ψ	X
ap-3493	182	39	(	(	PUNCT
ap-3493	182	40	m	m	NOUN
ap-3493	182	41	)	)	PUNCT
ap-3493	182	42	j1,j2,j3	j1,j2,j3	PROPN
ap-3493	182	43	(	(	PUNCT
ap-3493	182	44	~s	~s	NUM
ap-3493	182	45	)	)	PUNCT
ap-3493	182	46	.	.	PUNCT
ap-3493	183	1	(	(	PUNCT
ap-3493	183	2	4.20	4.20	NUM
ap-3493	183	3	)	)	PUNCT
ap-3493	183	4	recalling	recall	VERB
ap-3493	183	5	(	(	PUNCT
ap-3493	183	6	3.12	3.12	NUM
ap-3493	183	7	)	)	PUNCT
ap-3493	183	8	,	,	PUNCT
ap-3493	183	9	this	this	PRON
ap-3493	183	10	also	also	ADV
ap-3493	183	11	implies	imply	VERB
ap-3493	183	12	hψ	hψ	NOUN
ap-3493	183	13	(	(	PUNCT
ap-3493	183	14	m	m	NOUN
ap-3493	183	15	)	)	PUNCT
ap-3493	183	16	j1,j2,j3	j1,j2,j3	PROPN
ap-3493	183	17	(	(	PUNCT
ap-3493	183	18	~s	~s	NUM
ap-3493	183	19	)	)	PUNCT
ap-3493	183	20	=	=	SYM
ap-3493	183	21	(	(	PUNCT
ap-3493	183	22	m+	m+	NOUN
ap-3493	183	23	γ[4])(m+	γ[4])(m+	PROPN
ap-3493	183	24	γ[4	γ[4	PROPN
ap-3493	183	25	]	]	PUNCT
ap-3493	183	26	−	−	PROPN
ap-3493	183	27	2)ψ(m	2)ψ(m	NUM
ap-3493	183	28	)	)	PUNCT
ap-3493	183	29	j1,j2,j3	j1,j2,j3	PROPN
ap-3493	183	30	(	(	PUNCT
ap-3493	183	31	~s	~s	NUM
ap-3493	183	32	)	)	PUNCT
ap-3493	183	33	.	.	PUNCT
ap-3493	184	1	(	(	PUNCT
ap-3493	184	2	4.21	4.21	NUM
ap-3493	184	3	)	)	PUNCT
ap-3493	184	4	finally	finally	ADV
ap-3493	184	5	,	,	PUNCT
ap-3493	184	6	we	we	PRON
ap-3493	184	7	can	can	AUX
ap-3493	184	8	normalize	normalize	VERB
ap-3493	184	9	these	these	DET
ap-3493	184	10	eigenfunctions	eigenfunction	NOUN
ap-3493	184	11	as	as	ADP
ap-3493	184	12	ψ(m	ψ(m	NOUN
ap-3493	184	13	)	)	PUNCT
ap-3493	184	14	j1,j2,j3	j1,j2,j3	PROPN
ap-3493	184	15	(	(	PUNCT
ap-3493	184	16	~s	~s	NUM
ap-3493	184	17	)	)	PUNCT
ap-3493	184	18	=	=	SYM
ap-3493	184	19	η1η2η3√	η1η2η3√	NOUN
ap-3493	184	20	2	2	NUM
ap-3493	184	21	ψ	ψ	X
ap-3493	184	22	(	(	PUNCT
ap-3493	184	23	m	m	NOUN
ap-3493	184	24	)	)	PUNCT
ap-3493	184	25	j1,j2,j3	j1,j2,j3	PROPN
ap-3493	184	26	(	(	PUNCT
ap-3493	184	27	~s	~s	NUM
ap-3493	184	28	)	)	PUNCT
ap-3493	184	29	,	,	PUNCT
ap-3493	184	30	(	(	PUNCT
ap-3493	184	31	4.22	4.22	NUM
ap-3493	184	32	)	)	PUNCT
ap-3493	184	33	where	where	SCONJ
ap-3493	184	34	η1	η1	X
ap-3493	184	35	=	=	SYM
ap-3493	184	36	γ2	γ2	ADJ
ap-3493	184	37	√	√	NUM
ap-3493	184	38	γ(a+	γ(a+	NOUN
ap-3493	184	39	γ[2	γ[2	NOUN
ap-3493	184	40	]	]	SYM
ap-3493	184	41	)	)	PUNCT
ap-3493	184	42	a!γ(a+	a!γ(a+	NOUN
ap-3493	184	43	γ1)γ(a+	γ1)γ(a+	PROPN
ap-3493	184	44	γ2	γ2	ADJ
ap-3493	184	45	)	)	PUNCT
ap-3493	184	46	×	×	NOUN
ap-3493	184	47	{	{	PUNCT
ap-3493	184	48	1	1	NUM
ap-3493	184	49	if	if	SCONJ
ap-3493	184	50	j1	j1	PROPN
ap-3493	184	51	=	=	SYM
ap-3493	184	52	2a,√	2a,√	NUM
ap-3493	184	53	a+γ2	a+γ2	NOUN
ap-3493	184	54	a+γ1	a+γ1	VERB
ap-3493	184	55	if	if	SCONJ
ap-3493	184	56	j1	j1	PROPN
ap-3493	184	57	=	=	PUNCT
ap-3493	184	58	2a+	2a+	NUM
ap-3493	184	59	1	1	NUM
ap-3493	184	60	,	,	PUNCT
ap-3493	184	61	(	(	PUNCT
ap-3493	184	62	4.23	4.23	NUM
ap-3493	184	63	)	)	PUNCT
ap-3493	184	64	η2	η2	PROPN
ap-3493	184	65	=	=	SYM
ap-3493	184	66	γ3	γ3	NOUN
ap-3493	184	67	√	√	PROPN
ap-3493	184	68	γ(b+	γ(b+	PROPN
ap-3493	184	69	j1	j1	PROPN
ap-3493	184	70	+	+	CCONJ
ap-3493	184	71	γ[3	γ[3	NOUN
ap-3493	184	72	]	]	PUNCT
ap-3493	184	73	)	)	PUNCT
ap-3493	184	74	b!γ(b+	b!γ(b+	VERB
ap-3493	184	75	γ3)γ(b+	γ3)γ(b+	PROPN
ap-3493	184	76	j1	j1	PROPN
ap-3493	184	77	+	+	X
ap-3493	184	78	γ[2	γ[2	PROPN
ap-3493	184	79	]	]	SYM
ap-3493	184	80	)	)	PUNCT
ap-3493	184	81	×	×	NOUN
ap-3493	184	82	{	{	PUNCT
ap-3493	184	83	1	1	NUM
ap-3493	184	84	if	if	SCONJ
ap-3493	184	85	j2	j2	PROPN
ap-3493	184	86	=	=	SYM
ap-3493	184	87	2b,√	2b,√	NUM
ap-3493	184	88	b+γ3	b+γ3	PROPN
ap-3493	184	89	b+j1+γ[2	b+j1+γ[2	NOUN
ap-3493	184	90	]	]	PUNCT
ap-3493	184	91	if	if	SCONJ
ap-3493	184	92	j2	j2	PROPN
ap-3493	184	93	=	=	SYM
ap-3493	184	94	2b+	2b+	NUM
ap-3493	184	95	1	1	NUM
ap-3493	184	96	,	,	PUNCT
ap-3493	184	97	(	(	PUNCT
ap-3493	184	98	4.24	4.24	NUM
ap-3493	184	99	)	)	PUNCT
ap-3493	184	100	η3	η3	NOUN
ap-3493	184	101	=	=	PUNCT
ap-3493	184	102	γ4	γ4	VERB
ap-3493	184	103	√	√	NUM
ap-3493	184	104	γ(c+	γ(c+	NOUN
ap-3493	184	105	j1	j1	PROPN
ap-3493	184	106	+	+	CCONJ
ap-3493	184	107	j2	j2	PROPN
ap-3493	184	108	+	+	CCONJ
ap-3493	184	109	γ[4	γ[4	PROPN
ap-3493	184	110	]	]	PUNCT
ap-3493	184	111	)	)	PUNCT
ap-3493	184	112	c!γ(c+	c!γ(c+	PROPN
ap-3493	184	113	γ4)γ(c+	γ4)γ(c+	PROPN
ap-3493	184	114	j1	j1	PROPN
ap-3493	184	115	+	+	CCONJ
ap-3493	184	116	j2	j2	PROPN
ap-3493	184	117	+	+	CCONJ
ap-3493	184	118	γ[3	γ[3	PROPN
ap-3493	184	119	]	]	SYM
ap-3493	184	120	)	)	PUNCT
ap-3493	184	121	×	×	NOUN
ap-3493	184	122	{	{	PUNCT
ap-3493	184	123	1	1	NUM
ap-3493	184	124	if	if	SCONJ
ap-3493	184	125	j3	j3	PROPN
ap-3493	184	126	=	=	SYM
ap-3493	184	127	2c,√	2c,√	NUM
ap-3493	184	128	c+γ4	c+γ4	PROPN
ap-3493	184	129	c+j1+j2+γ[3	c+j1+j2+γ[3	NOUN
ap-3493	184	130	]	]	PUNCT
