id	sid	tid	token	lemma	pos
ap-1872	1	1	acta	acta	PROPN
ap-1872	1	2	polytechnica	polytechnica	PROPN
ap-1872	1	3	doi:10.14311	doi:10.14311	PROPN
ap-1872	1	4	/	/	PROPN
ap-1872	1	5	ap.2013.53.0462	ap.2013.53.0462	PROPN
ap-1872	1	6	acta	acta	PROPN
ap-1872	1	7	polytechnica	polytechnica	PROPN
ap-1872	1	8	53(5):462–469	53(5):462–469	PROPN
ap-1872	1	9	,	,	PUNCT
ap-1872	1	10	2013	2013	NUM
ap-1872	1	11	©	©	PROPN
ap-1872	1	12	czech	czech	PROPN
ap-1872	1	13	technical	technical	PROPN
ap-1872	1	14	university	university	PROPN
ap-1872	1	15	in	in	ADP
ap-1872	1	16	prague	prague	PROPN
ap-1872	1	17	,	,	PUNCT
ap-1872	1	18	2013	2013	NUM
ap-1872	1	19	available	available	ADJ
ap-1872	1	20	online	online	ADV
ap-1872	1	21	at	at	ADP
ap-1872	1	22	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-1872	1	23	gln+1	gln+1	NOUN
ap-1872	1	24	algebra	algebra	NOUN
ap-1872	1	25	of	of	ADP
ap-1872	1	26	matrix	matrix	NOUN
ap-1872	1	27	differential	differential	NOUN
ap-1872	1	28	operators	operator	NOUN
ap-1872	1	29	and	and	CCONJ
ap-1872	1	30	matrix	matrix	NOUN
ap-1872	1	31	quasi	quasi	ADJ
ap-1872	1	32	-	-	ADJ
ap-1872	1	33	exactly	exactly	ADV
ap-1872	1	34	-	-	PUNCT
ap-1872	1	35	solvable	solvable	ADJ
ap-1872	1	36	problems	problem	NOUN
ap-1872	1	37	yuri	yuri	PROPN
ap-1872	1	38	f.	f.	PROPN
ap-1872	1	39	smirnov	smirnov	PROPN
ap-1872	1	40	(	(	PUNCT
ap-1872	1	41	deceased	deceased	ADJ
ap-1872	1	42	)	)	PUNCT
ap-1872	1	43	,	,	PUNCT
ap-1872	1	44	alexander	alexander	PROPN
ap-1872	1	45	v.	v.	PROPN
ap-1872	1	46	turbiner∗	turbiner∗	PROPN
ap-1872	1	47	instituto	instituto	PROPN
ap-1872	1	48	de	de	PROPN
ap-1872	1	49	ciencias	ciencias	PROPN
ap-1872	1	50	nucleares	nucleare	NOUN
ap-1872	1	51	,	,	PUNCT
ap-1872	1	52	universidad	universidad	PROPN
ap-1872	1	53	nacional	nacional	PROPN
ap-1872	1	54	autónoma	autónoma	PROPN
ap-1872	1	55	de	de	PROPN
ap-1872	1	56	méxico	méxico	PROPN
ap-1872	1	57	,	,	PUNCT
ap-1872	1	58	apartado	apartado	X
ap-1872	1	59	postal	postal	ADJ
ap-1872	1	60	70	70	NUM
ap-1872	1	61	-	-	SYM
ap-1872	1	62	543	543	NUM
ap-1872	1	63	,	,	PUNCT
ap-1872	1	64	04510	04510	NUM
ap-1872	1	65	méxico	méxico	PROPN
ap-1872	1	66	,	,	PUNCT
ap-1872	1	67	d.f	d.f	PROPN
ap-1872	1	68	.	.	PROPN
ap-1872	1	69	,	,	PUNCT
ap-1872	1	70	mexico	mexico	PROPN
ap-1872	1	71	∗	∗	VERB
ap-1872	1	72	corresponding	correspond	VERB
ap-1872	1	73	author	author	NOUN
ap-1872	1	74	:	:	PUNCT
ap-1872	1	75	turbiner@nucleares.unam.mx	turbiner@nucleares.unam.mx	DET
ap-1872	1	76	abstract	abstract	ADJ
ap-1872	1	77	.	.	PUNCT
ap-1872	2	1	the	the	DET
ap-1872	2	2	generators	generator	NOUN
ap-1872	2	3	of	of	ADP
ap-1872	2	4	the	the	DET
ap-1872	2	5	algebra	algebra	NOUN
ap-1872	2	6	gln+1	gln+1	ADJ
ap-1872	2	7	in	in	ADP
ap-1872	2	8	the	the	DET
ap-1872	2	9	form	form	NOUN
ap-1872	2	10	of	of	ADP
ap-1872	2	11	differential	differential	ADJ
ap-1872	2	12	operators	operator	NOUN
ap-1872	2	13	of	of	ADP
ap-1872	2	14	the	the	DET
ap-1872	2	15	first	first	ADJ
ap-1872	2	16	order	order	NOUN
ap-1872	2	17	acting	act	VERB
ap-1872	2	18	on	on	ADP
ap-1872	2	19	rn	rn	PROPN
ap-1872	2	20	with	with	ADP
ap-1872	2	21	matrix	matrix	NOUN
ap-1872	2	22	coefficients	coefficient	NOUN
ap-1872	2	23	are	be	AUX
ap-1872	2	24	explicitly	explicitly	ADV
ap-1872	2	25	written	write	VERB
ap-1872	2	26	.	.	PUNCT
ap-1872	3	1	the	the	DET
ap-1872	3	2	algebraic	algebraic	ADJ
ap-1872	3	3	hamiltonians	hamiltonian	NOUN
ap-1872	3	4	for	for	ADP
ap-1872	3	5	matrix	matrix	NOUN
ap-1872	3	6	generalization	generalization	NOUN
ap-1872	3	7	of	of	ADP
ap-1872	3	8	3−body	3−body	NUM
ap-1872	3	9	calogero	calogero	NOUN
ap-1872	3	10	and	and	CCONJ
ap-1872	3	11	sutherland	sutherland	NOUN
ap-1872	3	12	models	model	NOUN
ap-1872	3	13	are	be	AUX
ap-1872	3	14	presented	present	VERB
ap-1872	3	15	.	.	PUNCT
ap-1872	4	1	keywords	keyword	NOUN
ap-1872	4	2	:	:	PUNCT
ap-1872	4	3	algebra	algebra	NOUN
ap-1872	4	4	of	of	ADP
ap-1872	4	5	differential	differential	ADJ
ap-1872	4	6	operators	operator	NOUN
ap-1872	4	7	,	,	PUNCT
ap-1872	4	8	exactly	exactly	ADV
ap-1872	4	9	-	-	PUNCT
ap-1872	4	10	solvable	solvable	ADJ
ap-1872	4	11	problems	problem	NOUN
ap-1872	4	12	.	.	PUNCT
ap-1872	5	1	submitted	submit	VERB
ap-1872	5	2	:	:	PUNCT
ap-1872	5	3	13	13	NUM
ap-1872	5	4	may	may	PROPN
ap-1872	5	5	2013	2013	NUM
ap-1872	5	6	.	.	PUNCT
ap-1872	6	1	accepted	accept	VERB
ap-1872	6	2	:	:	PUNCT
ap-1872	6	3	6	6	NUM
ap-1872	6	4	june	june	PROPN
ap-1872	6	5	2013	2013	NUM
ap-1872	6	6	.	.	PUNCT
ap-1872	7	1	1	1	X
ap-1872	7	2	.	.	X
ap-1872	7	3	introduction	introduction	NOUN
ap-1872	7	4	this	this	DET
ap-1872	7	5	work	work	NOUN
ap-1872	7	6	has	have	VERB
ap-1872	7	7	a	a	DET
ap-1872	7	8	certain	certain	ADJ
ap-1872	7	9	history	history	NOUN
ap-1872	7	10	related	relate	VERB
ap-1872	7	11	to	to	ADP
ap-1872	7	12	miloslav	miloslav	NOUN
ap-1872	7	13	havlicek	havlicek	NOUN
ap-1872	7	14	.	.	PUNCT
ap-1872	8	1	on	on	ADP
ap-1872	8	2	the	the	DET
ap-1872	8	3	important	important	ADJ
ap-1872	8	4	occasion	occasion	NOUN
ap-1872	8	5	of	of	ADP
ap-1872	8	6	miloslav	miloslav	NOUN
ap-1872	8	7	’s	’s	PART
ap-1872	8	8	75th	75th	ADJ
ap-1872	8	9	birthday	birthday	NOUN
ap-1872	8	10	,	,	PUNCT
ap-1872	8	11	we	we	PRON
ap-1872	8	12	think	think	VERB
ap-1872	8	13	this	this	DET
ap-1872	8	14	story	story	NOUN
ap-1872	8	15	should	should	AUX
ap-1872	8	16	be	be	AUX
ap-1872	8	17	revealed	reveal	VERB
ap-1872	8	18	.	.	PUNCT
ap-1872	9	1	about	about	ADP
ap-1872	9	2	25	25	NUM
ap-1872	9	3	years	year	NOUN
ap-1872	9	4	ago	ago	ADV
ap-1872	9	5	,	,	PUNCT
ap-1872	9	6	when	when	SCONJ
ap-1872	9	7	quasi	quasi	ADJ
ap-1872	9	8	-	-	ADJ
ap-1872	9	9	exactlysolvable	exactlysolvable	ADJ
ap-1872	9	10	schroedinger	schroedinger	NOUN
ap-1872	9	11	equations	equation	NOUN
ap-1872	9	12	with	with	ADP
ap-1872	9	13	the	the	DET
ap-1872	9	14	hidden	hide	VERB
ap-1872	9	15	algebra	algebra	NOUN
ap-1872	9	16	sl2	sl2	PROPN
ap-1872	9	17	were	be	AUX
ap-1872	9	18	discovered	discover	VERB
ap-1872	9	19	[	[	X
ap-1872	9	20	1	1	NUM
ap-1872	9	21	]	]	PUNCT
ap-1872	9	22	,	,	PUNCT
ap-1872	9	23	one	one	NUM
ap-1872	9	24	of	of	ADP
ap-1872	9	25	the	the	DET
ap-1872	9	26	present	present	ADJ
ap-1872	9	27	authors	author	NOUN
ap-1872	9	28	(	(	PUNCT
ap-1872	9	29	avt	avt	PROPN
ap-1872	9	30	)	)	PUNCT
ap-1872	9	31	approached	approach	VERB
ap-1872	9	32	israel	israel	PROPN
ap-1872	9	33	m.	m.	NOUN
ap-1872	9	34	gelfand	gelfand	PROPN
ap-1872	9	35	and	and	CCONJ
ap-1872	9	36	asked	ask	VERB
ap-1872	9	37	about	about	ADP
ap-1872	9	38	the	the	DET
ap-1872	9	39	existence	existence	NOUN
ap-1872	9	40	of	of	ADP
ap-1872	9	41	the	the	DET
ap-1872	9	42	algebra	algebra	NOUN
ap-1872	9	43	gln+1	gln+1	NOUN
ap-1872	9	44	of	of	ADP
ap-1872	9	45	matrix	matrix	NOUN
ap-1872	9	46	differential	differential	NOUN
ap-1872	9	47	operators	operator	NOUN
ap-1872	9	48	.	.	PUNCT
ap-1872	10	1	instead	instead	ADV
ap-1872	10	2	of	of	ADP
ap-1872	10	3	giving	give	VERB
ap-1872	10	4	an	an	DET
ap-1872	10	5	answer	answer	NOUN
ap-1872	10	6	,	,	PUNCT
ap-1872	10	7	israel	israel	PROPN
ap-1872	10	8	moiseevich	moiseevich	PROPN
ap-1872	10	9	said	say	VERB
ap-1872	10	10	that	that	SCONJ
ap-1872	10	11	m.	m.	NOUN
ap-1872	10	12	havlicek	havlicek	PROPN
ap-1872	10	13	knows	know	VERB
ap-1872	10	14	the	the	DET
ap-1872	10	15	answer	answer	NOUN
ap-1872	10	16	and	and	CCONJ
ap-1872	10	17	that	that	SCONJ
ap-1872	10	18	he	he	PRON
ap-1872	10	19	must	must	AUX
ap-1872	10	20	be	be	AUX
ap-1872	10	21	asked	ask	VERB
ap-1872	10	22	.	.	PUNCT
ap-1872	11	1	a	a	DET
ap-1872	11	2	set	set	NOUN
ap-1872	11	3	of	of	ADP
ap-1872	11	4	dubna	dubna	PROPN
ap-1872	11	5	preprints	preprint	NOUN
ap-1872	11	6	was	be	AUX
ap-1872	11	7	given	give	VERB
ap-1872	11	8	(	(	PUNCT
ap-1872	11	9	see	see	VERB
ap-1872	11	10	[	[	X
ap-1872	11	11	2	2	NUM
ap-1872	11	12	,	,	PUNCT
ap-1872	11	13	3	3	NUM
ap-1872	11	14	]	]	PUNCT
ap-1872	11	15	and	and	CCONJ
ap-1872	11	16	reference	reference	NOUN
ap-1872	11	17	therein	therein	ADV
ap-1872	11	18	)	)	PUNCT
ap-1872	11	19	.	.	PUNCT
ap-1872	12	1	then	then	ADV
ap-1872	12	2	avt	avt	PROPN
ap-1872	12	3	studied	study	VERB
ap-1872	12	4	them	they	PRON
ap-1872	12	5	for	for	ADP
ap-1872	12	6	many	many	ADJ
ap-1872	12	7	years	year	NOUN
ap-1872	12	8	,	,	PUNCT
ap-1872	12	9	at	at	ADP
ap-1872	12	10	first	first	ADV
ap-1872	12	11	separately	separately	ADV
ap-1872	12	12	and	and	CCONJ
ap-1872	12	13	then	then	ADV
ap-1872	12	14	together	together	ADV
ap-1872	12	15	with	with	ADP
ap-1872	12	16	the	the	DET
ap-1872	12	17	first	first	ADJ
ap-1872	12	18	author	author	NOUN
ap-1872	12	19	(	(	PUNCT
ap-1872	12	20	yufs	yufs	NOUN
ap-1872	12	21	)	)	PUNCT
ap-1872	12	22	,	,	PUNCT
ap-1872	12	23	who	who	PRON
ap-1872	12	24	also	also	ADV
ap-1872	12	25	happened	happen	VERB
ap-1872	12	26	to	to	PART