ap-3493	184	131	if	if	SCONJ
ap-3493	184	132	j3	j3	PROPN
ap-3493	184	133	=	=	PUNCT
ap-3493	184	134	2c+	2c+	NUM
ap-3493	184	135	1	1	NUM
ap-3493	184	136	,	,	PUNCT
ap-3493	184	137	(	(	PUNCT
ap-3493	184	138	4.25	4.25	NUM
ap-3493	184	139	)	)	PUNCT
ap-3493	184	140	so	so	SCONJ
ap-3493	184	141	that	that	SCONJ
ap-3493	184	142	∫	∫	PROPN
ap-3493	184	143	s3	s3	PROPN
ap-3493	184	144	ψ(m)†	ψ(m)†	PROPN
ap-3493	184	145	j1,j2,j3	j1,j2,j3	PROPN
ap-3493	184	146	(	(	PUNCT
ap-3493	184	147	~s)ψ(n	~s)ψ(n	NUM
ap-3493	184	148	)	)	PUNCT
ap-3493	184	149	k1,k2,k3	k1,k2,k3	PUNCT
ap-3493	184	150	(	(	PUNCT
ap-3493	184	151	~s	~s	NUM
ap-3493	184	152	)	)	PUNCT
ap-3493	185	1	d	d	PUNCT
ap-3493	185	2	~	~	SYM
ap-3493	185	3	s	s	X
ap-3493	185	4	=	=	SYM
ap-3493	185	5	δn	δn	ADJ
ap-3493	185	6	,	,	PUNCT
ap-3493	185	7	mδj1,k1δj2,k2	mδj1,k1δj2,k2	NOUN
ap-3493	185	8	.	.	PUNCT
ap-3493	186	1	(	(	PUNCT
ap-3493	186	2	4.26	4.26	NUM
ap-3493	186	3	)	)	PUNCT
ap-3493	186	4	this	this	PRON
ap-3493	186	5	can	can	AUX
ap-3493	186	6	be	be	AUX
ap-3493	186	7	verified	verify	VERB
ap-3493	186	8	directly	directly	ADV
ap-3493	186	9	from	from	ADP
ap-3493	186	10	the	the	DET
ap-3493	186	11	orthogonality	orthogonality	NOUN
ap-3493	186	12	relation	relation	NOUN
ap-3493	186	13	of	of	ADP
ap-3493	186	14	the	the	DET
ap-3493	186	15	jacobi	jacobi	PROPN
ap-3493	186	16	polynomials	polynomial	NOUN
ap-3493	186	17	[	[	X
ap-3493	186	18	1	1	NUM
ap-3493	186	19	]	]	PUNCT
ap-3493	186	20	.	.	PUNCT
ap-3493	187	1	5	5	X
ap-3493	187	2	.	.	X
ap-3493	187	3	conclusion	conclusion	NOUN
ap-3493	187	4	to	to	PART
ap-3493	187	5	sum	sum	VERB
ap-3493	187	6	up	up	ADP
ap-3493	187	7	,	,	PUNCT
ap-3493	187	8	we	we	PRON
ap-3493	187	9	have	have	AUX
ap-3493	187	10	introduced	introduce	VERB
ap-3493	187	11	a	a	DET
ap-3493	187	12	new	new	ADJ
ap-3493	187	13	quantum	quantum	ADJ
ap-3493	187	14	superintegrable	superintegrable	ADJ
ap-3493	187	15	model	model	NOUN
ap-3493	187	16	with	with	ADP
ap-3493	187	17	reflections	reflection	NOUN
ap-3493	187	18	on	on	ADP
ap-3493	187	19	the	the	DET
ap-3493	187	20	three	three	NUM
ap-3493	187	21	-	-	PUNCT
ap-3493	187	22	sphere	sphere	NOUN
ap-3493	187	23	.	.	PUNCT
ap-3493	188	1	its	its	PRON
ap-3493	188	2	symmetries	symmetry	NOUN
ap-3493	188	3	were	be	AUX
ap-3493	188	4	given	give	VERB
ap-3493	188	5	explicitly	explicitly	ADV
ap-3493	188	6	and	and	CCONJ
ap-3493	188	7	were	be	AUX
ap-3493	188	8	shown	show	VERB
ap-3493	188	9	to	to	PART
ap-3493	188	10	realize	realize	VERB
ap-3493	188	11	a	a	DET
ap-3493	188	12	rank	rank	NOUN
ap-3493	188	13	-	-	PUNCT
ap-3493	188	14	two	two	NUM
ap-3493	188	15	bannai	bannai	PROPN
ap-3493	188	16	-	-	PUNCT
ap-3493	188	17	ito	ito	PROPN
ap-3493	188	18	algebra	algebra	NOUN
ap-3493	188	19	.	.	PUNCT
ap-3493	189	1	it	it	PRON
ap-3493	189	2	was	be	AUX
ap-3493	189	3	observed	observe	VERB
ap-3493	189	4	that	that	SCONJ
ap-3493	189	5	the	the	DET
ap-3493	189	6	model	model	NOUN
ap-3493	189	7	can	can	AUX
ap-3493	189	8	be	be	AUX
ap-3493	189	9	constructed	construct	VERB
ap-3493	189	10	through	through	ADP
ap-3493	189	11	the	the	DET
ap-3493	189	12	combination	combination	NOUN
ap-3493	189	13	of	of	ADP
ap-3493	189	14	four	four	NUM
ap-3493	189	15	independent	independent	ADJ
ap-3493	189	16	realizations	realization	NOUN
ap-3493	189	17	of	of	ADP
ap-3493	189	18	the	the	DET
ap-3493	189	19	superalgebra	superalgebra	NOUN
ap-3493	189	20	osp(1|2	osp(1|2	PROPN
ap-3493	189	21	)	)	PUNCT
ap-3493	189	22	.	.	PUNCT
ap-3493	190	1	a	a	DET
ap-3493	190	2	quadratic	quadratic	ADJ
ap-3493	190	3	expression	expression	NOUN
ap-3493	190	4	in	in	ADP
ap-3493	190	5	the	the	DET
ap-3493	190	6	total	total	ADJ
ap-3493	190	7	scasimir	scasimir	NOUN
ap-3493	190	8	operator	operator	NOUN
ap-3493	190	9	was	be	AUX
ap-3493	190	10	found	find	VERB
ap-3493	190	11	to	to	PART
ap-3493	190	12	coincide	coincide	VERB
ap-3493	190	13	with	with	ADP
ap-3493	190	14	the	the	DET
ap-3493	190	15	hamiltonian	hamiltonian	NOUN
ap-3493	190	16	while	while	SCONJ
ap-3493	190	17	the	the	DET
ap-3493	190	18	intermediate	intermediate	ADJ
ap-3493	190	19	casimir	casimir	NOUN
ap-3493	190	20	operators	operator	NOUN
ap-3493	190	21	were	be	AUX
ap-3493	190	22	seen	see	VERB
ap-3493	190	23	to	to	PART
ap-3493	190	24	coincide	coincide	VERB
ap-3493	190	25	with	with	ADP
ap-3493	190	26	its	its	PRON
ap-3493	190	27	symmetries	symmetry	NOUN
ap-3493	190	28	.	.	PUNCT
ap-3493	191	1	the	the	DET
ap-3493	191	2	exact	exact	ADJ
ap-3493	191	3	solutions	solution	NOUN
ap-3493	191	4	have	have	AUX
ap-3493	191	5	been	be	AUX
ap-3493	191	6	obtained	obtain	VERB
ap-3493	191	7	by	by	ADP
ap-3493	191	8	using	use	VERB
ap-3493	191	9	a	a	DET
ap-3493	191	10	cauchy	cauchy	PROPN
ap-3493	191	11	-	-	PUNCT
ap-3493	191	12	kovalevskaia	kovalevskaia	PROPN
ap-3493	191	13	extension	extension	NOUN