ap-1872	12	27	have	have	VERB
ap-1872	12	28	the	the	DET
ap-1872	12	29	same	same	ADJ
ap-1872	12	30	set	set	NOUN
ap-1872	12	31	of	of	ADP
ap-1872	12	32	preprints	preprint	NOUN
ap-1872	12	33	.	.	PUNCT
ap-1872	13	1	the	the	DET
ap-1872	13	2	results	result	NOUN
ap-1872	13	3	of	of	ADP
ap-1872	13	4	these	these	DET
ap-1872	13	5	studies	study	NOUN
ap-1872	13	6	are	be	AUX
ap-1872	13	7	presented	present	VERB
ap-1872	13	8	below	below	ADV
ap-1872	13	9	.	.	PUNCT
ap-1872	14	1	while	while	SCONJ
ap-1872	14	2	carrying	carry	VERB
ap-1872	14	3	out	out	ADP
ap-1872	14	4	these	these	DET
ap-1872	14	5	studies	study	NOUN
ap-1872	14	6	,	,	PUNCT
ap-1872	14	7	we	we	PRON
ap-1872	14	8	always	always	ADV
ap-1872	14	9	kept	keep	VERB
ap-1872	14	10	in	in	ADP
ap-1872	14	11	mind	mind	NOUN
ap-1872	14	12	that	that	SCONJ
ap-1872	14	13	a	a	DET
ap-1872	14	14	constructive	constructive	ADJ
ap-1872	14	15	answer	answer	NOUN
ap-1872	14	16	exists	exist	VERB
ap-1872	14	17	and	and	CCONJ
ap-1872	14	18	is	be	AUX
ap-1872	14	19	known	know	VERB
ap-1872	14	20	to	to	AUX
ap-1872	14	21	miloslav	miloslav	VERB
ap-1872	14	22	.	.	PUNCT
ap-1872	15	1	thus	thus	ADV
ap-1872	15	2	,	,	PUNCT
ap-1872	15	3	we	we	PRON
ap-1872	15	4	are	be	AUX
ap-1872	15	5	certain	certain	ADJ
ap-1872	15	6	that	that	SCONJ
ap-1872	15	7	at	at	ADV
ap-1872	15	8	least	least	ADJ
ap-1872	15	9	some	some	PRON
ap-1872	15	10	of	of	ADP
ap-1872	15	11	results	result	NOUN
ap-1872	15	12	presented	present	VERB
ap-1872	15	13	here	here	ADV
ap-1872	15	14	are	be	AUX
ap-1872	15	15	known	know	VERB
ap-1872	15	16	to	to	PART
ap-1872	15	17	miloslav	miloslav	VERB
ap-1872	15	18	.	.	PUNCT
ap-1872	16	1	having	have	VERB
ap-1872	16	2	difficulty	difficulty	NOUN
ap-1872	16	3	to	to	PART
ap-1872	16	4	understand	understand	VERB
ap-1872	16	5	what	what	PRON
ap-1872	16	6	is	be	AUX
ap-1872	16	7	written	write	VERB
ap-1872	16	8	in	in	ADP
ap-1872	16	9	the	the	DET
ap-1872	16	10	texts	text	NOUN
ap-1872	16	11	we	we	PRON
ap-1872	16	12	did	do	AUX
ap-1872	16	13	not	not	PART
ap-1872	16	14	know	know	VERB
ap-1872	16	15	what	what	PRON
ap-1872	16	16	he	he	PRON
ap-1872	16	17	really	really	ADV
ap-1872	16	18	knew	know	VERB
ap-1872	16	19	,	,	PUNCT
ap-1872	16	20	and	and	CCONJ
ap-1872	16	21	were	be	AUX
ap-1872	16	22	therefore	therefore	ADV
ap-1872	16	23	unable	unable	ADJ
ap-1872	16	24	to	to	PART
ap-1872	16	25	indicate	indicate	VERB
ap-1872	16	26	it	it	PRON
ap-1872	16	27	in	in	ADP
ap-1872	16	28	our	our	PRON
ap-1872	16	29	text	text	NOUN
ap-1872	16	30	.	.	PUNCT
ap-1872	17	1	our	our	PRON
ap-1872	17	2	main	main	ADJ
ap-1872	17	3	goal	goal	NOUN
ap-1872	17	4	is	be	AUX
ap-1872	17	5	to	to	PART
ap-1872	17	6	find	find	VERB
ap-1872	17	7	a	a	DET
ap-1872	17	8	mixed	mixed	ADJ
ap-1872	17	9	representation	representation	NOUN
ap-1872	17	10	of	of	ADP
ap-1872	17	11	the	the	DET
ap-1872	17	12	algebra	algebra	NOUN
ap-1872	17	13	gln+1	gln+1	ADJ
ap-1872	17	14	which	which	PRON
ap-1872	17	15	contains	contain	VERB
ap-1872	17	16	both	both	DET
ap-1872	17	17	matrices	matrix	NOUN
ap-1872	17	18	and	and	CCONJ
ap-1872	17	19	differential	differential	ADJ
ap-1872	17	20	operators	operator	NOUN
ap-1872	17	21	in	in	ADP
ap-1872	17	22	a	a	DET
ap-1872	17	23	non	non	ADJ
ap-1872	17	24	-	-	ADJ
ap-1872	17	25	trivial	trivial	ADJ
ap-1872	17	26	way	way	NOUN
ap-1872	17	27	.	.	PUNCT
ap-1872	18	1	then	then	ADV
ap-1872	18	2	to	to	PART
ap-1872	18	3	generalize	generalize	VERB
ap-1872	18	4	it	it	PRON
ap-1872	18	5	to	to	ADP
ap-1872	18	6	a	a	DET
ap-1872	18	7	polynomial	polynomial	ADJ
ap-1872	18	8	algebra	algebra	NOUN
ap-1872	18	9	which	which	PRON
ap-1872	18	10	we	we	PRON
ap-1872	18	11	call	call	VERB
ap-1872	18	12	g(m	g(m	NOUN
ap-1872	18	13	)	)	PUNCT
ap-1872	18	14	(	(	PUNCT
ap-1872	18	15	see	see	VERB
ap-1872	18	16	below	below	ADV
ap-1872	18	17	,	,	PUNCT
ap-1872	18	18	section	section	NOUN
ap-1872	18	19	4	4	NUM
ap-1872	18	20	)	)	PUNCT
ap-1872	18	21	.	.	PUNCT
ap-1872	19	1	another	another	DET
ap-1872	19	2	goal	goal	NOUN
ap-1872	19	3	is	be	AUX
ap-1872	19	4	to	to	PART
ap-1872	19	5	apply	apply	VERB
ap-1872	19	6	the	the	DET
ap-1872	19	7	obtained	obtain	VERB
ap-1872	19	8	representations	representation	NOUN
ap-1872	19	9	for	for	ADP
ap-1872	19	10	a	a	DET
ap-1872	19	11	construction	construction	NOUN
ap-1872	19	12	of	of	ADP
ap-1872	19	13	the	the	DET
ap-1872	19	14	algebraic	algebraic	ADJ
ap-1872	19	15	forms	form	NOUN
ap-1872	19	16	of	of	ADP
ap-1872	19	17	(	(	PUNCT
ap-1872	19	18	quasi)-exactly	quasi)-exactly	ADV
ap-1872	19	19	-	-	PUNCT
ap-1872	19	20	solvable	solvable	ADJ
ap-1872	19	21	matrix	matrix	NOUN
ap-1872	19	22	hamiltonians	hamiltonian	NOUN
ap-1872	19	23	.	.	PUNCT
ap-1872	20	1	2	2	X
ap-1872	20	2	.	.	X
ap-1872	20	3	the	the	DET
ap-1872	20	4	algebra	algebra	PROPN
ap-1872	20	5	gln	gln	NOUN
ap-1872	20	6	in	in	ADP
ap-1872	20	7	mixed	mixed	ADJ
ap-1872	20	8	representation	representation	NOUN
ap-1872	20	9	let	let	VERB
ap-1872	20	10	us	we	PRON
ap-1872	20	11	take	take	VERB
ap-1872	20	12	the	the	DET
ap-1872	20	13	algebra	algebra	NOUN
ap-1872	20	14	gln	gln	NOUN
ap-1872	20	15	and	and	CCONJ
ap-1872	20	16	consider	consider	VERB
ap-1872	20	17	the	the	DET
ap-1872	20	18	vector	vector	NOUN
ap-1872	20	19	field	field	NOUN
ap-1872	20	20	representation	representation	NOUN
ap-1872	20	21	ẽij	ẽij	PROPN
ap-1872	20	22	=	=	SYM
ap-1872	20	23	xi∂j	xi∂j	PROPN
ap-1872	20	24	,	,	PUNCT
ap-1872	20	25	i	i	PRON
ap-1872	20	26	,	,	PUNCT
ap-1872	20	27	j	j	PROPN
ap-1872	20	28	=	=	SYM
ap-1872	20	29	1	1	NUM
ap-1872	20	30	,	,	PUNCT
ap-1872	20	31	.	.	PUNCT
ap-1872	20	32	.	.	PUNCT
ap-1872	20	33	.	.	PUNCT
ap-1872	21	1	n	n	X
ap-1872	21	2	,	,	PUNCT
ap-1872	21	3	x	x	PROPN
ap-1872	21	4	∈	∈	PROPN
ap-1872	21	5	rn	rn	PROPN
ap-1872	21	6	.	.	PROPN
ap-1872	22	1	(	(	PUNCT
ap-1872	22	2	1	1	X
ap-1872	22	3	)	)	PUNCT
ap-1872	22	4	it	it	PRON
ap-1872	22	5	obeys	obey	VERB
ap-1872	22	6	the	the	DET
ap-1872	22	7	canonical	canonical	ADJ
ap-1872	22	8	commutation	commutation	NOUN
ap-1872	22	9	relations	relation	NOUN
ap-1872	23	1	[	[	X
ap-1872	23	2	ẽij	ẽij	PROPN
ap-1872	23	3	,	,	PUNCT
ap-1872	23	4	ẽkl	ẽkl	PROPN
ap-1872	23	5	]	]	X
ap-1872	23	6	=	=	PUNCT
ap-1872	23	7	δjkẽil	δjkẽil	PROPN
ap-1872	23	8	−	−	PROPN
ap-1872	24	1	δilẽkj	δilẽkj	PROPN
ap-1872	24	2	.	.	PUNCT
ap-1872	25	1	(	(	PUNCT
ap-1872	25	2	2	2	X
ap-1872	25	3	)	)	PUNCT
ap-1872	25	4	on	on	ADP
ap-1872	25	5	the	the	DET
ap-1872	25	6	other	other	ADJ
ap-1872	25	7	hand	hand	NOUN
ap-1872	25	8	,	,	PUNCT
ap-1872	25	9	let	let	VERB
ap-1872	25	10	us	we	PRON
ap-1872	25	11	consider	consider	VERB
ap-1872	25	12	another	another	DET
ap-1872	25	13	representation	representation	NOUN
ap-1872	25	14	mpm	mpm	NOUN
ap-1872	25	15	,	,	PUNCT
ap-1872	25	16	p	p	X
ap-1872	25	17	,	,	PUNCT
ap-1872	25	18	m	m	VERB
ap-1872	25	19	=	=	NOUN
ap-1872	25	20	1	1	NUM
ap-1872	25	21	,	,	PUNCT
ap-1872	25	22	.	.	PUNCT
ap-1872	25	23	.	.	PUNCT
ap-1872	26	1	.	.	PUNCT
ap-1872	27	1	,	,	PUNCT
ap-1872	27	2	n	n	PROPN
ap-1872	27	3	of	of	ADP
ap-1872	27	4	the	the	DET
ap-1872	27	5	algebra	algebra	NOUN
ap-1872	27	6	gln	gln	NOUN
ap-1872	27	7	in	in	ADP
ap-1872	27	8	terms	term	NOUN
ap-1872	27	9	of	of	ADP
ap-1872	27	10	some	some	DET
ap-1872	27	11	operators	operator	NOUN
ap-1872	27	12	(	(	PUNCT
ap-1872	27	13	matrix	matrix	NOUN
ap-1872	27	14	,	,	PUNCT
ap-1872	27	15	finite	finite	NOUN
ap-1872	27	16	-	-	NOUN
ap-1872	27	17	difference	difference	NOUN
ap-1872	27	18	,	,	PUNCT
ap-1872	27	19	etc	etc	X
ap-1872	27	20	)	)	PUNCT
ap-1872	27	21	with	with	ADP
ap-1872	27	22	the	the	DET
ap-1872	27	23	condition	condition	NOUN
ap-1872	27	24	that	that	SCONJ
ap-1872	27	25	all	all	DET
ap-1872	27	26	‘	'	PUNCT
ap-1872	27	27	cross	cros	NOUN
ap-1872	27	28	-	-	NOUN
ap-1872	27	29	commutators	commutator	NOUN
ap-1872	27	30	’	'	PUNCT
ap-1872	27	31	between	between	ADP
ap-1872	27	32	these	these	DET
ap-1872	27	33	two	two	NUM
ap-1872	27	34	representations	representation	NOUN
ap-1872	27	35	vanish	vanish	VERB
ap-1872	27	36	[	[	X
ap-1872	27	37	ẽij	ẽij	PROPN
ap-1872	27	38	,	,	PUNCT
ap-1872	27	39	mpm	mpm	NOUN
ap-1872	27	40	]	]	X
ap-1872	27	41	=	=	SYM
ap-1872	27	42	0	0	X
ap-1872	27	43	.	.	PUNCT
ap-1872	28	1	(	(	PUNCT
ap-1872	28	2	3	3	X
ap-1872	28	3	)	)	PUNCT
ap-1872	28	4	let	let	VERB
ap-1872	28	5	us	we	PRON
ap-1872	28	6	choosempm	choosempm	VERB
ap-1872	28	7	to	to	PART
ap-1872	28	8	obey	obey	VERB
ap-1872	28	9	the	the	DET
ap-1872	28	10	canonical	canonical	ADJ
ap-1872	28	11	commutation	commutation	NOUN
ap-1872	28	12	relations	relation	NOUN
ap-1872	28	13	[	[	X
ap-1872	28	14	mij	mij	X
ap-1872	28	15	,	,	PUNCT
ap-1872	28	16	mkl	mkl	PROPN
ap-1872	28	17	]	]	X
ap-1872	28	18	=	=	SYM
ap-1872	28	19	δjkmil	δjkmil	NOUN
ap-1872	28	20	−	−	PROPN
ap-1872	28	21	δilmkj	δilmkj	NOUN
ap-1872	28	22	,	,	PUNCT
ap-1872	28	23	(	(	PUNCT