ap-3493	191	14	theorem	theorem	VERB
ap-3493	191	15	.	.	PUNCT
ap-3493	192	1	we	we	PRON
ap-3493	192	2	did	do	AUX
ap-3493	192	3	not	not	PART
ap-3493	192	4	find	find	VERB
ap-3493	192	5	many	many	ADJ
ap-3493	192	6	occurences	occurence	NOUN
ap-3493	192	7	of	of	ADP
ap-3493	192	8	this	this	DET
ap-3493	192	9	remarkably	remarkably	ADV
ap-3493	192	10	simple	simple	ADJ
ap-3493	192	11	technique	technique	NOUN
ap-3493	192	12	in	in	ADP
ap-3493	192	13	the	the	DET
ap-3493	192	14	superintegrability	superintegrability	NOUN
ap-3493	192	15	literature	literature	NOUN
ap-3493	192	16	and	and	CCONJ
ap-3493	192	17	we	we	PRON
ap-3493	192	18	trust	trust	VERB
ap-3493	192	19	it	it	PRON
ap-3493	192	20	could	could	AUX
ap-3493	192	21	find	find	VERB
ap-3493	192	22	many	many	ADJ
ap-3493	192	23	other	other	ADJ
ap-3493	192	24	applications	application	NOUN
ap-3493	192	25	.	.	PUNCT
ap-3493	193	1	furthermore	furthermore	ADV
ap-3493	193	2	,	,	PUNCT
ap-3493	193	3	an	an	DET
ap-3493	193	4	interesting	interesting	ADJ
ap-3493	193	5	feature	feature	NOUN
ap-3493	193	6	of	of	ADP
ap-3493	193	7	this	this	DET
ap-3493	193	8	model	model	NOUN
ap-3493	193	9	is	be	AUX
ap-3493	193	10	the	the	DET
ap-3493	193	11	appearance	appearance	NOUN
ap-3493	193	12	in	in	ADP
ap-3493	193	13	a	a	DET
ap-3493	193	14	scalar	scalar	ADJ
ap-3493	193	15	model	model	NOUN
ap-3493	193	16	of	of	ADP
ap-3493	193	17	the	the	DET
ap-3493	193	18	rank	rank	NOUN
ap-3493	193	19	2	2	NUM
ap-3493	193	20	bannai	bannai	PROPN
ap-3493	193	21	-	-	PUNCT
ap-3493	193	22	ito	ito	PROPN
ap-3493	193	23	algebra	algebra	NOUN
ap-3493	193	24	which	which	PRON
ap-3493	193	25	arose	arise	VERB
ap-3493	193	26	as	as	ADP
ap-3493	193	27	a	a	DET
ap-3493	193	28	particular	particular	ADJ
ap-3493	193	29	case	case	NOUN
ap-3493	193	30	in	in	ADP
ap-3493	193	31	the	the	DET
ap-3493	193	32	analysis	analysis	NOUN
ap-3493	193	33	of	of	ADP
ap-3493	193	34	the	the	DET
ap-3493	193	35	dirac	dirac	NOUN
ap-3493	193	36	-	-	PUNCT
ap-3493	193	37	dunkl	dunkl	NOUN
ap-3493	193	38	equation	equation	NOUN
ap-3493	193	39	[	[	X
ap-3493	193	40	8	8	NUM
ap-3493	193	41	]	]	PUNCT
ap-3493	193	42	.	.	PUNCT
ap-3493	194	1	one	one	PRON
ap-3493	194	2	expects	expect	VERB
ap-3493	194	3	that	that	SCONJ
ap-3493	194	4	the	the	DET
ap-3493	194	5	bivariate	bivariate	ADJ
ap-3493	194	6	bannai	bannai	PROPN
ap-3493	194	7	-	-	PUNCT
ap-3493	194	8	ito	ito	PROPN
ap-3493	194	9	polynomials	polynomial	NOUN
ap-3493	194	10	will	will	AUX
ap-3493	194	11	arise	arise	VERB
ap-3493	194	12	as	as	ADP
ap-3493	194	13	overlaps	overlap	NOUN
ap-3493	194	14	between	between	ADP
ap-3493	194	15	wavefunctions	wavefunction	NOUN
ap-3493	194	16	of	of	ADP
ap-3493	194	17	this	this	DET
ap-3493	194	18	model	model	NOUN
ap-3493	194	19	separated	separate	VERB
ap-3493	194	20	in	in	ADP
ap-3493	194	21	different	different	ADJ
ap-3493	194	22	hyperspherical	hyperspherical	ADJ
ap-3493	194	23	coordinate	coordinate	NOUN
ap-3493	194	24	systems	system	NOUN
ap-3493	194	25	.	.	PUNCT
ap-3493	195	1	these	these	DET
ap-3493	195	2	polynomials	polynomial	NOUN
ap-3493	195	3	have	have	AUX
ap-3493	195	4	never	never	ADV
ap-3493	195	5	been	be	AUX
ap-3493	195	6	identified	identify	VERB
ap-3493	195	7	so	so	ADV
ap-3493	195	8	far	far	ADV
ap-3493	195	9	and	and	CCONJ
ap-3493	195	10	we	we	PRON
ap-3493	195	11	aim	aim	VERB
ap-3493	195	12	to	to	PART
ap-3493	195	13	study	study	VERB
ap-3493	195	14	this	this	DET
ap-3493	195	15	question	question	NOUN
ap-3493	195	16	in	in	ADP
ap-3493	195	17	the	the	DET
ap-3493	195	18	near	near	ADJ
ap-3493	195	19	future	future	NOUN
ap-3493	195	20	.	.	PUNCT
ap-3493	196	1	acknowledgements	acknowledgement	VERB
ap-3493	196	2	the	the	DET
ap-3493	196	3	research	research	NOUN
ap-3493	196	4	of	of	ADP
ap-3493	196	5	hdb	hdb	NOUN
ap-3493	196	6	is	be	AUX
ap-3493	196	7	supported	support	VERB
ap-3493	196	8	by	by	ADP
ap-3493	196	9	the	the	DET
ap-3493	196	10	fund	fund	NOUN
ap-3493	196	11	for	for	ADP
ap-3493	196	12	scientific	scientific	ADJ
ap-3493	196	13	research	research	NOUN
ap-3493	196	14	-	-	PUNCT
ap-3493	196	15	flanders	flanders	NOUN
ap-3493	196	16	(	(	PUNCT
ap-3493	196	17	fwo	fwo	NOUN
ap-3493	196	18	-	-	PUNCT
ap-3493	196	19	v	v	NOUN
ap-3493	196	20	)	)	PUNCT
ap-3493	196	21	,	,	PUNCT
ap-3493	196	22	project	project	NOUN
ap-3493	196	23	“	"	PUNCT
ap-3493	196	24	construction	construction	NOUN
ap-3493	196	25	of	of	ADP
ap-3493	196	26	algebra	algebra	NOUN
ap-3493	196	27	realisations	realisation	NOUN
ap-3493	196	28	using	use	VERB
ap-3493	196	29	dirac	dirac	NOUN
ap-3493	196	30	-	-	PUNCT
ap-3493	196	31	operators	operator	NOUN
ap-3493	196	32	”	"	PUNCT
ap-3493	196	33	,	,	PUNCT
ap-3493	196	34	grant	grant	PROPN
ap-3493	196	35	g.0116.13n	g.0116.13n	PROPN
ap-3493	196	36	.	.	PUNCT
ap-3493	197	1	vxg	vxg	PROPN
ap-3493	197	2	holds	hold	VERB
ap-3493	197	3	a	a	DET
ap-3493	197	4	postdoctoral	postdoctoral	ADJ
ap-3493	197	5	fellowship	fellowship	NOUN
ap-3493	197	6	from	from	ADP
ap-3493	197	7	the	the	DET
ap-3493	197	8	natural	natural	ADJ
ap-3493	197	9	science	science	NOUN
ap-3493	197	10	and	and	CCONJ
ap-3493	197	11	engineering	engineering	NOUN
ap-3493	197	12	research	research	NOUN
ap-3493	197	13	council	council	PROPN
ap-3493	197	14	of	of	ADP
ap-3493	197	15	canada	canada	PROPN
ap-3493	197	16	(	(	PUNCT
ap-3493	197	17	nserc	nserc	PROPN
ap-3493	197	18	)	)	PUNCT
ap-3493	197	19	.	.	PUNCT
ap-3493	198	1	jml	jml	PROPN
ap-3493	198	2	holds	hold	VERB
ap-3493	198	3	a	a	DET
ap-3493	198	4	scholarship	scholarship	NOUN
ap-3493	198	5	from	from	ADP
ap-3493	198	6	the	the	DET
ap-3493	198	7	fonds	fonds	X
ap-3493	198	8	de	de	X
ap-3493	198	9	recherche	recherche	X
ap-3493	198	10	du	du	PROPN
ap-3493	198	11	québec	québec	PROPN
ap-3493	198	12	–	–	PUNCT
ap-3493	198	13	nature	nature	NOUN
ap-3493	198	14	et	et	NOUN
ap-3493	198	15	technologies	technology	NOUN
ap-3493	198	16	(	(	PUNCT
ap-3493	198	17	frqnt	frqnt	NOUN
ap-3493	198	18	)	)	PUNCT
ap-3493	198	19	.	.	PUNCT
ap-3493	199	1	the	the	DET
ap-3493	199	2	research	research	NOUN
ap-3493	199	3	of	of	ADP
ap-3493	199	4	lv	lv	PROPN
ap-3493	199	5	is	be	AUX
ap-3493	199	6	supported	support	VERB
ap-3493	199	7	in	in	ADP
ap-3493	199	8	part	part	NOUN
ap-3493	199	9	by	by	ADP
ap-3493	199	10	nserc	nserc	NOUN
ap-3493	199	11	.	.	PUNCT
ap-3493	200	1	171	171	NUM
ap-3493	200	2	hendrik	hendrik	PROPN
ap-3493	200	3	de	de	X
ap-3493	200	4	bie	bie	PROPN
ap-3493	200	5	,	,	PUNCT
ap-3493	200	6	vincent	vincent	PROPN
ap-3493	200	7	x.	x.	PROPN
ap-3493	200	8	genest	genest	PROPN
ap-3493	200	9	,	,	PUNCT
ap-3493	200	10	jean	jean	PROPN
ap-3493	200	11	-	-	PUNCT
ap-3493	200	12	michel	michel	PROPN
ap-3493	200	13	lemay	lemay	PROPN
ap-3493	200	14	,	,	PUNCT
ap-3493	200	15	luc	luc	PROPN
ap-3493	200	16	vinet	vinet	PROPN
ap-3493	200	17	acta	acta	PROPN
ap-3493	200	18	polytechnica	polytechnica	PROPN
ap-3493	200	19	references	reference	NOUN
ap-3493	200	20	[	[	X
ap-3493	200	21	1	1	NUM
ap-3493	200	22	]	]	PUNCT
ap-3493	200	23	r.	r.	PROPN
ap-3493	200	24	koekoek	koekoek	PROPN
ap-3493	200	25	,	,	PUNCT
ap-3493	200	26	p.a	p.a	PROPN
ap-3493	200	27	.	.	PROPN
ap-3493	200	28	lesky	lesky	PROPN
ap-3493	200	29	,	,	PUNCT
ap-3493	200	30	r.f	r.f	PROPN
ap-3493	200	31	.	.	PROPN
ap-3493	200	32	swarttouw	swarttouw	PROPN
ap-3493	200	33	,	,	PUNCT
ap-3493	200	34	hypergeometric	hypergeometric	ADJ
ap-3493	200	35	orthogonal	orthogonal	ADJ
ap-3493	200	36	polynomials	polynomial	NOUN
ap-3493	200	37	and	and	CCONJ
ap-3493	200	38	their	their	PRON
ap-3493	200	39	q	q	NOUN
ap-3493	200	40	-	-	PUNCT
ap-3493	200	41	analogues	analogue	NOUN
ap-3493	200	42	.	.	PUNCT
ap-3493	201	1	springer	springer	NOUN
ap-3493	201	2	,	,	PUNCT
ap-3493	201	3	1st	1st	PROPN
ap-3493	201	4	edition	edition	NOUN
ap-3493	201	5	,	,	PUNCT
ap-3493	201	6	2010	2010	NUM
ap-3493	201	7	.	.	PUNCT
ap-3493	202	1	[	[	X
ap-3493	202	2	2	2	NUM
ap-3493	202	3	]	]	X
ap-3493	202	4	v.x	v.x	PROPN
ap-3493	202	5	.	.	PROPN
ap-3493	202	6	genest	genest	PROPN
ap-3493	202	7	,	,	PUNCT
ap-3493	202	8	m.e.h	m.e.h	PROPN
ap-3493	202	9	.	.	PUNCT
ap-3493	203	1	ismail	ismail	PROPN
ap-3493	203	2	,	,	PUNCT
ap-3493	203	3	l.	l.	PROPN
ap-3493	203	4	vinet	vinet	PROPN
ap-3493	203	5	,	,	PUNCT
ap-3493	203	6	a.	a.	PROPN
ap-3493	203	7	zhedanov	zhedanov	PROPN
ap-3493	203	8	,	,	PUNCT
ap-3493	203	9	the	the	DET
ap-3493	203	10	dunkl	dunkl	NOUN
ap-3493	203	11	oscillator	oscillator	NOUN
ap-3493	203	12	in	in	ADP
ap-3493	203	13	the	the	DET
ap-3493	203	14	plane	plane	NOUN
ap-3493	204	1	i	i	PRON
ap-3493	204	2	:	:	PUNCT
ap-3493	204	3	superintegrability	superintegrability	NOUN
ap-3493	204	4	,	,	PUNCT
ap-3493	204	5	separated	separate	VERB
ap-3493	204	6	wavefunctions	wavefunction	NOUN
ap-3493	204	7	and	and	CCONJ
ap-3493	204	8	overlap	overlap	NOUN
ap-3493	204	9	coefficients	coefficient	NOUN
ap-3493	204	10	.	.	PUNCT
ap-3493	205	1	j.	j.	PROPN
ap-3493	205	2	phys	phys	PROPN
ap-3493	205	3	.	.	PUNCT
ap-3493	206	1	a	a	DET
ap-3493	206	2	:	:	PUNCT
ap-3493	206	3	math	math	NOUN
ap-3493	206	4	.	.	PUNCT
ap-3493	207	1	theor	theor	PROPN
ap-3493	207	2	.	.	PROPN
ap-3493	207	3	,	,	PUNCT
ap-3493	207	4	46:145201	46:145201	NUM
ap-3493	207	5	,	,	PUNCT
ap-3493	207	6	2013	2013	NUM
ap-3493	207	7	.	.	PUNCT
ap-3493	208	1	[	[	X
ap-3493	208	2	3	3	X
ap-3493	208	3	]	]	X
ap-3493	208	4	v.x	v.x	PROPN
ap-3493	208	5	.	.	PROPN
ap-3493	208	6	genest	genest	PROPN
ap-3493	208	7	,	,	PUNCT
ap-3493	208	8	m.e.h	m.e.h	PROPN
ap-3493	208	9	.	.	PUNCT
ap-3493	209	1	ismail	ismail	PROPN
ap-3493	209	2	,	,	PUNCT
ap-3493	209	3	l.	l.	PROPN
ap-3493	209	4	vinet	vinet	PROPN
ap-3493	209	5	,	,	PUNCT
ap-3493	209	6	a.	a.	PROPN