ap-1872	28	24	4	4	NUM
ap-1872	28	25	)	)	PUNCT
ap-1872	28	26	(	(	PUNCT
ap-1872	28	27	cf	cf	NOUN
ap-1872	28	28	.	.	PUNCT
ap-1872	29	1	(	(	PUNCT
ap-1872	29	2	2	2	NUM
ap-1872	29	3	)	)	PUNCT
ap-1872	29	4	)	)	PUNCT
ap-1872	29	5	.	.	PUNCT
ap-1872	30	1	it	it	PRON
ap-1872	30	2	is	be	AUX
ap-1872	30	3	evident	evident	ADJ
ap-1872	30	4	that	that	SCONJ
ap-1872	30	5	the	the	DET
ap-1872	30	6	sum	sum	NOUN
ap-1872	30	7	of	of	ADP
ap-1872	30	8	these	these	DET
ap-1872	30	9	two	two	NUM
ap-1872	30	10	representations	representation	NOUN
ap-1872	30	11	is	be	AUX
ap-1872	30	12	also	also	ADV
ap-1872	30	13	the	the	DET
ap-1872	30	14	representation	representation	NOUN
ap-1872	30	15	,	,	PUNCT
ap-1872	30	16	eij	eij	PROPN
ap-1872	30	17	≡	≡	PROPN
ap-1872	30	18	ẽij	ẽij	PROPN
ap-1872	31	1	+	+	PROPN
ap-1872	31	2	mij	mij	NOUN
ap-1872	31	3	∈	∈	PROPN
ap-1872	31	4	gln	gln	NOUN
ap-1872	31	5	.	.	PUNCT
ap-1872	32	1	(	(	PUNCT
ap-1872	32	2	5	5	X
ap-1872	32	3	)	)	PUNCT
ap-1872	32	4	now	now	ADV
ap-1872	32	5	we	we	PRON
ap-1872	32	6	consider	consider	VERB
ap-1872	32	7	an	an	DET
ap-1872	32	8	embedding	embedding	NOUN
ap-1872	32	9	of	of	ADP
ap-1872	32	10	gln	gln	NOUN
ap-1872	32	11	⊂	⊂	PROPN
ap-1872	32	12	gln+1	gln+1	VERB
ap-1872	32	13	trying	try	VERB
ap-1872	32	14	to	to	PART
ap-1872	32	15	complement	complement	VERB
ap-1872	32	16	the	the	DET
ap-1872	32	17	representation	representation	NOUN
ap-1872	32	18	(	(	PUNCT
ap-1872	32	19	1	1	NUM
ap-1872	32	20	)	)	PUNCT
ap-1872	32	21	of	of	ADP
ap-1872	32	22	the	the	DET
ap-1872	32	23	algebra	algebra	NOUN
ap-1872	32	24	gln	gln	VERB
ap-1872	32	25	up	up	ADP
ap-1872	32	26	to	to	ADP
ap-1872	32	27	the	the	DET
ap-1872	32	28	representation	representation	NOUN
ap-1872	32	29	of	of	ADP
ap-1872	32	30	the	the	DET
ap-1872	32	31	algebra	algebra	NOUN
ap-1872	32	32	gln+1	gln+1	NOUN
ap-1872	32	33	.	.	PUNCT
ap-1872	33	1	in	in	ADP
ap-1872	33	2	principle	principle	NOUN
ap-1872	33	3	,	,	PUNCT
ap-1872	33	4	this	this	PRON
ap-1872	33	5	can	can	AUX
ap-1872	33	6	be	be	AUX
ap-1872	33	7	done	do	VERB
ap-1872	33	8	due	due	ADP
ap-1872	33	9	to	to	ADP
ap-1872	33	10	the	the	DET
ap-1872	33	11	existence	existence	NOUN
ap-1872	33	12	of	of	ADP
ap-1872	33	13	the	the	DET
ap-1872	33	14	weyl	weyl	VERB
ap-1872	33	15	-	-	ADJ
ap-1872	33	16	cartan	cartan	ADJ
ap-1872	33	17	decomposition	decomposition	NOUN
ap-1872	33	18	,	,	PUNCT
ap-1872	33	19	gln+1	gln+1	VERB
ap-1872	33	20	=	=	SYM
ap-1872	33	21	l⊕	l⊕	X
ap-1872	33	22	(	(	PUNCT
ap-1872	33	23	gln	gln	PROPN
ap-1872	33	24	⊕	⊕	PROPN
ap-1872	34	1	i)⊕	i)⊕	PROPN
ap-1872	34	2	u	u	NOUN
ap-1872	34	3	with	with	ADP
ap-1872	34	4	the	the	DET
ap-1872	34	5	property	property	NOUN
ap-1872	34	6	gln+1	gln+1	NOUN
ap-1872	34	7	=	=	SYM
ap-1872	34	8	lo	lo	PROPN
ap-1872	34	9	(	(	PUNCT
ap-1872	34	10	gln	gln	PROPN
ap-1872	34	11	⊕	⊕	PROPN
ap-1872	34	12	i	i	NOUN
ap-1872	34	13	)	)	PUNCT
ap-1872	34	14	n	n	PRON
ap-1872	34	15	u	u	NOUN
ap-1872	34	16	,	,	PUNCT
ap-1872	34	17	(	(	PUNCT
ap-1872	34	18	6	6	NUM
ap-1872	34	19	)	)	PUNCT
ap-1872	34	20	where	where	SCONJ
ap-1872	34	21	l(u	l(u	PROPN
ap-1872	34	22	)	)	PUNCT
ap-1872	34	23	is	be	AUX
ap-1872	34	24	the	the	DET
ap-1872	34	25	commutative	commutative	ADJ
ap-1872	34	26	algebra	algebra	NOUN
ap-1872	34	27	of	of	ADP
ap-1872	34	28	the	the	DET
ap-1872	34	29	lowering	lower	VERB
ap-1872	34	30	(	(	PUNCT
ap-1872	34	31	raising	raise	VERB
ap-1872	34	32	)	)	PUNCT
ap-1872	34	33	generators	generator	NOUN
ap-1872	34	34	with	with	ADP
ap-1872	34	35	the	the	DET
ap-1872	34	36	property	property	NOUN
ap-1872	35	1	[	[	X
ap-1872	35	2	l	l	NOUN
ap-1872	35	3	,	,	PUNCT
ap-1872	35	4	u	u	NOUN
ap-1872	35	5	]	]	X
ap-1872	35	6	=	=	PUNCT
ap-1872	35	7	gln⊕	gln⊕	PROPN
ap-1872	35	8	i.	i.	NOUN
ap-1872	35	9	thus	thus	ADV
ap-1872	35	10	,	,	PUNCT
ap-1872	35	11	it	it	PRON
ap-1872	35	12	realizes	realize	VERB
ap-1872	35	13	a	a	DET
ap-1872	35	14	property	property	NOUN
ap-1872	35	15	of	of	ADP
ap-1872	35	16	the	the	DET
ap-1872	35	17	gauss	gauss	ADJ
ap-1872	35	18	decomposition	decomposition	NOUN
ap-1872	35	19	of	of	ADP
ap-1872	35	20	gln+1	gln+1	PROPN
ap-1872	35	21	.	.	PUNCT
ap-1872	36	1	it	it	PRON
ap-1872	36	2	is	be	AUX
ap-1872	36	3	worth	worth	ADJ
ap-1872	36	4	emphasizing	emphasize	VERB
ap-1872	36	5	that	that	SCONJ
ap-1872	36	6	dim(l	dim(l	NOUN
ap-1872	36	7	)	)	PUNCT
ap-1872	36	8	=	=	SYM
ap-1872	36	9	dim(u	dim(u	X
ap-1872	36	10	)	)	PUNCT
ap-1872	36	11	=	=	VERB
ap-1872	36	12	n.	n.	NOUN
ap-1872	36	13	obviously	obviously	ADV
ap-1872	36	14	,	,	PUNCT
ap-1872	36	15	the	the	DET
ap-1872	36	16	lowering	lower	VERB
ap-1872	36	17	generators	generator	NOUN
ap-1872	36	18	(	(	PUNCT
ap-1872	36	19	of	of	ADP
ap-1872	36	20	negative	negative	ADJ
ap-1872	36	21	grading	grading	NOUN
ap-1872	36	22	)	)	PUNCT
ap-1872	36	23	from	from	ADP
ap-1872	36	24	l	l	NOUN
ap-1872	36	25	can	can	AUX
ap-1872	36	26	be	be	AUX
ap-1872	36	27	given	give	VERB
ap-1872	36	28	by	by	ADP
ap-1872	36	29	derivations	derivation	NOUN
ap-1872	36	30	t−	t−	PUNCT
ap-1872	37	1	i	i	PRON
ap-1872	37	2	=	=	SYM
ap-1872	37	3	∂i	∂i	PROPN
ap-1872	37	4	,	,	PUNCT
ap-1872	37	5	i	i	NOUN
ap-1872	37	6	=	=	NOUN
ap-1872	37	7	1	1	NUM
ap-1872	37	8	,	,	PUNCT
ap-1872	37	9	.	.	PUNCT
ap-1872	37	10	.	.	PUNCT
ap-1872	37	11	.	.	PUNCT
ap-1872	37	12	,	,	PUNCT
ap-1872	37	13	n	n	CCONJ
ap-1872	37	14	,	,	PUNCT
ap-1872	37	15	∂i	∂i	PROPN
ap-1872	37	16	≡	≡	PROPN
ap-1872	37	17	∂	∂	NUM
ap-1872	37	18	∂xi	∂xi	NOUN
ap-1872	37	19	,	,	PUNCT
ap-1872	37	20	(	(	PUNCT
ap-1872	37	21	7	7	NUM
ap-1872	37	22	)	)	PUNCT
ap-1872	37	23	(	(	PUNCT
ap-1872	37	24	see	see	VERB
ap-1872	37	25	e.g.	e.g.	ADV
ap-1872	37	26	[	[	X
ap-1872	37	27	5	5	NUM
ap-1872	37	28	]	]	PUNCT
ap-1872	37	29	)	)	PUNCT
ap-1872	37	30	when	when	SCONJ
ap-1872	37	31	assuming	assume	VERB
ap-1872	37	32	that	that	SCONJ
ap-1872	37	33	all	all	DET
ap-1872	37	34	commutators	commutator	NOUN
ap-1872	37	35	[	[	PUNCT
ap-1872	37	36	t−	t−	NOUN
ap-1872	37	37	i	i	PROPN
ap-1872	37	38	,	,	PUNCT
ap-1872	37	39	mpm	mpm	NOUN
ap-1872	37	40	]	]	X
ap-1872	37	41	=	=	SYM
ap-1872	37	42	0	0	NUM
ap-1872	37	43	,	,	PUNCT
ap-1872	37	44	(	(	PUNCT
ap-1872	37	45	8)	8)	NUM
ap-1872	37	46	462	462	NUM
ap-1872	37	47	http://dx.doi.org/10.14311/ap.2013.53.0462	http://dx.doi.org/10.14311/ap.2013.53.0462	DET
ap-1872	37	48	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-1872	37	49	vol	vol	NOUN
ap-1872	37	50	.	.	PUNCT
ap-1872	38	1	53	53	NUM
ap-1872	38	2	no	no	NOUN
ap-1872	38	3	.	.	PUNCT
ap-1872	39	1	5/2013	5/2013	NUM
ap-1872	39	2	gln+1	gln+1	VERB
ap-1872	39	3	algebra	algebra	NOUN
ap-1872	39	4	of	of	ADP
ap-1872	39	5	matrix	matrix	NOUN
ap-1872	39	6	differential	differential	NOUN
ap-1872	39	7	operators	operator	NOUN
ap-1872	39	8	vanish	vanish	VERB
ap-1872	39	9	.	.	PUNCT
ap-1872	40	1	this	this	PRON
ap-1872	40	2	probably	probably	ADV
ap-1872	40	3	implies	imply	VERB
ap-1872	40	4	that	that	SCONJ
ap-1872	40	5	the	the	DET
ap-1872	40	6	only	only	ADJ
ap-1872	40	7	possible	possible	ADJ
ap-1872	40	8	choice	choice	NOUN
ap-1872	40	9	for	for	ADP
ap-1872	40	10	mpm	mpm	NOUN
ap-1872	40	11	exists	exist	VERB
ap-1872	40	12	when	when	SCONJ
ap-1872	40	13	they	they	PRON
ap-1872	40	14	are	be	AUX
ap-1872	40	15	either	either	ADV
ap-1872	40	16	given	give	VERB
ap-1872	40	17	by	by	ADP
ap-1872	40	18	matrices	matrix	NOUN
ap-1872	40	19	or	or	CCONJ
ap-1872	40	20	act	act	VERB
ap-1872	40	21	in	in	ADP
ap-1872	40	22	a	a	DET
ap-1872	40	23	space	space	NOUN
ap-1872	40	24	which	which	PRON
ap-1872	40	25	is	be	AUX
ap-1872	40	26	a	a	DET
ap-1872	40	27	complement	complement	NOUN
ap-1872	40	28	to	to	ADP
ap-1872	40	29	x	x	PROPN
ap-1872	40	30	∈	∈	PROPN
ap-1872	40	31	rn	rn	PROPN
ap-1872	40	32	.	.	PUNCT
ap-1872	41	1	it	it	PRON
ap-1872	41	2	is	be	AUX
ap-1872	41	3	easy	easy	ADJ
ap-1872	41	4	to	to	PART
ap-1872	41	5	check	check	VERB
ap-1872	41	6	that	that	PRON
ap-1872	42	1	[	[	X
ap-1872	42	2	eij	eij	PROPN
ap-1872	42	3	,	,	PUNCT
ap-1872	42	4	t−	t−	PROPN
ap-1872	42	5	k	k	X
ap-1872	42	6	]	]	X
ap-1872	43	1	=	=	PUNCT
ap-1872	43	2	−δikt−	−δikt−	PROPN
ap-1872	43	3	j	j	PROPN
ap-1872	43	4	.	.	PUNCT
ap-1872	44	1	now	now	ADV
ap-1872	44	2	we	we	PRON
ap-1872	44	3	have	have	VERB
ap-1872	44	4	to	to	PART
ap-1872	44	5	add	add	VERB
ap-1872	44	6	the	the	DET
ap-1872	44	7	euler	euler	PROPN
ap-1872	44	8	-	-	PUNCT
ap-1872	44	9	cartan	cartan	PROPN
ap-1872	44	10	generator	generator	NOUN
ap-1872	44	11	of	of	ADP
ap-1872	44	12	the	the	DET
ap-1872	44	13	gln	gln	NOUN
ap-1872	44	14	algebra	algebra	PROPN
ap-1872	44	15	,	,	PUNCT
ap-1872	44	16	see	see	VERB
ap-1872	44	17	(	(	PUNCT
ap-1872	44	18	6	6	NUM
ap-1872	44	19	)	)	PUNCT
ap-1872	44	20	−	−	PROPN
ap-1872	44	21	e0	e0	PROPN
ap-1872	45	1	=	=	PUNCT
ap-1872	46	1	n∑	n∑	PROPN
ap-1872	46	2	j=1	j=1	PROPN
ap-1872	46	3	xj∂j	xj∂j	PUNCT