ap-3493	209	7	zhedanov	zhedanov	PROPN
ap-3493	209	8	,	,	PUNCT
ap-3493	209	9	the	the	DET
ap-3493	209	10	dunkl	dunkl	NOUN
ap-3493	209	11	oscillator	oscillator	NOUN
ap-3493	209	12	in	in	ADP
ap-3493	209	13	the	the	DET
ap-3493	209	14	plane	plane	NOUN
ap-3493	209	15	ii	ii	NOUN
ap-3493	209	16	:	:	PUNCT
ap-3493	209	17	representations	representation	NOUN
ap-3493	209	18	of	of	ADP
ap-3493	209	19	the	the	DET
ap-3493	209	20	symmetry	symmetry	NOUN
ap-3493	209	21	algebra	algebra	PROPN
ap-3493	209	22	.	.	PUNCT
ap-3493	210	1	comm	comm	NOUN
ap-3493	210	2	.	.	PUNCT
ap-3493	210	3	math	math	NOUN
ap-3493	210	4	.	.	PUNCT
ap-3493	211	1	phys	phy	NOUN
ap-3493	211	2	.	.	PUNCT
ap-3493	211	3	329	329	NUM
ap-3493	211	4	,	,	PUNCT
ap-3493	211	5	999	999	NUM
ap-3493	211	6	-	-	SYM
ap-3493	211	7	1029	1029	NUM
ap-3493	211	8	,	,	PUNCT
ap-3493	211	9	2014	2014	NUM
ap-3493	211	10	.	.	PUNCT
ap-3493	212	1	[	[	X
ap-3493	212	2	4	4	X
ap-3493	212	3	]	]	X
ap-3493	212	4	v.x	v.x	PROPN
ap-3493	212	5	.	.	PROPN
ap-3493	212	6	genest	genest	PROPN
ap-3493	212	7	,	,	PUNCT
ap-3493	212	8	m.e.h	m.e.h	PROPN
ap-3493	212	9	.	.	PUNCT
ap-3493	213	1	ismail	ismail	PROPN
ap-3493	213	2	,	,	PUNCT
ap-3493	213	3	l.	l.	PROPN
ap-3493	213	4	vinet	vinet	PROPN
ap-3493	213	5	,	,	PUNCT
ap-3493	213	6	a.	a.	PROPN
ap-3493	213	7	zhedanov	zhedanov	PROPN
ap-3493	213	8	,	,	PUNCT
ap-3493	213	9	the	the	DET
ap-3493	213	10	singular	singular	NOUN
ap-3493	213	11	and	and	CCONJ
ap-3493	213	12	2:1	2:1	NUM
ap-3493	213	13	anisotropic	anisotropic	NOUN
ap-3493	213	14	dunkl	dunkl	NOUN
ap-3493	213	15	oscillators	oscillator	NOUN
ap-3493	213	16	in	in	ADP
ap-3493	213	17	the	the	DET
ap-3493	213	18	plane	plane	NOUN
ap-3493	213	19	.	.	PUNCT
ap-3493	214	1	j.	j.	PROPN
ap-3493	214	2	phys	phys	PROPN
ap-3493	214	3	.	.	PUNCT
ap-3493	215	1	a	a	DET
ap-3493	215	2	:	:	PUNCT
ap-3493	215	3	math	math	NOUN
ap-3493	215	4	.	.	PUNCT
ap-3493	216	1	theor	theor	PROPN
ap-3493	216	2	.	.	PROPN
ap-3493	216	3	,	,	PUNCT
ap-3493	216	4	46:325201	46:325201	NUM
ap-3493	216	5	,	,	PUNCT
ap-3493	216	6	2013	2013	NUM
ap-3493	216	7	.	.	PUNCT
ap-3493	217	1	[	[	X
ap-3493	217	2	5	5	NUM
ap-3493	217	3	]	]	X
ap-3493	217	4	v.x	v.x	PROPN
ap-3493	217	5	.	.	PROPN
ap-3493	217	6	genest	genest	PROPN
ap-3493	217	7	,	,	PUNCT
ap-3493	217	8	l.	l.	PROPN
ap-3493	217	9	vinet	vinet	PROPN
ap-3493	217	10	,	,	PUNCT
ap-3493	217	11	a.	a.	PROPN
ap-3493	217	12	zhedanov	zhedanov	PROPN
ap-3493	217	13	,	,	PUNCT
ap-3493	217	14	the	the	DET
ap-3493	217	15	dunkl	dunkl	NOUN
ap-3493	217	16	oscillator	oscillator	NOUN
ap-3493	217	17	in	in	ADP
ap-3493	217	18	three	three	NUM
ap-3493	217	19	dimensions	dimension	NOUN
ap-3493	217	20	.	.	PUNCT
ap-3493	218	1	j.	j.	PROPN
ap-3493	218	2	phys	phys	PROPN
ap-3493	218	3	.	.	PUNCT
ap-3493	218	4	:	:	PUNCT
ap-3493	218	5	conf	conf	PROPN
ap-3493	218	6	.	.	PUNCT
ap-3493	218	7	ser	ser	PROPN
ap-3493	218	8	.	.	PROPN
ap-3493	219	1	512	512	NUM
ap-3493	219	2	012010	012010	NUM
ap-3493	219	3	,	,	PUNCT
ap-3493	219	4	2014	2014	NUM
ap-3493	219	5	.	.	PUNCT
ap-3493	220	1	[	[	X
ap-3493	220	2	6	6	NUM
ap-3493	220	3	]	]	X
ap-3493	220	4	v.x	v.x	PROPN
ap-3493	220	5	.	.	PROPN
ap-3493	220	6	genest	genest	PROPN
ap-3493	220	7	,	,	PUNCT
ap-3493	220	8	l.	l.	PROPN
ap-3493	220	9	vinet	vinet	PROPN
ap-3493	220	10	,	,	PUNCT
ap-3493	220	11	a.	a.	PROPN
ap-3493	220	12	zhedanov	zhedanov	PROPN
ap-3493	220	13	,	,	PUNCT
ap-3493	220	14	a	a	DET
ap-3493	220	15	laplace	laplace	NOUN
ap-3493	220	16	-	-	PUNCT
ap-3493	220	17	dunkl	dunkl	NOUN
ap-3493	220	18	equation	equation	NOUN
ap-3493	220	19	on	on	ADP
ap-3493	220	20	s2	s2	PROPN
ap-3493	220	21	and	and	CCONJ
ap-3493	220	22	the	the	DET
ap-3493	220	23	bannai	bannai	PROPN
ap-3493	220	24	-	-	PUNCT
ap-3493	220	25	ito	ito	PROPN
ap-3493	220	26	algebra	algebra	PROPN
ap-3493	220	27	.	.	PUNCT
ap-3493	221	1	comm	comm	NOUN
ap-3493	221	2	.	.	PUNCT
ap-3493	221	3	math	math	NOUN
ap-3493	221	4	.	.	PUNCT
ap-3493	222	1	phys	phy	NOUN
ap-3493	222	2	.	.	PUNCT
ap-3493	223	1	336	336	NUM
ap-3493	223	2	,	,	PUNCT
ap-3493	223	3	243	243	NUM
ap-3493	223	4	-	-	SYM
ap-3493	223	5	259	259	NUM
ap-3493	223	6	,	,	PUNCT
ap-3493	223	7	2015	2015	NUM
ap-3493	223	8	.	.	PUNCT
ap-3493	224	1	[	[	X
ap-3493	224	2	7	7	X
ap-3493	224	3	]	]	X
ap-3493	224	4	v.x	v.x	PROPN
ap-3493	224	5	.	.	PROPN
ap-3493	224	6	genest	genest	PROPN
ap-3493	224	7	,	,	PUNCT
ap-3493	224	8	l.	l.	PROPN
ap-3493	224	9	vinet	vinet	PROPN
ap-3493	224	10	,	,	PUNCT
ap-3493	224	11	a.	a.	PROPN
ap-3493	224	12	zhedanov	zhedanov	PROPN
ap-3493	224	13	,	,	PUNCT
ap-3493	224	14	the	the	DET
ap-3493	224	15	bannai	bannai	PROPN
ap-3493	224	16	-	-	PUNCT
ap-3493	224	17	ito	ito	PROPN
ap-3493	224	18	algebra	algebra	PROPN
ap-3493	224	19	and	and	CCONJ
ap-3493	224	20	a	a	DET
ap-3493	224	21	superintegrable	superintegrable	ADJ