ap-1872	47	1	−	−	PROPN
ap-1872	48	1	k	k	NOUN
ap-1872	48	2	,	,	PUNCT
ap-1872	48	3	(	(	PUNCT
ap-1872	48	4	9	9	NUM
ap-1872	48	5	)	)	PUNCT
ap-1872	48	6	where	where	SCONJ
ap-1872	48	7	k	k	PROPN
ap-1872	48	8	is	be	AUX
ap-1872	48	9	arbitrary	arbitrary	ADJ
ap-1872	48	10	constant	constant	ADJ
ap-1872	48	11	.	.	PUNCT
ap-1872	49	1	raising	raise	VERB
ap-1872	49	2	generators	generator	NOUN
ap-1872	49	3	from	from	ADP
ap-1872	49	4	u	u	NOUN
ap-1872	49	5	are	be	AUX
ap-1872	49	6	chosen	choose	VERB
ap-1872	49	7	as	as	ADP
ap-1872	49	8	−	−	PROPN
ap-1872	49	9	t+	t+	PUNCT
ap-1872	49	10	i	i	PRON
ap-1872	49	11	=	=	SYM
ap-1872	49	12	−xie0	−xie0	PROPN
ap-1872	50	1	+	+	SYM
ap-1872	50	2	n∑	n∑	ADJ
ap-1872	50	3	j=1	j=1	ADJ
ap-1872	50	4	xjmij	xjmij	PROPN
ap-1872	50	5	=	=	PRON
ap-1872	51	1	xi	xi	X
ap-1872	51	2	(	(	PUNCT
ap-1872	51	3	n∑	n∑	NOUN
ap-1872	51	4	j=1	j=1	PROPN
ap-1872	51	5	xj∂j	xj∂j	PUNCT
ap-1872	52	1	−	−	PROPN
ap-1872	52	2	k	k	PROPN
ap-1872	52	3	)	)	PUNCT
ap-1872	53	1	+	+	PUNCT
ap-1872	53	2	n∑	n∑	ADJ
ap-1872	53	3	j=1	j=1	ADJ
ap-1872	53	4	xjmij	xjmij	NOUN
ap-1872	53	5	,	,	PUNCT
ap-1872	53	6	i	i	PRON
ap-1872	53	7	=	=	NOUN
ap-1872	53	8	1	1	NUM
ap-1872	53	9	,	,	PUNCT
ap-1872	53	10	.	.	PUNCT
ap-1872	53	11	.	.	PUNCT
ap-1872	53	12	.	.	PUNCT
ap-1872	54	1	,	,	PUNCT
ap-1872	54	2	n.	n.	NOUN
ap-1872	54	3	(	(	PUNCT
ap-1872	54	4	10	10	NUM
ap-1872	54	5	)	)	PUNCT
ap-1872	54	6	(	(	PUNCT
ap-1872	54	7	cf	cf	NOUN
ap-1872	54	8	.	.	PUNCT
ap-1872	55	1	for	for	ADP
ap-1872	55	2	instance	instance	NOUN
ap-1872	55	3	[	[	X
ap-1872	55	4	5	5	NUM
ap-1872	55	5	]	]	NUM
ap-1872	55	6	)	)	PUNCT
ap-1872	55	7	.	.	PUNCT
ap-1872	56	1	needless	needless	ADJ
ap-1872	56	2	to	to	PART
ap-1872	56	3	say	say	VERB
ap-1872	56	4	that	that	SCONJ
ap-1872	56	5	one	one	PRON
ap-1872	56	6	can	can	AUX
ap-1872	56	7	check	check	VERB
ap-1872	56	8	explicitly	explicitly	ADV
ap-1872	56	9	that	that	SCONJ
ap-1872	57	1	t−	t−	PROPN
ap-1872	57	2	i	i	PROPN
ap-1872	57	3	,	,	PUNCT
ap-1872	57	4	eij	eij	PROPN
ap-1872	57	5	,	,	PUNCT
ap-1872	57	6	e0	e0	PROPN
ap-1872	57	7	,	,	PUNCT
ap-1872	57	8	t	t	PROPN
ap-1872	58	1	+	+	CCONJ
ap-1872	58	2	i	i	PRON
ap-1872	58	3	span	span	VERB
ap-1872	58	4	the	the	DET
ap-1872	58	5	algebra	algebra	NOUN
ap-1872	58	6	gln+1	gln+1	NOUN
ap-1872	58	7	.	.	PUNCT
ap-1872	59	1	in	in	ADP
ap-1872	59	2	particular	particular	ADJ
ap-1872	59	3	,	,	PUNCT
ap-1872	59	4	[	[	X
ap-1872	59	5	e	e	NOUN
ap-1872	59	6	,	,	PUNCT
ap-1872	59	7	t+	t+	PUNCT
ap-1872	59	8	]	]	X
ap-1872	59	9	=	=	SYM
ap-1872	59	10	t+	t+	VERB
ap-1872	59	11	,	,	PUNCT
ap-1872	59	12	and	and	CCONJ
ap-1872	60	1	[	[	X
ap-1872	60	2	t+	t+	X
ap-1872	60	3	i	i	PRON
ap-1872	60	4	,	,	PUNCT
ap-1872	60	5	t	t	PROPN
ap-1872	60	6	−	−	PROPN
ap-1872	60	7	j	j	PROPN
ap-1872	60	8	]	]	X
ap-1872	60	9	=	=	SYM
ap-1872	60	10	eii	eii	PROPN
ap-1872	60	11	−	−	PROPN
ap-1872	60	12	δije0	δije0	PROPN
ap-1872	60	13	.	.	PUNCT
ap-1872	61	1	if	if	SCONJ
ap-1872	61	2	parameter	parameter	PROPN
ap-1872	61	3	k	k	PROPN
ap-1872	61	4	takes	take	VERB
ap-1872	61	5	non	non	ADJ
ap-1872	61	6	-	-	ADJ
ap-1872	61	7	negative	negative	ADJ
ap-1872	61	8	integer	integer	NOUN
ap-1872	61	9	the	the	DET
ap-1872	61	10	algebra	algebra	NOUN
ap-1872	61	11	gln+1	gln+1	NOUN
ap-1872	61	12	spanned	span	VERB
ap-1872	61	13	by	by	ADP
ap-1872	61	14	the	the	DET
ap-1872	61	15	generators	generator	NOUN
ap-1872	61	16	(	(	PUNCT
ap-1872	61	17	5	5	NUM
ap-1872	61	18	)	)	PUNCT
ap-1872	61	19	,	,	PUNCT
ap-1872	61	20	(	(	PUNCT
ap-1872	61	21	7	7	NUM
ap-1872	61	22	)	)	PUNCT
ap-1872	61	23	,	,	PUNCT
ap-1872	61	24	(	(	PUNCT
ap-1872	61	25	9	9	NUM
ap-1872	61	26	)	)	PUNCT
ap-1872	61	27	,	,	PUNCT
ap-1872	61	28	(	(	PUNCT
ap-1872	61	29	10	10	NUM
ap-1872	61	30	)	)	PUNCT
ap-1872	61	31	appears	appear	VERB
ap-1872	61	32	in	in	ADP
ap-1872	61	33	a	a	DET
ap-1872	61	34	finite	finite	ADJ
ap-1872	61	35	-	-	ADJ
ap-1872	61	36	dimensional	dimensional	ADJ
ap-1872	61	37	representation	representation	NOUN
ap-1872	61	38	.	.	PUNCT
ap-1872	62	1	there	there	PRON
ap-1872	62	2	exists	exist	VERB
ap-1872	62	3	a	a	DET
ap-1872	62	4	linear	linear	ADJ
ap-1872	62	5	finite	finite	ADJ
ap-1872	62	6	-	-	ADJ
ap-1872	62	7	dimensional	dimensional	ADJ
ap-1872	62	8	space	space	NOUN
ap-1872	62	9	of	of	ADP
ap-1872	62	10	polynomials	polynomial	NOUN
ap-1872	62	11	of	of	ADP
ap-1872	62	12	finite	finite	NOUN
ap-1872	62	13	-	-	NOUN
ap-1872	62	14	order	order	NOUN
ap-1872	62	15	in	in	ADP
ap-1872	62	16	the	the	DET
ap-1872	62	17	space	space	NOUN
ap-1872	62	18	of	of	ADP
ap-1872	62	19	columns	column	NOUN
ap-1872	62	20	/	/	SYM
ap-1872	62	21	spinors	spinor	NOUN
ap-1872	62	22	of	of	ADP
ap-1872	62	23	finite	finite	ADJ
ap-1872	62	24	length	length	NOUN
ap-1872	62	25	which	which	PRON
ap-1872	62	26	is	be	AUX
ap-1872	62	27	a	a	DET
ap-1872	62	28	common	common	ADJ
ap-1872	62	29	invariant	invariant	ADJ
ap-1872	62	30	subspace	subspace	NOUN
ap-1872	62	31	for	for	ADP
ap-1872	62	32	all	all	DET
ap-1872	62	33	generators	generator	NOUN
ap-1872	62	34	(	(	PUNCT
ap-1872	62	35	5	5	NUM
ap-1872	62	36	)	)	PUNCT
ap-1872	62	37	,	,	PUNCT
ap-1872	62	38	(	(	PUNCT
ap-1872	62	39	7	7	NUM
ap-1872	62	40	)	)	PUNCT
ap-1872	62	41	,	,	PUNCT
ap-1872	62	42	(	(	PUNCT
ap-1872	62	43	9	9	NUM
ap-1872	62	44	)	)	PUNCT
ap-1872	62	45	,	,	PUNCT
ap-1872	62	46	(	(	PUNCT
ap-1872	62	47	10	10	NUM
ap-1872	62	48	)	)	PUNCT
ap-1872	62	49	.	.	PUNCT
ap-1872	63	1	this	this	DET
ap-1872	63	2	finite	finite	ADJ
ap-1872	63	3	-	-	ADJ
ap-1872	63	4	dimensional	dimensional	ADJ
ap-1872	63	5	representation	representation	NOUN
ap-1872	63	6	is	be	AUX
ap-1872	63	7	irreducible	irreducible	ADJ
ap-1872	63	8	.	.	PUNCT
ap-1872	64	1	the	the	DET
ap-1872	64	2	non	non	ADJ
ap-1872	64	3	-	-	ADJ
ap-1872	64	4	negative	negative	ADJ
ap-1872	64	5	integer	integer	NOUN
ap-1872	64	6	parameter	parameter	PROPN
ap-1872	64	7	k	k	PROPN
ap-1872	64	8	has	have	VERB
ap-1872	64	9	the	the	DET
ap-1872	64	10	meaning	meaning	NOUN
ap-1872	64	11	of	of	ADP
ap-1872	64	12	the	the	DET
ap-1872	64	13	length	length	NOUN
ap-1872	64	14	of	of	ADP
ap-1872	64	15	the	the	DET
ap-1872	64	16	first	first	ADJ
ap-1872	64	17	row	row	NOUN
ap-1872	64	18	of	of	ADP
ap-1872	64	19	the	the	DET
ap-1872	64	20	young	young	ADJ
ap-1872	64	21	tableau	tableau	NOUN
ap-1872	64	22	of	of	ADP
ap-1872	64	23	gln+1	gln+1	PROPN
ap-1872	64	24	,	,	PUNCT
ap-1872	64	25	describing	describe	VERB
ap-1872	64	26	a	a	DET
ap-1872	64	27	totally	totally	ADV
ap-1872	64	28	symmetric	symmetric	ADJ
ap-1872	64	29	representation	representation	NOUN
ap-1872	64	30	(	(	PUNCT
ap-1872	64	31	see	see	VERB
ap-1872	64	32	below	below	ADV
ap-1872	64	33	)	)	PUNCT
ap-1872	64	34	.	.	PUNCT
ap-1872	65	1	all	all	DET
ap-1872	65	2	other	other	ADJ
ap-1872	65	3	parameters	parameter	NOUN
ap-1872	65	4	are	be	AUX
ap-1872	65	5	coded	code	VERB
ap-1872	65	6	in	in	ADP
ap-1872	65	7	mij	mij	NOUN
ap-1872	65	8	,	,	PUNCT
ap-1872	65	9	which	which	PRON
ap-1872	65	10	corresponds	correspond	VERB
ap-1872	65	11	to	to	ADP
ap-1872	65	12	an	an	DET
ap-1872	65	13	arbitrary	arbitrary	ADJ
ap-1872	65	14	young	young	ADJ
ap-1872	65	15	tableau	tableau	NOUN
ap-1872	65	16	of	of	ADP
ap-1872	65	17	gln	gln	PROPN
ap-1872	65	18	.	.	PUNCT
ap-1872	66	1	thus	thus	ADV
ap-1872	66	2	,	,	PUNCT
ap-1872	66	3	we	we	PRON
ap-1872	66	4	have	have	VERB
ap-1872	66	5	some	some	DET
ap-1872	66	6	peculiar	peculiar	ADJ
ap-1872	66	7	splitting	splitting	NOUN
ap-1872	66	8	of	of	ADP
ap-1872	66	9	the	the	DET
ap-1872	66	10	young	young	ADJ
ap-1872	66	11	tableau	tableau	NOUN
ap-1872	66	12	.	.	PUNCT
ap-1872	67	1	each	each	DET
ap-1872	67	2	representation	representation	NOUN
ap-1872	67	3	is	be	AUX
ap-1872	67	4	characterized	characterize	VERB
ap-1872	67	5	by	by	ADP
ap-1872	67	6	the	the	DET
ap-1872	67	7	gelfandtseitlin	gelfandtseitlin	PROPN
ap-1872	67	8	signature	signature	NOUN
ap-1872	67	9	,	,	PUNCT
ap-1872	68	1	[	[	X
ap-1872	68	2	m1,n	m1,n	PROPN
ap-1872	68	3	,	,	PUNCT
ap-1872	68	4	.	.	PUNCT
ap-1872	68	5	.	.	PUNCT
ap-1872	69	1	.mnn	.mnn	NOUN
ap-1872	69	2	]	]	X
ap-1872	69	3	,	,	PUNCT
ap-1872	69	4	where	where	SCONJ
ap-1872	69	5	min	min	PROPN
ap-1872	69	6	≥	≥	PROPN
ap-1872	69	7	mi+1,n	mi+1,n	PROPN
ap-1872	69	8	and	and	CCONJ
ap-1872	69	9	their	their	PRON
ap-1872	69	10	difference	difference	NOUN
ap-1872	69	11	is	be	AUX
ap-1872	69	12	positive	positive	ADJ
ap-1872	69	13	integer	integer	NOUN
ap-1872	69	14	.	.	PUNCT
ap-1872	70	1	each	each	DET
ap-1872	70	2	basic	basic	ADJ
ap-1872	70	3	vector	vector	NOUN
ap-1872	70	4	is	be	AUX
ap-1872	70	5	characterized	characterize	VERB
ap-1872	70	6	by	by	ADP
ap-1872	70	7	the	the	DET
ap-1872	70	8	gelfand	gelfand	PROPN
ap-1872	70	9	-	-	PUNCT
ap-1872	70	10	tseitlin	tseitlin	NOUN
ap-1872	70	11	scheme	scheme	NOUN
ap-1872	70	12	.	.	PUNCT
ap-1872	71	1	an	an	DET
ap-1872	71	2	explicit	explicit	ADJ
ap-1872	71	3	form	form	NOUN
ap-1872	71	4	of	of	ADP
ap-1872	71	5	the	the	DET
ap-1872	71	6	representation	representation	NOUN
ap-1872	71	7	is	be	AUX
ap-1872	71	8	given	give	VERB
ap-1872	71	9	by	by	ADP
ap-1872	71	10	the	the	DET
ap-1872	71	11	gelfand	gelfand	NOUN
ap-1872	71	12	-	-	PUNCT
ap-1872	71	13	tseitlin	tseitlin	NOUN
ap-1872	71	14	formulas	formula	NOUN
ap-1872	71	15	[	[	X
ap-1872	71	16	4	4	NUM
ap-1872	71	17	]	]	PUNCT
ap-1872	71	18	.	.	PUNCT
ap-1872	72	1	it	it	PRON
ap-1872	72	2	can	can	AUX
ap-1872	72	3	be	be	AUX
ap-1872	72	4	demonstrated	demonstrate	VERB
ap-1872	72	5	that	that	SCONJ
ap-1872	72	6	all	all	DET
ap-1872	72	7	casimir	casimir	NOUN
ap-1872	72	8	operators	operator	NOUN
ap-1872	72	9	of	of	ADP
ap-1872	72	10	gln+1	gln+1	NOUN
ap-1872	72	11	in	in	ADP
ap-1872	72	12	this	this	DET
ap-1872	72	13	realization	realization	NOUN
ap-1872	72	14	(	(	PUNCT
ap-1872	72	15	5	5	NUM
ap-1872	72	16	)	)	PUNCT
ap-1872	72	17	,	,	PUNCT
ap-1872	72	18	(	(	PUNCT
ap-1872	72	19	7	7	NUM
ap-1872	72	20	)	)	PUNCT
ap-1872	72	21	,	,	PUNCT
ap-1872	72	22	(	(	PUNCT
ap-1872	72	23	9	9	NUM
ap-1872	72	24	)	)	PUNCT
ap-1872	72	25	,	,	PUNCT
ap-1872	72	26	(	(	PUNCT
ap-1872	72	27	10	10	NUM
ap-1872	72	28	)	)	PUNCT
ap-1872	72	29	are	be	AUX
ap-1872	72	30	expressed	express	VERB
ap-1872	72	31	in	in	ADP
ap-1872	72	32	mij	mij	NOUN
ap-1872	72	33	,	,	PUNCT
ap-1872	72	34	and	and	CCONJ
ap-1872	72	35	thus	thus	ADV
ap-1872	72	36	do	do	AUX
ap-1872	72	37	not	not	PART
ap-1872	72	38	depend	depend	VERB
ap-1872	72	39	on	on	ADP
ap-1872	72	40	x.	x.	NOUN
ap-1872	72	41	they	they	PRON
ap-1872	72	42	coincide	coincide	VERB
ap-1872	72	43	with	with	ADP
ap-1872	72	44	the	the	DET
ap-1872	72	45	casimir	casimir	NOUN
ap-1872	72	46	operators	operator	NOUN
ap-1872	72	47	of	of	ADP
ap-1872	72	48	the	the	DET
ap-1872	72	49	gln	gln	NOUN
ap-1872	72	50	-	-	PUNCT
ap-1872	72	51	subalgebra	subalgebra	NOUN
ap-1872	72	52	realized	realize	VERB
ap-1872	72	53	by	by	ADP
ap-1872	72	54	matrices	matrix	NOUN
ap-1872	72	55	mij	mij	X
ap-1872	72	56	.	.	PUNCT
ap-1872	73	1	3	3	X
ap-1872	73	2	.	.	X
ap-1872	73	3	example	example	NOUN
ap-1872	73	4	:	:	PUNCT
ap-1872	73	5	the	the	DET
ap-1872	73	6	algebra	algebra	NOUN
ap-1872	73	7	gl3	gl3	VERB
ap-1872	73	8	in	in	ADP
ap-1872	73	9	mixed	mixed	ADJ
ap-1872	73	10	representation	representation	NOUN
ap-1872	73	11	in	in	ADP
ap-1872	73	12	the	the	DET
ap-1872	73	13	case	case	NOUN
ap-1872	73	14	of	of	ADP
ap-1872	73	15	the	the	DET
ap-1872	73	16	algebra	algebra	NOUN
ap-1872	73	17	gl3	gl3	PROPN
ap-1872	73	18	,	,	PUNCT
ap-1872	73	19	the	the	DET
ap-1872	73	20	generators	generator	NOUN
ap-1872	73	21	(	(	PUNCT
ap-1872	73	22	5	5	NUM
ap-1872	73	23	)	)	PUNCT
ap-1872	73	24	,	,	PUNCT
ap-1872	73	25	(	(	PUNCT
ap-1872	73	26	7	7	NUM
ap-1872	73	27	)	)	PUNCT
ap-1872	73	28	,	,	PUNCT
ap-1872	73	29	(	(	PUNCT
ap-1872	73	30	9	9	NUM
ap-1872	73	31	)	)	PUNCT
ap-1872	73	32	,	,	PUNCT
ap-1872	73	33	(	(	PUNCT
ap-1872	73	34	10	10	NUM
ap-1872	73	35	)	)	PUNCT
ap-1872	73	36	take	take	VERB
ap-1872	73	37	the	the	DET
ap-1872	73	38	form	form	NOUN
ap-1872	73	39	e11	e11	NOUN
ap-1872	73	40	=	=	SYM
ap-1872	74	1	x1∂1	x1∂1	PROPN
ap-1872	74	2	+	+	PROPN
ap-1872	74	3	m11	m11	NOUN
ap-1872	74	4	,	,	PUNCT
ap-1872	74	5	e22	e22	NOUN
ap-1872	74	6	=	=	SYM
ap-1872	75	1	x2∂2	x2∂2	PROPN
ap-1872	76	1	+	+	PROPN
ap-1872	76	2	m22	m22	PROPN
ap-1872	76	3	,	,	PUNCT
ap-1872	76	4	e12	e12	NOUN
ap-1872	76	5	=	=	SYM
ap-1872	76	6	x1∂2	x1∂2	PROPN
ap-1872	76	7	+	+	NOUN
ap-1872	76	8	m12	m12	ADJ
ap-1872	76	9	,	,	PUNCT
ap-1872	76	10	e21	e21	PROPN
ap-1872	77	1	=	=	SYM
ap-1872	77	2	x2∂1	x2∂1	PROPN
ap-1872	77	3	+	+	NOUN
ap-1872	77	4	m21	m21	NOUN
ap-1872	77	5	,	,	PUNCT
ap-1872	77	6	e0	e0	PROPN
ap-1872	77	7	=	=	PUNCT
ap-1872	78	1	k	k	PROPN
ap-1872	78	2	−	−	PROPN
ap-1872	79	1	x1∂1	x1∂1	PROPN
ap-1872	79	2	−	−	PROPN
ap-1872	80	1	x2∂2	x2∂2	PROPN
ap-1872	80	2	,	,	PUNCT
ap-1872	80	3	t−	t−	PROPN
ap-1872	80	4	1	1	NUM
ap-1872	80	5	=	=	SYM
ap-1872	80	6	∂1	∂1	ADJ
ap-1872	80	7	,	,	PUNCT
ap-1872	80	8	t−	t−	PROPN
ap-1872	80	9	2	2	NUM
ap-1872	80	10	=	=	SYM
ap-1872	80	11	∂2	∂2	NOUN
ap-1872	80	12	,	,	PUNCT
ap-1872	80	13	t+	t+	X
ap-1872	80	14	1	1	NUM
ap-1872	80	15	=	=	SYM
ap-1872	80	16	x1(k	x1(k	PROPN
ap-1872	81	1	−	−	NOUN
ap-1872	81	2	x1∂1	x1∂1	PROPN
ap-1872	81	3	−	−	PROPN
ap-1872	81	4	x2∂2)−	x2∂2)−	PROPN
ap-1872	81	5	x1m11	x1m11	X
ap-1872	82	1	−	−	PROPN
ap-1872	82	2	x2m12	x2m12	PROPN
ap-1872	82	3	,	,	PUNCT
ap-1872	82	4	t+	t+	X
ap-1872	82	5	2	2	NUM
ap-1872	82	6	=	=	SYM
ap-1872	82	7	x2(k	x2(k	PROPN
ap-1872	82	8	−	−	PROPN
ap-1872	83	1	x1∂1	x1∂1	PROPN
ap-1872	83	2	−	−	PROPN
ap-1872	83	3	x2∂2)−	x2∂2)−	PUNCT
ap-1872	83	4	x1m21	x1m21	X
ap-1872	84	1	−	−	PROPN
ap-1872	84	2	x2m22	x2m22	PROPN
ap-1872	84	3	.	.	PUNCT
ap-1872	85	1	(	(	PUNCT
ap-1872	85	2	11	11	NUM
ap-1872	85	3	)	)	PUNCT
ap-1872	85	4	the	the	DET
ap-1872	85	5	casimir	casimir	PROPN
ap-1872	85	6	operators	operator	NOUN
ap-1872	85	7	of	of	ADP
ap-1872	85	8	gl3	gl3	PROPN
ap-1872	85	9	in	in	ADP
ap-1872	85	10	this	this	DET
ap-1872	85	11	realization	realization	NOUN
ap-1872	85	12	are	be	AUX
ap-1872	85	13	given	give	VERB
ap-1872	85	14	by	by	ADP
ap-1872	85	15	c1	c1	PROPN
ap-1872	85	16	=	=	PUNCT
ap-1872	85	17	e11	e11	PROPN
ap-1872	86	1	+	+	NOUN
ap-1872	86	2	e22	e22	X
ap-1872	86	3	+	+	NOUN
ap-1872	86	4	e0	e0	NOUN
ap-1872	86	5	=	=	PUNCT
ap-1872	86	6	k+m11	k+m11	PROPN
ap-1872	86	7	+	+	NOUN
ap-1872	86	8	m22	m22	NOUN
ap-1872	86	9	=	=	SYM
ap-1872	86	10	k+c1(m	k+c1(m	PROPN
ap-1872	86	11	)	)	PUNCT
ap-1872	86	12	,	,	PUNCT
ap-1872	86	13	c2	c2	PROPN
ap-1872	86	14	=	=	PUNCT
ap-1872	86	15	e12e21	e12e21	VERB
ap-1872	86	16	+	+	CCONJ
ap-1872	86	17	e21e12	e21e12	VERB
ap-1872	86	18	+	+	CCONJ
ap-1872	86	19	t+	t+	NOUN
ap-1872	86	20	1	1	NUM
ap-1872	86	21	t	t	NOUN
ap-1872	86	22	−	−	NOUN
ap-1872	86	23	1	1	NUM
ap-1872	86	24	+	+	CCONJ
ap-1872	86	25	t−	t−	PROPN
ap-1872	86	26	1	1	NUM
ap-1872	86	27	t	t	NOUN
ap-1872	86	28	+	+	CCONJ
ap-1872	86	29	1	1	NUM
ap-1872	86	30	+	+	CCONJ
ap-1872	86	31	t+	t+	PUNCT
ap-1872	86	32	2	2	NUM
ap-1872	86	33	t	t	NOUN
ap-1872	86	34	−	−	NOUN
ap-1872	86	35	2	2	NUM
ap-1872	86	36	+	+	CCONJ
ap-1872	86	37	t−	t−	PROPN
ap-1872	86	38	2	2	NUM
ap-1872	86	39	t	t	NOUN
ap-1872	86	40	+	+	CCONJ
ap-1872	86	41	2	2	NUM
ap-1872	86	42	+	+	CCONJ
ap-1872	86	43	e2	e2	PROPN
ap-1872	86	44	11	11	NUM
ap-1872	86	45	+	+	CCONJ
ap-1872	86	46	e2	e2	PROPN
ap-1872	86	47	22	22	NUM
ap-1872	87	1	+	+	CCONJ
ap-1872	87	2	e2	e2	PROPN
ap-1872	87	3	0	0	PUNCT
ap-1872	88	1	=	=	PUNCT
ap-1872	89	1	k(k	k(k	NOUN
ap-1872	89	2	+	+	CCONJ
ap-1872	89	3	2	2	X
ap-1872	89	4	)	)	PUNCT
ap-1872	90	1	+	+	NOUN
ap-1872	90	2	m2	m2	PROPN
ap-1872	90	3	11	11	NUM
ap-1872	90	4	+	+	NOUN
ap-1872	90	5	m2	m2	PROPN
ap-1872	90	6	22	22	NUM
ap-1872	90	7	+	+	NOUN
ap-1872	90	8	m12m21	m12m21	PROPN
ap-1872	90	9	+	+	NOUN
ap-1872	90	10	m21m12	m21m12	NUM
ap-1872	90	11	−m11	−m11	PRON
ap-1872	90	12	−m22	−m22	NOUN
ap-1872	90	13	=	=	SYM
ap-1872	91	1	k(k	k(k	NOUN
ap-1872	91	2	+	+	CCONJ
ap-1872	91	3	2	2	X
ap-1872	91	4	)	)	PUNCT
ap-1872	91	5	+	+	NUM
ap-1872	91	6	c2(m)−	c2(m)−	PROPN
ap-1872	91	7	c1(m	c1(m	NOUN
ap-1872	91	8	)	)	PUNCT
ap-1872	91	9	,	,	PUNCT
ap-1872	91	10	and	and	CCONJ
ap-1872	91	11	,	,	PUNCT
ap-1872	91	12	finally	finally	ADV
ap-1872	91	13	,	,	PUNCT
ap-1872	91	14	c3	c3	PROPN
ap-1872	91	15	=	=	SYM
ap-1872	91	16	−1	−1	NOUN
ap-1872	91	17	2c	2c	NOUN
ap-1872	91	18	3	3	NUM
ap-1872	91	19	1	1	NUM
ap-1872	91	20	+	+	CCONJ
ap-1872	91	21	3	3	NUM
ap-1872	91	22	2c1c2	2c1c2	NUM
ap-1872	91	23	+	+	CCONJ
ap-1872	91	24	3c2	3c2	NUM
ap-1872	91	25	−	−	NUM
ap-1872	91	26	2c2	2c2	NUM
ap-1872	91	27	1	1	NUM
ap-1872	91	28	−	−	NOUN
ap-1872	91	29	2c1	2c1	NUM
ap-1872	91	30	.	.	PUNCT
ap-1872	92	1	in	in	ADP
ap-1872	92	2	this	this	DET
ap-1872	92	3	realization	realization	NOUN
ap-1872	92	4	,	,	PUNCT
ap-1872	92	5	the	the	DET
ap-1872	92	6	casimir	casimir	NOUN
ap-1872	92	7	operator	operator	NOUN
ap-1872	92	8	c3	c3	PROPN
ap-1872	92	9	is	be	AUX
ap-1872	92	10	algebraically	algebraically	ADV
ap-1872	92	11	dependent	dependent	ADJ
ap-1872	92	12	on	on	ADP
ap-1872	92	13	c1	c1	PROPN
ap-1872	92	14	and	and	CCONJ
ap-1872	92	15	c2	c2	PROPN
ap-1872	92	16	.	.	PUNCT
ap-1872	93	1	in	in	ADP
ap-1872	93	2	fact	fact	NOUN
ap-1872	93	3	,	,	PUNCT
ap-1872	93	4	c1	c1	PROPN
ap-1872	93	5	and	and	CCONJ
ap-1872	93	6	c2	c2	PROPN
ap-1872	93	7	are	be	AUX
ap-1872	93	8	nothing	nothing	PRON
ap-1872	93	9	but	but	SCONJ
ap-1872	93	10	the	the	DET
ap-1872	93	11	casimir	casimir	PROPN
ap-1872	93	12	operators	operator	NOUN
ap-1872	93	13	of	of	ADP
ap-1872	93	14	the	the	DET
ap-1872	93	15	gl2	gl2	PROPN
ap-1872	93	16	sub	sub	NOUN
ap-1872	93	17	-	-	NOUN
ap-1872	93	18	algebra	algebra	NOUN