ap-3493	224	22	system	system	NOUN
ap-3493	224	23	with	with	ADP
ap-3493	224	24	reflections	reflection	NOUN
ap-3493	224	25	on	on	ADP
ap-3493	224	26	the	the	DET
ap-3493	224	27	2	2	NUM
ap-3493	224	28	-	-	PUNCT
ap-3493	224	29	sphere	sphere	NOUN
ap-3493	224	30	.	.	PUNCT
ap-3493	225	1	j.	j.	PROPN
ap-3493	225	2	phys	phys	PROPN
ap-3493	225	3	.	.	PUNCT
ap-3493	226	1	a	a	DET
ap-3493	226	2	:	:	PUNCT
ap-3493	226	3	math	math	NOUN
ap-3493	226	4	.	.	PUNCT
ap-3493	227	1	theor	theor	PROPN
ap-3493	227	2	.	.	PROPN
ap-3493	227	3	,	,	PUNCT
ap-3493	227	4	47:205202	47:205202	PROPN
ap-3493	227	5	,	,	PUNCT
ap-3493	227	6	2014	2014	NUM
ap-3493	227	7	.	.	PUNCT
ap-3493	228	1	[	[	X
ap-3493	228	2	8	8	NUM
ap-3493	228	3	]	]	X
ap-3493	228	4	h.	h.	PROPN
ap-3493	228	5	de	de	PROPN
ap-3493	228	6	bie	bie	PROPN
ap-3493	228	7	,	,	PUNCT
ap-3493	228	8	v.x	v.x	PROPN
ap-3493	228	9	.	.	PROPN
ap-3493	228	10	genest	genest	PROPN
ap-3493	228	11	,	,	PUNCT
ap-3493	228	12	l.	l.	PROPN
ap-3493	228	13	vinet	vinet	PROPN
ap-3493	228	14	,	,	PUNCT
ap-3493	228	15	the	the	DET
ap-3493	228	16	zn	zn	PROPN
ap-3493	228	17	2	2	NUM
ap-3493	228	18	dirac	dirac	NOUN
ap-3493	228	19	-	-	PUNCT
ap-3493	228	20	dunkl	dunkl	NOUN
ap-3493	228	21	operator	operator	NOUN
ap-3493	228	22	and	and	CCONJ
ap-3493	228	23	a	a	DET
ap-3493	228	24	higher	high	ADJ
ap-3493	228	25	rank	rank	NOUN
ap-3493	228	26	bannai	bannai	PROPN
ap-3493	228	27	-	-	PUNCT
ap-3493	228	28	ito	ito	PROPN
ap-3493	228	29	algebra	algebra	PROPN
ap-3493	228	30	.	.	PUNCT
ap-3493	229	1	arxiv:1511.02177	arxiv:1511.02177	PRON
ap-3493	230	1	[	[	X
ap-3493	230	2	math	math	NOUN
ap-3493	230	3	-	-	PUNCT
ap-3493	230	4	ph	ph	NOUN
ap-3493	230	5	]	]	X
ap-3493	230	6	2015	2015	NUM
ap-3493	230	7	.	.	PUNCT
ap-3493	231	1	[	[	X
ap-3493	231	2	9	9	NUM
ap-3493	231	3	]	]	PUNCT
ap-3493	231	4	s.	s.	PROPN
ap-3493	231	5	post	post	PROPN
ap-3493	231	6	,	,	PUNCT
ap-3493	231	7	l.	l.	PROPN
ap-3493	231	8	vinet	vinet	PROPN
ap-3493	231	9	,	,	PUNCT
ap-3493	231	10	a.	a.	PROPN
ap-3493	231	11	zhedanov	zhedanov	PROPN
ap-3493	231	12	,	,	PUNCT
ap-3493	231	13	supersymmetric	supersymmetric	ADJ
ap-3493	231	14	quantum	quantum	ADJ
ap-3493	231	15	mechanics	mechanic	NOUN
ap-3493	231	16	with	with	ADP
ap-3493	231	17	reflections	reflection	NOUN
ap-3493	231	18	.	.	PUNCT
ap-3493	232	1	j.	j.	PROPN
ap-3493	232	2	phys	phys	PROPN
ap-3493	232	3	.	.	PUNCT
ap-3493	233	1	a	a	DET
ap-3493	233	2	:	:	PUNCT
ap-3493	233	3	math	math	NOUN
ap-3493	233	4	.	.	PUNCT
ap-3493	234	1	theor	theor	PROPN
ap-3493	234	2	.	.	PROPN
ap-3493	234	3	,	,	PUNCT
ap-3493	234	4	44:435301	44:435301	X
ap-3493	234	5	,	,	PUNCT
ap-3493	234	6	2011	2011	NUM
ap-3493	234	7	.	.	PUNCT
ap-3493	235	1	[	[	X
ap-3493	235	2	10	10	NUM
ap-3493	235	3	]	]	PUNCT
ap-3493	235	4	e.g.	e.g.	ADV
ap-3493	235	5	kalnins	kalnin	NOUN
ap-3493	235	6	,	,	PUNCT
ap-3493	235	7	w.	w.	PROPN
ap-3493	235	8	miller	miller	PROPN
ap-3493	235	9	,	,	PUNCT
ap-3493	235	10	s.	s.	PROPN
ap-3493	235	11	post	post	PROPN
ap-3493	235	12	,	,	PUNCT
ap-3493	235	13	two	two	NUM
ap-3493	235	14	-	-	PUNCT
ap-3493	235	15	variable	variable	NOUN
ap-3493	235	16	wilson	wilson	PROPN
ap-3493	235	17	polynomials	polynomial	NOUN
ap-3493	235	18	and	and	CCONJ
ap-3493	235	19	the	the	DET
ap-3493	235	20	generic	generic	ADJ
ap-3493	235	21	superintegrable	superintegrable	ADJ
ap-3493	235	22	system	system	NOUN
ap-3493	235	23	on	on	ADP
ap-3493	235	24	the	the	DET
ap-3493	235	25	3	3	NUM
ap-3493	235	26	-	-	PUNCT
ap-3493	235	27	sphere	sphere	NOUN
ap-3493	235	28	.	.	PUNCT
ap-3493	236	1	sigma	sigma	PROPN
ap-3493	236	2	,	,	PUNCT
ap-3493	236	3	7:51	7:51	NUM
ap-3493	236	4	-	-	SYM
ap-3493	236	5	76	76	NUM
ap-3493	236	6	,	,	PUNCT
ap-3493	236	7	2011	2011	NUM
ap-3493	236	8	.	.	PUNCT
ap-3493	237	1	[	[	X
ap-3493	237	2	11	11	NUM
ap-3493	237	3	]	]	PUNCT
ap-3493	237	4	e.g.	e.g.	ADV
ap-3493	237	5	kalnins	kalnin	NOUN
ap-3493	237	6	,	,	PUNCT
ap-3493	237	7	w.	w.	PROPN
ap-3493	237	8	miller	miller	PROPN
ap-3493	237	9	,	,	PUNCT
ap-3493	237	10	s.	s.	PROPN
ap-3493	237	11	post	post	PROPN
ap-3493	237	12	,	,	PUNCT
ap-3493	237	13	contractions	contraction	NOUN
ap-3493	237	14	of	of	ADP
ap-3493	237	15	2d	2d	NUM
ap-3493	237	16	2nd	2nd	ADJ
ap-3493	237	17	order	order	NOUN
ap-3493	237	18	quantum	quantum	ADJ
ap-3493	237	19	superintegrable	superintegrable	ADJ
ap-3493	237	20	systems	system	NOUN
ap-3493	237	21	and	and	CCONJ
ap-3493	237	22	the	the	DET
ap-3493	237	23	askey	askey	ADJ
ap-3493	237	24	scheme	scheme	NOUN
ap-3493	237	25	for	for	ADP
ap-3493	237	26	hypergeometric	hypergeometric	ADJ
ap-3493	237	27	orthogonal	orthogonal	ADJ
ap-3493	237	28	polynomials	polynomial	NOUN
ap-3493	237	29	.	.	PUNCT
ap-3493	238	1	sigma	sigma	NOUN
ap-3493	238	2	,	,	PUNCT
ap-3493	238	3	9:57	9:57	NUM
ap-3493	238	4	-	-	SYM
ap-3493	238	5	84	84	NUM