ap-1872	93	19	.	.	PUNCT
ap-1872	94	1	therefore	therefore	ADV
ap-1872	94	2	,	,	PUNCT
ap-1872	94	3	the	the	DET
ap-1872	94	4	center	center	NOUN
ap-1872	94	5	of	of	ADP
ap-1872	94	6	the	the	DET
ap-1872	94	7	gl3	gl3	ADJ
ap-1872	94	8	universal	universal	ADJ
ap-1872	94	9	enveloping	enveloping	NOUN
ap-1872	94	10	algebra	algebra	NOUN
ap-1872	94	11	in	in	ADP
ap-1872	94	12	realization	realization	NOUN
ap-1872	94	13	(	(	PUNCT
ap-1872	94	14	11	11	NUM
ap-1872	94	15	)	)	PUNCT
ap-1872	94	16	is	be	AUX
ap-1872	94	17	generated	generate	VERB
ap-1872	94	18	by	by	ADP
ap-1872	94	19	the	the	DET
ap-1872	94	20	casimir	casimir	PROPN
ap-1872	94	21	operators	operator	NOUN
ap-1872	94	22	of	of	ADP
ap-1872	94	23	the	the	DET
ap-1872	94	24	gl2	gl2	PROPN
ap-1872	94	25	sub	sub	NOUN
ap-1872	94	26	-	-	NOUN
ap-1872	94	27	algebra	algebra	NOUN
ap-1872	94	28	realized	realize	VERB
ap-1872	94	29	by	by	ADP
ap-1872	94	30	mij	mij	NOUN
ap-1872	94	31	.	.	PUNCT
ap-1872	95	1	thus	thus	ADV
ap-1872	95	2	,	,	PUNCT
ap-1872	95	3	it	it	PRON
ap-1872	95	4	seems	seem	VERB
ap-1872	95	5	natural	natural	ADJ
ap-1872	95	6	that	that	SCONJ
ap-1872	95	7	these	these	DET
ap-1872	95	8	reps	rep	NOUN
ap-1872	95	9	are	be	AUX
ap-1872	95	10	irreducible	irreducible	ADJ
ap-1872	95	11	.	.	PUNCT
ap-1872	96	1	now	now	ADV
ap-1872	96	2	we	we	PRON
ap-1872	96	3	consider	consider	VERB
ap-1872	96	4	concrete	concrete	ADJ
ap-1872	96	5	matrix	matrix	NOUN
ap-1872	96	6	realizations	realization	NOUN
ap-1872	96	7	of	of	ADP
ap-1872	96	8	the	the	DET
ap-1872	96	9	gl2	gl2	NOUN
ap-1872	96	10	-	-	PUNCT
ap-1872	96	11	subalgebra	subalgebra	NOUN
ap-1872	96	12	in	in	ADP
ap-1872	96	13	our	our	PRON
ap-1872	96	14	scheme	scheme	NOUN
ap-1872	96	15	.	.	PUNCT
ap-1872	97	1	3.1	3.1	NUM
ap-1872	97	2	.	.	NUM
ap-1872	97	3	reps	rep	NOUN
ap-1872	97	4	in	in	ADP
ap-1872	97	5	1×	1×	NUM
ap-1872	97	6	1	1	NUM
ap-1872	97	7	matrices	matrix	NOUN
ap-1872	97	8	this	this	DET
ap-1872	97	9	corresponds	correspond	VERB
ap-1872	97	10	to	to	ADP
ap-1872	97	11	the	the	DET
ap-1872	97	12	trivial	trivial	ADJ
ap-1872	97	13	representation	representation	NOUN
ap-1872	97	14	of	of	ADP
ap-1872	97	15	gl2	gl2	PROPN
ap-1872	97	16	,	,	PUNCT
ap-1872	97	17	m11	m11	NOUN
ap-1872	97	18	=	=	SYM
ap-1872	97	19	m12	m12	NOUN
ap-1872	97	20	=	=	SYM
ap-1872	97	21	m21	m21	PROPN
ap-1872	97	22	=	=	PUNCT
ap-1872	97	23	m22	m22	PROPN
ap-1872	97	24	=	=	SYM
ap-1872	97	25	0	0	PROPN
ap-1872	97	26	.	.	PUNCT
ap-1872	98	1	this	this	PRON
ap-1872	98	2	is	be	AUX
ap-1872	98	3	[	[	X
ap-1872	98	4	k	k	X
ap-1872	98	5	,	,	PUNCT
ap-1872	98	6	0	0	NUM
ap-1872	98	7	]	]	PUNCT
ap-1872	98	8	or	or	CCONJ
ap-1872	98	9	,	,	PUNCT
ap-1872	98	10	in	in	ADP
ap-1872	98	11	other	other	ADJ
ap-1872	98	12	words	word	NOUN
ap-1872	98	13	,	,	PUNCT
ap-1872	98	14	a	a	DET
ap-1872	98	15	symmetric	symmetric	ADJ
ap-1872	98	16	representation	representation	NOUN
ap-1872	98	17	(	(	PUNCT
ap-1872	98	18	the	the	DET
ap-1872	98	19	young	young	ADJ
ap-1872	98	20	tableau	tableau	PROPN
ap-1872	98	21	has	have	AUX
ap-1872	98	22	two	two	NUM
ap-1872	98	23	rows	row	NOUN
ap-1872	98	24	of	of	ADP
ap-1872	98	25	length	length	NOUN
ap-1872	98	26	k	k	PROPN
ap-1872	98	27	and	and	CCONJ
ap-1872	98	28	0	0	NUM
ap-1872	98	29	,	,	PUNCT
ap-1872	98	30	correspondingly	correspondingly	ADV
ap-1872	98	31	)	)	PUNCT
ap-1872	98	32	.	.	PUNCT
ap-1872	99	1	we	we	PRON
ap-1872	99	2	also	also	ADV
ap-1872	99	3	can	can	AUX
ap-1872	99	4	call	call	VERB
ap-1872	99	5	it	it	PRON
ap-1872	99	6	a	a	DET
ap-1872	99	7	scalar	scalar	ADJ
ap-1872	99	8	representation	representation	NOUN
ap-1872	99	9	,	,	PUNCT
ap-1872	99	10	since	since	SCONJ
ap-1872	99	11	the	the	DET
ap-1872	99	12	generators	generator	NOUN
ap-1872	99	13	e11	e11	X
ap-1872	99	14	=	=	SYM
ap-1872	99	15	x1∂1	x1∂1	PROPN
ap-1872	99	16	,	,	PUNCT
ap-1872	99	17	e22	e22	PROPN
ap-1872	99	18	=	=	SYM
ap-1872	99	19	x2∂2	x2∂2	PROPN
ap-1872	99	20	,	,	PUNCT
ap-1872	99	21	e12	e12	NOUN
ap-1872	99	22	=	=	SYM
ap-1872	99	23	x1∂2	x1∂2	PROPN
ap-1872	99	24	,	,	PUNCT
ap-1872	99	25	e21	e21	PROPN
ap-1872	99	26	=	=	SYM
ap-1872	99	27	x2∂1	x2∂1	PROPN
ap-1872	99	28	,	,	PUNCT
ap-1872	99	29	e0	e0	PROPN
ap-1872	99	30	=	=	PUNCT
ap-1872	100	1	k	k	PROPN
ap-1872	100	2	−	−	PROPN
ap-1872	101	1	x1∂1	x1∂1	PROPN
ap-1872	101	2	−	−	PROPN
ap-1872	102	1	x2∂2	x2∂2	PROPN
ap-1872	102	2	,	,	PUNCT
ap-1872	102	3	t−	t−	PROPN
ap-1872	102	4	1	1	NUM
ap-1872	102	5	=	=	SYM
ap-1872	102	6	∂1	∂1	ADJ
ap-1872	102	7	,	,	PUNCT
ap-1872	102	8	t−	t−	PROPN
ap-1872	102	9	2	2	NUM
ap-1872	102	10	=	=	SYM
ap-1872	102	11	∂2	∂2	NOUN
ap-1872	102	12	,	,	PUNCT
ap-1872	102	13	t+	t+	X
ap-1872	102	14	1	1	NUM
ap-1872	102	15	=	=	SYM
ap-1872	102	16	x1(k	x1(k	PROPN
ap-1872	103	1	−	−	NOUN
ap-1872	103	2	x1∂1	x1∂1	PROPN
ap-1872	103	3	−	−	PROPN
ap-1872	103	4	x2∂2	x2∂2	PROPN
ap-1872	103	5	)	)	PUNCT
ap-1872	103	6	,	,	PUNCT
ap-1872	103	7	t+	t+	X
ap-1872	103	8	2	2	NUM
ap-1872	103	9	=	=	SYM
ap-1872	103	10	x2(k	x2(k	PROPN
ap-1872	104	1	−	−	PROPN
ap-1872	104	2	x1∂1	x1∂1	PROPN
ap-1872	104	3	−	−	PROPN
ap-1872	105	1	x2∂2	x2∂2	PROPN
ap-1872	105	2	)	)	PUNCT
ap-1872	105	3	,	,	PUNCT
ap-1872	105	4	(	(	PUNCT
ap-1872	105	5	12	12	NUM
ap-1872	105	6	)	)	PUNCT
ap-1872	105	7	act	act	NOUN
ap-1872	105	8	on	on	ADP
ap-1872	105	9	one	one	NUM
ap-1872	105	10	-	-	PUNCT
ap-1872	105	11	component	component	NOUN
ap-1872	105	12	spinors	spinor	NOUN
ap-1872	105	13	or	or	CCONJ
ap-1872	105	14	,	,	PUNCT
ap-1872	105	15	in	in	ADP
ap-1872	105	16	other	other	ADJ
ap-1872	105	17	words	word	NOUN
ap-1872	105	18	,	,	PUNCT
ap-1872	105	19	on	on	ADP
ap-1872	105	20	scalar	scalar	ADJ
ap-1872	105	21	functions	function	NOUN
ap-1872	105	22	(	(	PUNCT
ap-1872	105	23	see	see	VERB
ap-1872	106	1	e.g.	e.g.	ADV
ap-1872	106	2	[	[	X
ap-1872	106	3	5	5	NUM
ap-1872	106	4	]	]	NUM
ap-1872	106	5	)	)	PUNCT
ap-1872	106	6	.	.	PUNCT
ap-1872	107	1	the	the	DET
ap-1872	107	2	casimir	casimir	PROPN
ap-1872	107	3	operators	operator	NOUN
ap-1872	107	4	are	be	AUX
ap-1872	107	5	:	:	PUNCT
ap-1872	107	6	c1	c1	PROPN
ap-1872	107	7	=	=	PROPN
ap-1872	107	8	k	k	PROPN
ap-1872	107	9	,	,	PUNCT
ap-1872	107	10	c2	c2	PROPN
ap-1872	107	11	=	=	PUNCT
ap-1872	108	1	k(k	k(k	PROPN
ap-1872	108	2	+	+	CCONJ
ap-1872	108	3	2	2	NUM
ap-1872	108	4	)	)	PUNCT
ap-1872	108	5	.	.	PUNCT
ap-1872	109	1	463	463	NUM
ap-1872	109	2	yu	yu	PROPN
ap-1872	109	3	.	.	PUNCT
ap-1872	109	4	f.	f.	PROPN
ap-1872	109	5	smirnov	smirnov	PROPN
ap-1872	109	6	,	,	PUNCT
ap-1872	109	7	a.	a.	NOUN
ap-1872	109	8	v.	v.	PROPN
ap-1872	109	9	turbiner	turbiner	PROPN
ap-1872	109	10	acta	acta	PROPN
ap-1872	109	11	polytechnica	polytechnica	PROPN
ap-1872	109	12	if	if	SCONJ
ap-1872	109	13	parameter	parameter	PROPN
ap-1872	109	14	k	k	PROPN
ap-1872	109	15	takes	take	VERB
ap-1872	109	16	non	non	ADJ
ap-1872	109	17	-	-	ADJ
ap-1872	109	18	negative	negative	ADJ
ap-1872	109	19	integer	integer	NOUN
ap-1872	109	20	the	the	DET
ap-1872	109	21	algebra	algebra	NOUN
ap-1872	109	22	gl3	gl3	ADV
ap-1872	109	23	spanned	span	VERB
ap-1872	109	24	by	by	ADP
ap-1872	109	25	the	the	DET
ap-1872	109	26	generators	generator	NOUN
ap-1872	109	27	(	(	PUNCT
ap-1872	109	28	12	12	NUM
ap-1872	109	29	)	)	PUNCT
ap-1872	109	30	appears	appear	VERB
ap-1872	109	31	in	in	ADP
ap-1872	109	32	finitedimensional	finitedimensional	ADJ
ap-1872	109	33	representation	representation	NOUN
ap-1872	109	34	.	.	PUNCT
ap-1872	110	1	its	its	PRON
ap-1872	110	2	finite	finite	ADJ
ap-1872	110	3	-	-	ADJ
ap-1872	110	4	dimensional	dimensional	ADJ
ap-1872	110	5	representation	representation	NOUN
ap-1872	110	6	space	space	NOUN
ap-1872	110	7	is	be	AUX
ap-1872	110	8	a	a	DET
ap-1872	110	9	space	space	NOUN
ap-1872	110	10	of	of	ADP
ap-1872	110	11	polynomials	polynomial	NOUN
ap-1872	111	1	pk,0	pk,0	PROPN
ap-1872	111	2	=	=	SYM
ap-1872	111	3	〈	〈	PROPN
ap-1872	111	4	x1	x1	PROPN
ap-1872	111	5	p1x2	p1x2	PROPN
ap-1872	111	6	p2	p2	X
ap-1872	111	7	∣∣	∣∣	NUM
ap-1872	111	8	0	0	NUM
ap-1872	111	9	≤	≤	NUM
ap-1872	112	1	p1+p2	p1+p2	VERB
ap-1872	112	2	≤	≤	NOUN
ap-1872	112	3	k	k	PROPN
ap-1872	112	4	〉	〉	NOUN
ap-1872	112	5	,	,	PUNCT
ap-1872	112	6	k	k	PROPN
ap-1872	112	7	=	=	SYM
ap-1872	112	8	0	0	NUM
ap-1872	112	9	,	,	PUNCT
ap-1872	112	10	1	1	NUM
ap-1872	112	11	,	,	PUNCT
ap-1872	112	12	2	2	NUM
ap-1872	112	13	,	,	PUNCT
ap-1872	112	14	.	.	PUNCT
ap-1872	112	15	.	.	PUNCT
ap-1872	112	16	.	.	PUNCT
ap-1872	112	17	.	.	PUNCT
ap-1872	113	1	(	(	PUNCT
ap-1872	113	2	13	13	NUM
ap-1872	113	3	)	)	PUNCT
ap-1872	113	4	namely	namely	ADV
ap-1872	113	5	in	in	ADP
ap-1872	113	6	this	this	DET
ap-1872	113	7	representation	representation	NOUN
ap-1872	113	8	(	(	PUNCT
ap-1872	113	9	12	12	NUM
ap-1872	113	10	)	)	PUNCT
ap-1872	113	11	,	,	PUNCT
ap-1872	113	12	the	the	DET
ap-1872	113	13	algebra	algebra	NOUN
ap-1872	113	14	gl3	gl3	PROPN
ap-1872	113	15	appears	appear	VERB
ap-1872	113	16	as	as	ADP
ap-1872	113	17	the	the	DET
ap-1872	113	18	hidden	hidden	ADJ
ap-1872	113	19	algebra	algebra	NOUN
ap-1872	113	20	of	of	ADP
ap-1872	113	21	the	the	DET
ap-1872	113	22	3	3	NUM
ap-1872	113	23	-	-	PUNCT
ap-1872	113	24	body	body	NOUN
ap-1872	113	25	calogero	calogero	NOUN
ap-1872	113	26	and	and	CCONJ
ap-1872	113	27	sutherland	sutherland	NOUN
ap-1872	113	28	models	model	NOUN
ap-1872	113	29	[	[	X
ap-1872	113	30	5	5	NUM
ap-1872	113	31	]	]	PUNCT
ap-1872	113	32	,	,	PUNCT
ap-1872	113	33	bc2	bc2	VERB
ap-1872	113	34	rational	rational	ADJ
ap-1872	113	35	and	and	CCONJ
ap-1872	113	36	trigonometric	trigonometric	ADJ
ap-1872	113	37	,	,	PUNCT
ap-1872	113	38	and	and	CCONJ
ap-1872	113	39	g2	g2	PROPN
ap-1872	113	40	rational	rational	ADJ
ap-1872	113	41	models	model	NOUN
ap-1872	113	42	[	[	X
ap-1872	113	43	6	6	NUM
ap-1872	113	44	]	]	PUNCT
ap-1872	113	45	and	and	CCONJ
ap-1872	113	46	even	even	ADV
ap-1872	113	47	of	of	ADP
ap-1872	113	48	the	the	DET
ap-1872	113	49	bc2	bc2	PROPN
ap-1872	113	50	elliptic	elliptic	ADJ
ap-1872	113	51	model	model	NOUN
ap-1872	113	52	[	[	X
ap-1872	113	53	7	7	NUM
ap-1872	113	54	]	]	SYM
ap-1872	113	55	.	.	PUNCT
ap-1872	114	1	3.2	3.2	NUM
ap-1872	114	2	.	.	PUNCT
ap-1872	114	3	reps	rep	NOUN
ap-1872	114	4	in	in	ADP
ap-1872	114	5	2×	2×	NUM
ap-1872	114	6	2	2	NUM
ap-1872	114	7	matrices	matrix	NOUN
ap-1872	114	8	take	take	VERB
ap-1872	114	9	gl2	gl2	PROPN
ap-1872	114	10	in	in	ADP
ap-1872	114	11	two	two	NUM
ap-1872	114	12	-	-	PUNCT
ap-1872	114	13	dimensional	dimensional	ADJ
ap-1872	114	14	reps	rep	NOUN
ap-1872	114	15	by	by	ADP
ap-1872	114	16	2×	2×	NUM
ap-1872	114	17	2	2	NUM
ap-1872	114	18	matrices	matrix	NOUN
ap-1872	114	19	,	,	PUNCT
ap-1872	114	20	m11	m11	NOUN
ap-1872	114	21	=	=	PUNCT
ap-1872	114	22	(	(	PUNCT
ap-1872	114	23	1	1	NUM
ap-1872	114	24	0	0	NUM
ap-1872	114	25	0	0	NUM
ap-1872	114	26	0	0	NUM
ap-1872	114	27	)	)	PUNCT
ap-1872	114	28	,	,	PUNCT
ap-1872	114	29	m22	m22	PROPN
ap-1872	114	30	=	=	SYM
ap-1872	114	31	(	(	PUNCT
ap-1872	114	32	0	0	NUM
ap-1872	114	33	0	0	NUM
ap-1872	114	34	0	0	NUM
ap-1872	114	35	1	1	NUM
ap-1872	114	36	)	)	PUNCT
ap-1872	114	37	,	,	PUNCT
ap-1872	114	38	m12	m12	NOUN
ap-1872	114	39	=	=	SYM
ap-1872	114	40	(	(	PUNCT
ap-1872	114	41	0	0	NUM
ap-1872	114	42	1	1	NUM
ap-1872	114	43	0	0	NUM
ap-1872	114	44	0	0	NUM
ap-1872	114	45	)	)	PUNCT
ap-1872	114	46	,	,	PUNCT
ap-1872	114	47	m21	m21	X
ap-1872	114	48	=	=	PUNCT
ap-1872	114	49	(	(	PUNCT
ap-1872	114	50	0	0	NUM
ap-1872	114	51	0	0	NUM
ap-1872	114	52	1	1	NUM
ap-1872	114	53	0	0	NUM
ap-1872	114	54	)	)	PUNCT
ap-1872	114	55	,	,	PUNCT
ap-1872	114	56	then	then	ADV
ap-1872	114	57	the	the	DET
ap-1872	114	58	generators	generator	NOUN
ap-1872	114	59	(	(	PUNCT
ap-1872	114	60	11	11	NUM
ap-1872	114	61	)	)	PUNCT
ap-1872	114	62	of	of	ADP
ap-1872	114	63	gl3	gl3	PROPN
ap-1872	114	64	are	be	AUX
ap-1872	114	65	:	:	PUNCT
ap-1872	114	66	t−	t−	PROPN
ap-1872	114	67	1	1	NUM
ap-1872	114	68	=	=	SYM
ap-1872	114	69	(	(	PUNCT
ap-1872	114	70	∂1	∂1	NUM
ap-1872	114	71	0	0	NUM
ap-1872	114	72	0	0	NUM
ap-1872	114	73	∂1	∂1	NOUN
ap-1872	114	74	)	)	PUNCT
ap-1872	114	75	,	,	PUNCT
ap-1872	115	1	t−	t−	PROPN
ap-1872	115	2	2	2	NUM
ap-1872	115	3	=	=	SYM
ap-1872	115	4	(	(	PUNCT
ap-1872	115	5	∂2	∂2	NUM
ap-1872	115	6	0	0	NUM
ap-1872	115	7	0	0	NUM
ap-1872	115	8	∂2	∂2	PROPN
ap-1872	115	9	)	)	PUNCT
ap-1872	115	10	,	,	PUNCT
ap-1872	115	11	e11	e11	NOUN
ap-1872	115	12	=	=	SYM
ap-1872	115	13	(	(	PUNCT
ap-1872	115	14	x1∂1	x1∂1	PROPN
ap-1872	115	15	+	+	PROPN
ap-1872	115	16	1	1	NUM
ap-1872	115	17	0	0	NUM
ap-1872	115	18	0	0	NUM
ap-1872	115	19	x1∂1	x1∂1	PROPN
ap-1872	115	20	)	)	PUNCT
ap-1872	115	21	,	,	PUNCT
ap-1872	115	22	e12	e12	NOUN
ap-1872	115	23	=	=	SYM
ap-1872	115	24	(	(	PUNCT
ap-1872	115	25	x1∂2	x1∂2	NOUN
ap-1872	115	26	1	1	NUM
ap-1872	115	27	0	0	NUM
ap-1872	115	28	x1∂2	x1∂2	NOUN
ap-1872	115	29	)	)	PUNCT
ap-1872	115	30	,	,	PUNCT
ap-1872	115	31	e21	e21	NUM
ap-1872	115	32	=	=	SYM
ap-1872	115	33	(	(	PUNCT
ap-1872	115	34	x2∂1	x2∂1	PROPN
ap-1872	115	35	0	0	NUM
ap-1872	115	36	1	1	NUM
ap-1872	115	37	x2∂1	x2∂1	PROPN
ap-1872	115	38	)	)	PUNCT
ap-1872	115	39	,	,	PUNCT
ap-1872	115	40	e22	e22	NOUN
ap-1872	115	41	=	=	SYM
ap-1872	115	42	(	(	PUNCT
ap-1872	115	43	x2∂2	x2∂2	ADV
ap-1872	115	44	0	0	NUM
ap-1872	115	45	0	0	NUM
ap-1872	116	1	x2∂2	x2∂2	PROPN
ap-1872	116	2	+	+	PROPN
ap-1872	116	3	1	1	NUM
ap-1872	116	4	)	)	PUNCT
ap-1872	116	5	,	,	PUNCT
ap-1872	116	6	e0	e0	PROPN
ap-1872	116	7	=	=	PUNCT
ap-1872	116	8	(	(	PUNCT
ap-1872	116	9	a	a	DET
ap-1872	116	10	0	0	NUM
ap-1872	116	11	0	0	NUM
ap-1872	116	12	a	a	PRON
ap-1872	116	13	)	)	PUNCT
ap-1872	116	14	,	,	PUNCT
ap-1872	116	15	t+	t+	X
ap-1872	116	16	1	1	NUM
ap-1872	116	17	=	=	SYM
ap-1872	116	18	(	(	PUNCT
ap-1872	116	19	x1(a−	x1(a−	PROPN
ap-1872	116	20	1	1	X
ap-1872	116	21	)	)	PUNCT
ap-1872	116	22	−x2	−x2	PROPN
ap-1872	116	23	0	0	NUM
ap-1872	116	24	x1a	x1a	PROPN
ap-1872	116	25	)	)	PUNCT
ap-1872	116	26	,	,	PUNCT
ap-1872	116	27	t+	t+	X
ap-1872	116	28	2	2	NUM
ap-1872	116	29	=	=	SYM
ap-1872	116	30	(	(	PUNCT
ap-1872	116	31	x2a	x2a	PROPN
ap-1872	116	32	0	0	NUM
ap-1872	116	33	−x1	−x1	PROPN
ap-1872	116	34	x2(a−	x2(a−	PROPN
ap-1872	116	35	1	1	NUM
ap-1872	116	36	)	)	PUNCT
ap-1872	116	37	)	)	PUNCT
ap-1872	116	38	,	,	PUNCT
ap-1872	116	39	(	(	PUNCT
ap-1872	116	40	14	14	NUM
ap-1872	116	41	)	)	PUNCT
ap-1872	116	42	wherea	wherea	NOUN
ap-1872	116	43	=	=	SYM
ap-1872	116	44	k−x1∂1−x2∂2	k−x1∂1−x2∂2	NOUN
ap-1872	116	45	.	.	PUNCT
ap-1872	117	1	this	this	PRON
ap-1872	117	2	is	be	AUX
ap-1872	117	3	[	[	X
ap-1872	117	4	k	k	X
ap-1872	117	5	,	,	PUNCT
ap-1872	117	6	1]-representation	1]-representation	NUM
ap-1872	117	7	(	(	PUNCT
ap-1872	117	8	the	the	DET
ap-1872	117	9	young	young	ADJ
ap-1872	117	10	tableau	tableau	PROPN
ap-1872	117	11	has	have	AUX
ap-1872	117	12	two	two	NUM
ap-1872	117	13	rows	row	NOUN
ap-1872	117	14	of	of	ADP
ap-1872	117	15	length	length	NOUN
ap-1872	117	16	k	k	PROPN
ap-1872	117	17	and	and	CCONJ
ap-1872	117	18	1	1	NUM
ap-1872	117	19	,	,	PUNCT
ap-1872	117	20	correspondingly	correspondingly	ADV
ap-1872	117	21	)	)	PUNCT
ap-1872	117	22	,	,	PUNCT
ap-1872	117	23	and	and	CCONJ
ap-1872	117	24	their	their	PRON
ap-1872	117	25	casimir	casimir	NOUN
ap-1872	117	26	operators	operator	NOUN
ap-1872	117	27	are	be	AUX
ap-1872	117	28	:	:	PUNCT
ap-1872	117	29	c1	c1	PROPN
ap-1872	117	30	=	=	PROPN
ap-1872	118	1	k	k	PROPN
ap-1872	119	1	+	+	PROPN
ap-1872	119	2	1	1	NUM
ap-1872	119	3	,	,	PUNCT
ap-1872	119	4	c2	c2	PROPN
ap-1872	119	5	=	=	PUNCT
ap-1872	119	6	(	(	PUNCT
ap-1872	119	7	k	k	X
ap-1872	119	8	+	+	PROPN
ap-1872	119	9	1)2	1)2	NUM
ap-1872	119	10	.	.	PUNCT
ap-1872	120	1	if	if	SCONJ
ap-1872	120	2	parameter	parameter	PROPN
ap-1872	120	3	k	k	PROPN
ap-1872	120	4	takes	take	VERB
ap-1872	120	5	non	non	ADJ
ap-1872	120	6	-	-	ADJ
ap-1872	120	7	negative	negative	ADJ
ap-1872	120	8	integer	integer	NOUN
ap-1872	120	9	the	the	DET
ap-1872	120	10	algebra	algebra	NOUN
ap-1872	120	11	gl3	gl3	ADV
ap-1872	120	12	spanned	span	VERB
ap-1872	120	13	by	by	ADP
ap-1872	120	14	the	the	DET
ap-1872	120	15	generators	generator	NOUN
ap-1872	120	16	(	(	PUNCT
ap-1872	120	17	14	14	NUM
ap-1872	120	18	)	)	PUNCT
ap-1872	120	19	appears	appear	VERB
ap-1872	120	20	in	in	ADP
ap-1872	120	21	finitedimensional	finitedimensional	ADJ
ap-1872	120	22	representation	representation	NOUN
ap-1872	120	23	.	.	PUNCT
ap-1872	121	1	let	let	VERB
ap-1872	121	2	us	we	PRON
ap-1872	121	3	consider	consider	VERB
ap-1872	121	4	several	several	ADJ
ap-1872	121	5	different	different	ADJ
ap-1872	121	6	values	value	NOUN
ap-1872	121	7	of	of	ADP
ap-1872	121	8	k	k	PROPN
ap-1872	121	9	in	in	ADP
ap-1872	121	10	detail	detail	NOUN
ap-1872	121	11	.	.	PUNCT
ap-1872	122	1	the	the	DET
ap-1872	122	2	case	case	NOUN
ap-1872	122	3	k	k	X
ap-1872	123	1	=	=	NOUN
ap-1872	124	1	1	1	X
ap-1872	124	2	.	.	PUNCT
ap-1872	124	3	then	then	ADV
ap-1872	124	4	three	three	NUM
ap-1872	124	5	-	-	PUNCT
ap-1872	124	6	dimensional	dimensional	ADJ
ap-1872	124	7	representation	representation	NOUN
ap-1872	124	8	space	space	NOUN
ap-1872	124	9	v	v	NOUN
ap-1872	124	10	(	(	PUNCT
ap-1872	124	11	2	2	NUM
ap-1872	124	12	)	)	PUNCT
ap-1872	124	13	1	1	NUM
ap-1872	124	14	appears	appear	VERB
ap-1872	124	15	to	to	PART
ap-1872	124	16	be	be	AUX
ap-1872	124	17	spanned	span	VERB
ap-1872	124	18	by	by	ADP
ap-1872	124	19	:	:	PUNCT
ap-1872	124	20	p−	p−	NOUN
ap-1872	124	21	=	=	PUNCT
ap-1872	124	22	[	[	PUNCT
ap-1872	124	23	0	0	NUM
ap-1872	124	24	1	1	NUM
ap-1872	124	25	]	]	PUNCT
ap-1872	124	26	,	,	PUNCT
ap-1872	124	27	p+	p+	X
ap-1872	124	28	=	=	X
ap-1872	124	29	[	[	PUNCT
ap-1872	124	30	1	1	NUM
ap-1872	124	31	0	0	NUM
ap-1872	124	32	]	]	PUNCT