ap-3493	238	6	,	,	PUNCT
ap-3493	238	7	2013	2013	NUM
ap-3493	238	8	.	.	PUNCT
ap-3493	239	1	[	[	X
ap-3493	239	2	12	12	NUM
ap-3493	239	3	]	]	X
ap-3493	239	4	w.	w.	PROPN
ap-3493	239	5	miller	miller	PROPN
ap-3493	239	6	,	,	PUNCT
ap-3493	239	7	s.	s.	PROPN
ap-3493	239	8	post	post	PROPN
ap-3493	239	9	,	,	PUNCT
ap-3493	239	10	p.	p.	PROPN
ap-3493	239	11	winternitz	winternitz	PROPN
ap-3493	239	12	,	,	PUNCT
ap-3493	239	13	classical	classical	ADJ
ap-3493	239	14	and	and	CCONJ
ap-3493	239	15	quantum	quantum	ADJ
ap-3493	239	16	superintegrability	superintegrability	NOUN
ap-3493	239	17	with	with	ADP
ap-3493	239	18	applications	application	NOUN
ap-3493	239	19	.	.	PUNCT
ap-3493	240	1	j.	j.	PROPN
ap-3493	240	2	phys	phys	PROPN
ap-3493	240	3	.	.	PUNCT
ap-3493	241	1	a	a	DET
ap-3493	241	2	:	:	PUNCT
ap-3493	241	3	math	math	NOUN
ap-3493	241	4	.	.	PUNCT
ap-3493	242	1	theor	theor	PROPN
ap-3493	242	2	.	.	PROPN
ap-3493	242	3	,	,	PUNCT
ap-3493	242	4	46:423001	46:423001	NUM
ap-3493	242	5	,	,	PUNCT
ap-3493	242	6	2013	2013	NUM
ap-3493	242	7	.	.	PUNCT
ap-3493	243	1	[	[	X
ap-3493	243	2	13	13	NUM
ap-3493	243	3	]	]	PUNCT
ap-3493	243	4	l.	l.	PROPN
ap-3493	243	5	vinet	vinet	PROPN
ap-3493	243	6	,	,	PUNCT
ap-3493	243	7	a.	a.	PROPN
ap-3493	243	8	zhedanov	zhedanov	PROPN
ap-3493	243	9	,	,	PUNCT
ap-3493	243	10	a	a	DET
ap-3493	243	11	missing	miss	VERB
ap-3493	243	12	family	family	NOUN
ap-3493	243	13	of	of	ADP
ap-3493	243	14	classical	classical	ADJ
ap-3493	243	15	orthogonal	orthogonal	ADJ
ap-3493	243	16	polynomials	polynomial	NOUN
ap-3493	243	17	.	.	PUNCT
ap-3493	244	1	j.	j.	PROPN
ap-3493	244	2	phys	phys	PROPN
ap-3493	244	3	.	.	PUNCT
ap-3493	245	1	a	a	DET
ap-3493	245	2	:	:	PUNCT
ap-3493	245	3	math	math	NOUN
ap-3493	245	4	.	.	PUNCT
ap-3493	246	1	theor	theor	PROPN
ap-3493	246	2	.	.	PROPN
ap-3493	246	3	,	,	PUNCT
ap-3493	246	4	44:085201	44:085201	NOUN
ap-3493	246	5	,	,	PUNCT
ap-3493	246	6	2011	2011	NUM
ap-3493	246	7	.	.	PUNCT
ap-3493	247	1	[	[	X
ap-3493	247	2	14	14	NUM
ap-3493	247	3	]	]	X
ap-3493	247	4	l.	l.	PROPN
ap-3493	247	5	vinet	vinet	PROPN
ap-3493	247	6	,	,	PUNCT
ap-3493	247	7	a.	a.	PROPN
ap-3493	247	8	zhedanov	zhedanov	PROPN
ap-3493	247	9	,	,	PUNCT
ap-3493	247	10	a	a	DET
ap-3493	247	11	limit	limit	NOUN
ap-3493	247	12	q	q	X
ap-3493	247	13	=	=	PUNCT
ap-3493	247	14	−1	−1	NOUN
ap-3493	247	15	for	for	ADP
ap-3493	247	16	the	the	DET
ap-3493	247	17	big	big	ADJ
ap-3493	247	18	q	q	ADJ
ap-3493	247	19	-	-	PUNCT
ap-3493	247	20	jacobi	jacobi	NOUN
ap-3493	247	21	polynomials	polynomial	NOUN
ap-3493	247	22	.	.	PUNCT
ap-3493	248	1	trans	trans	PROPN
ap-3493	248	2	.	.	PUNCT
ap-3493	249	1	amer	amer	PROPN
ap-3493	249	2	.	.	PUNCT
ap-3493	249	3	math	math	PROPN
ap-3493	249	4	.	.	PUNCT
ap-3493	250	1	soc	soc	PROPN
ap-3493	250	2	.	.	PUNCT
ap-3493	251	1	364	364	NUM
ap-3493	251	2	,	,	PUNCT
ap-3493	251	3	5491	5491	NUM
ap-3493	251	4	-	-	SYM
ap-3493	251	5	5507	5507	NUM
ap-3493	251	6	,	,	PUNCT
ap-3493	251	7	2012	2012	NUM
ap-3493	251	8	.	.	PUNCT
ap-3493	252	1	[	[	X
ap-3493	252	2	15	15	NUM
ap-3493	252	3	]	]	X
ap-3493	252	4	l.	l.	PROPN
ap-3493	252	5	vinet	vinet	PROPN
ap-3493	252	6	,	,	PUNCT
ap-3493	252	7	a.	a.	PROPN
ap-3493	252	8	zhedanov	zhedanov	PROPN
ap-3493	252	9	,	,	PUNCT
ap-3493	252	10	a	a	DET
ap-3493	252	11	bochner	bochner	NOUN
ap-3493	252	12	theorem	theorem	NOUN
ap-3493	252	13	for	for	ADP
ap-3493	252	14	dunkl	dunkl	NOUN
ap-3493	252	15	polynomials	polynomial	NOUN
ap-3493	252	16	.	.	PUNCT
ap-3493	253	1	sigma	sigma	PROPN
ap-3493	253	2	7:20	7:20	NUM
ap-3493	253	3	-	-	SYM
ap-3493	253	4	28	28	NUM
ap-3493	253	5	,	,	PUNCT
ap-3493	253	6	2011	2011	NUM
ap-3493	253	7	.	.	PUNCT
ap-3493	254	1	[	[	X
ap-3493	254	2	16	16	NUM
ap-3493	254	3	]	]	X
ap-3493	254	4	s.	s.	PROPN
ap-3493	254	5	tsujimoto	tsujimoto	PROPN
ap-3493	254	6	,	,	PUNCT
ap-3493	254	7	l.	l.	PROPN
ap-3493	254	8	vinet	vinet	PROPN
ap-3493	254	9	,	,	PUNCT
ap-3493	254	10	a.	a.	PROPN
ap-3493	254	11	zhedanov	zhedanov	PROPN
ap-3493	254	12	,	,	PUNCT
ap-3493	254	13	dual	dual	PROPN
ap-3493	254	14	-1	-1	PROPN
ap-3493	254	15	hahn	hahn	PROPN
ap-3493	254	16	polynomials	polynomials	PROPN
ap-3493	254	17	:	:	PUNCT
ap-3493	254	18	"	"	PUNCT
ap-3493	254	19	classical	classical	ADJ
ap-3493	254	20	"	"	PUNCT
ap-3493	254	21	polynomials	polynomial	NOUN
ap-3493	254	22	beyond	beyond	ADP
ap-3493	254	23	the	the	DET
ap-3493	254	24	leonard	leonard	PROPN
ap-3493	254	25	duality	duality	NOUN
ap-3493	254	26	.	.	PUNCT
ap-3493	255	1	proc	proc	PROPN
ap-3493	255	2	.	.	PUNCT
ap-3493	256	1	amer	amer	PROPN
ap-3493	256	2	.	.	PUNCT
ap-3493	256	3	math	math	PROPN
ap-3493	256	4	.	.	PUNCT
ap-3493	257	1	soc	soc	PROPN
ap-3493	257	2	.	.	PUNCT
ap-3493	258	1	141	141	NUM
ap-3493	258	2	,	,	PUNCT
ap-3493	258	3	959	959	NUM
ap-3493	258	4	-	-	SYM
ap-3493	258	5	970	970	NUM
ap-3493	258	6	,	,	PUNCT
ap-3493	258	7	2013	2013	NUM
ap-3493	258	8	.	.	PUNCT
ap-3493	259	1	[	[	X
ap-3493	259	2	17	17	NUM
ap-3493	259	3	]	]	X
ap-3493	259	4	s.	s.	PROPN
ap-3493	259	5	tsujimoto	tsujimoto	PROPN
ap-3493	259	6	,	,	PUNCT
ap-3493	259	7	l.	l.	PROPN
ap-3493	259	8	vinet	vinet	PROPN
ap-3493	259	9	,	,	PUNCT
ap-3493	259	10	a.	a.	PROPN
ap-3493	259	11	zhedanov	zhedanov	PROPN
ap-3493	259	12	,	,	PUNCT
ap-3493	259	13	dunkl	dunkl	VERB
ap-3493	259	14	shift	shift	NOUN
ap-3493	259	15	operators	operator	NOUN
ap-3493	259	16	and	and	CCONJ
ap-3493	259	17	bannai	bannai	PROPN
ap-3493	259	18	-	-	PUNCT
ap-3493	259	19	ito	ito	PROPN
ap-3493	259	20	polynomials	polynomial	NOUN
ap-3493	259	21	.	.	PUNCT
ap-3493	260	1	advances	advance	NOUN
ap-3493	260	2	in	in	ADP
ap-3493	260	3	mathematics	mathematics	PROPN
ap-3493	260	4	229	229	NUM
ap-3493	260	5	,	,	PUNCT
ap-3493	260	6	2123	2123	NUM
ap-3493	260	7	-	-	SYM
ap-3493	260	8	2158	2158	NUM
ap-3493	260	9	,	,	PUNCT
ap-3493	260	10	2012	2012	NUM
ap-3493	260	11	.	.	PUNCT
ap-3493	261	1	[	[	X
ap-3493	261	2	18	18	NUM
ap-3493	261	3	]	]	X
ap-3493	261	4	v.x	v.x	PROPN
ap-3493	261	5	.	.	PROPN
ap-3493	261	6	genest	genest	PROPN
ap-3493	261	7	,	,	PUNCT
ap-3493	261	8	l.	l.	PROPN
ap-3493	261	9	vinet	vinet	PROPN
ap-3493	261	10	,	,	PUNCT
ap-3493	261	11	a.	a.	PROPN
ap-3493	261	12	zhedanov	zhedanov	PROPN
ap-3493	261	13	,	,	PUNCT
ap-3493	261	14	bispectrality	bispectrality	NOUN
ap-3493	261	15	of	of	ADP
ap-3493	261	16	the	the	DET
ap-3493	261	17	complementary	complementary	ADJ
ap-3493	261	18	bannai	bannai	PROPN
ap-3493	261	19	-	-	PUNCT
ap-3493	261	20	ito	ito	PROPN
ap-3493	261	21	polynomials	polynomial	NOUN
ap-3493	261	22	.	.	PUNCT
ap-3493	262	1	sigma	sigma	PROPN
ap-3493	262	2	9:18	9:18	NUM
ap-3493	262	3	-	-	SYM
ap-3493	262	4	38	38	NUM
ap-3493	262	5	,	,	PUNCT
ap-3493	262	6	2013	2013	NUM
ap-3493	262	7	.	.	PUNCT
ap-3493	263	1	[	[	X
ap-3493	263	2	19	19	NUM
ap-3493	263	3	]	]	X
ap-3493	263	4	v.x	v.x	PROPN
ap-3493	263	5	.	.	PROPN
ap-3493	263	6	genest	genest	PROPN
ap-3493	263	7	,	,	PUNCT
ap-3493	263	8	l.	l.	PROPN
ap-3493	263	9	vinet	vinet	PROPN
ap-3493	263	10	,	,	PUNCT
ap-3493	263	11	a.	a.	PROPN
ap-3493	263	12	zhedanov	zhedanov	PROPN
ap-3493	263	13	,	,	PUNCT
ap-3493	263	14	a	a	DET
ap-3493	263	15	"	"	PUNCT
ap-3493	263	16	continuous	continuous	ADJ
ap-3493	263	17	"	"	PUNCT
ap-3493	263	18	limit	limit	NOUN
ap-3493	263	19	of	of	ADP
ap-3493	263	20	the	the	DET
ap-3493	263	21	complementary	complementary	ADJ
ap-3493	263	22	bannai	bannai	PROPN
ap-3493	263	23	-	-	PUNCT
ap-3493	263	24	ito	ito	PROPN
ap-3493	263	25	polynomials	polynomial	NOUN
ap-3493	263	26	:	:	PUNCT
ap-3493	263	27	chihara	chihara	NOUN
ap-3493	263	28	polynomials	polynomial	NOUN
ap-3493	263	29	.	.	PUNCT
ap-3493	264	1	sigma	sigma	PROPN
ap-3493	264	2	10:38	10:38	NUM
ap-3493	264	3	-	-	SYM
ap-3493	264	4	46	46	NUM
ap-3493	264	5	,	,	PUNCT
ap-3493	264	6	2014	2014	NUM
ap-3493	264	7	.	.	PUNCT
ap-3493	265	1	[	[	X
ap-3493	265	2	20	20	NUM
ap-3493	265	3	]	]	SYM
ap-3493	265	4	v.x	v.x	PROPN
ap-3493	265	5	.	.	PROPN
ap-3493	265	6	genest	genest	PROPN
ap-3493	265	7	,	,	PUNCT
ap-3493	265	8	l.	l.	PROPN
ap-3493	265	9	vinet	vinet	PROPN
ap-3493	265	10	,	,	PUNCT
ap-3493	265	11	a.	a.	PROPN
ap-3493	265	12	zhedanov	zhedanov	PROPN
ap-3493	265	13	,	,	PUNCT
ap-3493	265	14	embeddings	embedding	NOUN
ap-3493	265	15	of	of	ADP
ap-3493	265	16	the	the	DET
ap-3493	265	17	racah	racah	NOUN
ap-3493	265	18	algebra	algebra	NOUN
ap-3493	265	19	into	into	ADP
ap-3493	265	20	the	the	DET
ap-3493	265	21	bannai	bannai	PROPN
ap-3493	265	22	-	-	PUNCT
ap-3493	265	23	ito	ito	PROPN
ap-3493	265	24	algebra	algebra	PROPN
ap-3493	265	25	.	.	PUNCT
ap-3493	266	1	sigma	sigma	PROPN
ap-3493	266	2	11:50	11:50	NUM
ap-3493	266	3	-	-	SYM
ap-3493	266	4	61	61	NUM
ap-3493	266	5	,	,	PUNCT
ap-3493	266	6	2015	2015	NUM
ap-3493	266	7	.	.	PUNCT
ap-3493	267	1	172	172	NUM
ap-3493	267	2	acta	acta	PROPN
ap-3493	267	3	polytechnica	polytechnica	PROPN
ap-3493	267	4	56(3):166–172	56(3):166–172	PROPN
ap-3493	267	5	,	,	PUNCT
ap-3493	267	6	2016	2016	NUM
ap-3493	267	7	1	1	NUM
ap-3493	267	8	introduction	introduction	NOUN
ap-3493	267	9	2	2	NUM
ap-3493	267	10	a	a	DET
ap-3493	267	11	superintegrable	superintegrable	ADJ
ap-3493	267	12	model	model	NOUN
ap-3493	267	13	on	on	ADP
ap-3493	267	14	s3	s3	PROPN
ap-3493	267	15	3	3	NUM
ap-3493	267	16	algebraic	algebraic	ADJ
ap-3493	267	17	construction	construction	NOUN
ap-3493	267	18	from	from	ADP
ap-3493	267	19	osp(1|2	osp(1|2	PROPN
ap-3493	267	20	)	)	PUNCT
ap-3493	267	21	4	4	NUM
ap-3493	267	22	wavefunctions	wavefunction	NOUN
ap-3493	267	23	5	5	NUM
ap-3493	267	24	conclusion	conclusion	NOUN
ap-3493	267	25	acknowledgements	acknowledgement	NOUN
ap-3493	267	26	references	reference	NOUN