ap-1872	124	33	,	,	PUNCT
ap-1872	124	34	y1	y1	INTJ
ap-1872	124	35	=	=	PUNCT
ap-1872	124	36	[	[	PUNCT
ap-1872	124	37	x2	x2	NOUN
ap-1872	124	38	−x1	−x1	PROPN
ap-1872	124	39	]	]	PUNCT
ap-1872	124	40	.	.	PUNCT
ap-1872	125	1	(	(	PUNCT
ap-1872	125	2	15	15	X
ap-1872	125	3	)	)	PUNCT
ap-1872	125	4	this	this	PRON
ap-1872	125	5	corresponds	correspond	VERB
ap-1872	125	6	to	to	ADP
ap-1872	125	7	antiquark	antiquark	NOUN
ap-1872	125	8	multiplet	multiplet	NOUN
ap-1872	125	9	in	in	ADP
ap-1872	125	10	standard	standard	ADJ
ap-1872	125	11	(	(	PUNCT
ap-1872	125	12	fundamental	fundamental	ADJ
ap-1872	125	13	)	)	PUNCT
ap-1872	125	14	representation	representation	NOUN
ap-1872	125	15	.	.	PUNCT
ap-1872	126	1	the	the	DET
ap-1872	126	2	newton	newton	PROPN
ap-1872	126	3	polygon	polygon	PROPN
ap-1872	126	4	is	be	AUX
ap-1872	126	5	a	a	DET
ap-1872	126	6	triangle	triangle	NOUN
ap-1872	126	7	with	with	ADP
ap-1872	126	8	points	point	NOUN
ap-1872	126	9	p±	p±	PROPN
ap-1872	126	10	as	as	ADP
ap-1872	126	11	vortices	vortex	NOUN
ap-1872	126	12	at	at	ADP
ap-1872	126	13	the	the	DET
ap-1872	126	14	base	base	NOUN
ap-1872	126	15	.	.	PUNCT
ap-1872	127	1	figure	figure	NOUN
ap-1872	127	2	1	1	NUM
ap-1872	127	3	.	.	PUNCT
ap-1872	128	1	newton	newton	PROPN
ap-1872	128	2	hexagon	hexagon	PROPN
ap-1872	128	3	for	for	ADP
ap-1872	128	4	the	the	DET
ap-1872	128	5	representation	representation	NOUN
ap-1872	128	6	space	space	NOUN
ap-1872	128	7	v	v	NOUN
ap-1872	128	8	(	(	PUNCT
ap-1872	128	9	2	2	NUM
ap-1872	128	10	)	)	PUNCT
ap-1872	128	11	4	4	NUM
ap-1872	128	12	of	of	ADP
ap-1872	128	13	the	the	PRON
ap-1872	128	14	[	[	X
ap-1872	128	15	4	4	NUM
ap-1872	128	16	,	,	PUNCT
ap-1872	128	17	1]-representation	1]-representation	NUM
ap-1872	128	18	of	of	ADP
ap-1872	128	19	dimension	dimension	NOUN
ap-1872	128	20	24	24	NUM
ap-1872	128	21	.	.	PUNCT
ap-1872	129	1	the	the	DET
ap-1872	129	2	case	case	NOUN
ap-1872	129	3	k	k	X
ap-1872	130	1	=	=	SYM
ap-1872	131	1	2	2	X
ap-1872	131	2	.	.	PUNCT
ap-1872	131	3	then	then	ADV
ap-1872	131	4	eight	eight	NUM
ap-1872	131	5	-	-	PUNCT
ap-1872	131	6	dimensional	dimensional	ADJ
ap-1872	131	7	representation	representation	NOUN
ap-1872	131	8	space	space	NOUN
ap-1872	131	9	v	v	NOUN
ap-1872	131	10	(	(	PUNCT
ap-1872	131	11	2	2	NUM
ap-1872	131	12	)	)	PUNCT
ap-1872	131	13	2	2	NUM
ap-1872	131	14	appears	appear	VERB
ap-1872	131	15	to	to	PART
ap-1872	131	16	be	be	AUX
ap-1872	131	17	spanned	span	VERB
ap-1872	131	18	by	by	ADP
ap-1872	131	19	:	:	PUNCT
ap-1872	131	20	p−	p−	NOUN
ap-1872	131	21	=	=	PUNCT
ap-1872	131	22	[	[	PUNCT
ap-1872	131	23	0	0	NUM
ap-1872	131	24	1	1	NUM
ap-1872	131	25	]	]	PUNCT
ap-1872	131	26	,	,	PUNCT
ap-1872	131	27	p+	p+	X
ap-1872	131	28	=	=	X
ap-1872	131	29	[	[	PUNCT
ap-1872	131	30	1	1	NUM
ap-1872	131	31	0	0	NUM
ap-1872	131	32	]	]	PUNCT
ap-1872	131	33	,	,	PUNCT
ap-1872	131	34	p	p	X
ap-1872	131	35	(	(	PUNCT
ap-1872	131	36	1	1	NUM
ap-1872	131	37	)	)	PUNCT
ap-1872	131	38	−	−	NOUN
ap-1872	132	1	=	=	PUNCT
ap-1872	132	2	[	[	PUNCT
ap-1872	132	3	0	0	NUM
ap-1872	132	4	x2	x2	NOUN
ap-1872	132	5	]	]	PUNCT
ap-1872	132	6	,	,	PUNCT
ap-1872	132	7	y	y	PROPN
ap-1872	132	8	(	(	PUNCT
ap-1872	132	9	1	1	NUM
ap-1872	132	10	)	)	PUNCT
ap-1872	132	11	1	1	NUM
ap-1872	132	12	=	=	PUNCT
ap-1872	133	1	[	[	PUNCT
ap-1872	133	2	0	0	NUM
ap-1872	133	3	x1	x1	PRON
ap-1872	133	4	]	]	PUNCT
ap-1872	133	5	,	,	PUNCT
ap-1872	133	6	y	y	PROPN
ap-1872	133	7	(	(	PUNCT
ap-1872	133	8	2	2	NUM
ap-1872	133	9	)	)	PUNCT
ap-1872	133	10	1	1	NUM
ap-1872	133	11	=	=	PUNCT
ap-1872	134	1	[	[	PUNCT
ap-1872	134	2	x2	x2	NOUN
ap-1872	134	3	0	0	NUM
ap-1872	134	4	]	]	PUNCT
ap-1872	134	5	,	,	PUNCT
ap-1872	134	6	p	p	X
ap-1872	134	7	(	(	PUNCT
ap-1872	134	8	1	1	NUM
ap-1872	134	9	)	)	PUNCT
ap-1872	134	10	+	+	NOUN
ap-1872	134	11	=	=	PUNCT
ap-1872	135	1	[	[	PUNCT
ap-1872	135	2	x1	x1	PROPN
ap-1872	135	3	0	0	NUM
ap-1872	135	4	]	]	PUNCT
ap-1872	135	5	,	,	PUNCT
ap-1872	135	6	y2	y2	NOUN
ap-1872	135	7	=	=	PUNCT
ap-1872	136	1	[	[	PUNCT
ap-1872	136	2	x2	x2	NOUN
ap-1872	136	3	2	2	NUM
ap-1872	136	4	−x1x2	−x1x2	NOUN
ap-1872	136	5	]	]	PUNCT
ap-1872	136	6	,	,	PUNCT
ap-1872	136	7	y3	y3	NOUN
ap-1872	136	8	=	=	PUNCT
ap-1872	136	9	[	[	PUNCT
ap-1872	136	10	x1x2	x1x2	X
ap-1872	136	11	−x2	−x2	NOUN
ap-1872	136	12	1	1	NUM
ap-1872	136	13	]	]	PUNCT
ap-1872	136	14	.	.	PUNCT
ap-1872	137	1	(	(	PUNCT
ap-1872	137	2	16	16	NUM
ap-1872	137	3	)	)	PUNCT
ap-1872	137	4	this	this	PRON
ap-1872	137	5	corresponds	correspond	VERB
ap-1872	137	6	to	to	ADP
ap-1872	137	7	octet	octet	NOUN
ap-1872	137	8	in	in	ADP
ap-1872	137	9	standard	standard	ADJ
ap-1872	137	10	(	(	PUNCT
ap-1872	137	11	fundamental	fundamental	ADJ
ap-1872	137	12	)	)	PUNCT
ap-1872	137	13	representation	representation	NOUN
ap-1872	137	14	.	.	PUNCT
ap-1872	138	1	space	space	NOUN
ap-1872	138	2	v	v	NOUN
ap-1872	138	3	(	(	PUNCT
ap-1872	138	4	2	2	NUM
ap-1872	138	5	)	)	PUNCT
ap-1872	138	6	2	2	NUM
ap-1872	138	7	contains	contain	VERB
ap-1872	138	8	v	v	NOUN
ap-1872	138	9	(	(	PUNCT
ap-1872	138	10	2	2	NUM
ap-1872	138	11	)	)	PUNCT
ap-1872	138	12	1	1	NUM
ap-1872	138	13	as	as	ADP
ap-1872	138	14	a	a	DET
ap-1872	138	15	subspace	subspace	NOUN
ap-1872	138	16	,	,	PUNCT
ap-1872	138	17	v	v	NOUN
ap-1872	138	18	(	(	PUNCT
ap-1872	138	19	2	2	NUM
ap-1872	138	20	)	)	PUNCT
ap-1872	138	21	1	1	NUM
ap-1872	139	1	⊂	⊂	PROPN
ap-1872	139	2	v	v	X
ap-1872	139	3	(	(	PUNCT
ap-1872	139	4	2	2	NUM
ap-1872	139	5	)	)	PUNCT
ap-1872	139	6	2	2	NUM
ap-1872	139	7	.	.	PUNCT
ap-1872	140	1	it	it	PRON
ap-1872	140	2	should	should	AUX
ap-1872	140	3	be	be	AUX
ap-1872	140	4	mentioned	mention	VERB
ap-1872	140	5	that	that	SCONJ
ap-1872	140	6	y1	y1	NOUN
ap-1872	140	7	=	=	PUNCT
ap-1872	140	8	−y	−y	INTJ
ap-1872	140	9	(	(	PUNCT
ap-1872	140	10	1	1	NUM
ap-1872	140	11	)	)	PUNCT
ap-1872	140	12	1	1	NUM
ap-1872	141	1	+	+	CCONJ
ap-1872	141	2	y	y	PROPN
ap-1872	141	3	(	(	PUNCT
ap-1872	141	4	2	2	NUM
ap-1872	141	5	)	)	PUNCT
ap-1872	141	6	1	1	NUM
ap-1872	141	7	.	.	PUNCT
ap-1872	142	1	now	now	ADV
ap-1872	142	2	the	the	DET
ap-1872	142	3	newton	newton	PROPN
ap-1872	142	4	polygon	polygon	PROPN
ap-1872	142	5	is	be	AUX
ap-1872	142	6	a	a	DET
ap-1872	142	7	hexagon	hexagon	NOUN
ap-1872	142	8	where	where	SCONJ
ap-1872	142	9	the	the	DET
ap-1872	142	10	central	central	ADJ
ap-1872	142	11	point	point	NOUN
ap-1872	142	12	is	be	AUX
ap-1872	142	13	doubled	double	VERB
ap-1872	142	14	,	,	PUNCT
ap-1872	142	15	being	be	AUX
ap-1872	142	16	presented	present	VERB
ap-1872	142	17	by	by	ADP
ap-1872	142	18	y	y	PROPN
ap-1872	142	19	(	(	PUNCT
ap-1872	142	20	1,2	1,2	NUM
ap-1872	142	21	)	)	PUNCT
ap-1872	142	22	1	1	NUM
ap-1872	142	23	,	,	PUNCT
ap-1872	142	24	and	and	CCONJ
ap-1872	142	25	the	the	DET
ap-1872	142	26	lower	low	ADJ
ap-1872	142	27	(	(	PUNCT
ap-1872	142	28	upper	upper	ADJ
ap-1872	142	29	)	)	PUNCT
ap-1872	142	30	base	base	NOUN
ap-1872	142	31	has	have	VERB
ap-1872	142	32	length	length	NOUN
ap-1872	142	33	two	two	NUM
ap-1872	142	34	being	be	AUX
ap-1872	142	35	given	give	VERB
ap-1872	142	36	by	by	ADP
ap-1872	142	37	p±	p±	PROPN
ap-1872	142	38	(	(	PUNCT
ap-1872	142	39	y2,3	y2,3	NOUN
ap-1872	142	40	)	)	PUNCT
ap-1872	142	41	.	.	PUNCT
ap-1872	143	1	the	the	DET
ap-1872	143	2	case	case	NOUN
ap-1872	143	3	k	k	X
ap-1872	144	1	=	=	SYM
ap-1872	144	2	3	3	X
ap-1872	144	3	.	.	PUNCT
ap-1872	145	1	the	the	DET
ap-1872	145	2	representation	representation	NOUN
ap-1872	145	3	space	space	NOUN
ap-1872	145	4	v	v	NOUN
ap-1872	145	5	(	(	PUNCT
ap-1872	145	6	2	2	NUM
ap-1872	145	7	)	)	PUNCT
ap-1872	145	8	3	3	NUM
ap-1872	145	9	is	be	AUX
ap-1872	145	10	15	15	NUM
ap-1872	145	11	-	-	PUNCT
ap-1872	145	12	dimensional	dimensional	ADJ
ap-1872	145	13	.	.	PUNCT
ap-1872	146	1	in	in	ADP
ap-1872	146	2	addition	addition	NOUN
ap-1872	146	3	to	to	ADP
ap-1872	146	4	p±	p±	PROPN
ap-1872	146	5	,	,	PUNCT
ap-1872	146	6	p	p	X
ap-1872	146	7	(	(	PUNCT
ap-1872	146	8	1	1	NUM
ap-1872	146	9	)	)	PUNCT
ap-1872	146	10	±	±	NOUN
ap-1872	146	11	and	and	CCONJ
ap-1872	146	12	y	y	PROPN
ap-1872	146	13	(	(	PUNCT
ap-1872	146	14	1,2	1,2	NUM
ap-1872	146	15	)	)	PUNCT
ap-1872	146	16	1	1	NUM
ap-1872	146	17	(	(	PUNCT
ap-1872	146	18	see	see	VERB
ap-1872	146	19	(	(	PUNCT
ap-1872	146	20	15	15	NUM
ap-1872	146	21	)	)	PUNCT
ap-1872	146	22	and	and	CCONJ
ap-1872	146	23	(	(	PUNCT
ap-1872	146	24	16	16	NUM
ap-1872	146	25	)	)	PUNCT
ap-1872	146	26	)	)	PUNCT
ap-1872	146	27	,	,	PUNCT
ap-1872	146	28	it	it	PRON
ap-1872	146	29	contains	contain	VERB
ap-1872	146	30	several	several	ADJ
ap-1872	146	31	vectors	vector	NOUN
ap-1872	146	32	more	more	ADV
ap-1872	146	33	,	,	PUNCT
ap-1872	146	34	namely	namely	ADV
ap-1872	146	35	,	,	PUNCT
ap-1872	146	36	p	p	X
ap-1872	146	37	(	(	PUNCT
ap-1872	146	38	2	2	NUM
ap-1872	146	39	)	)	PUNCT
ap-1872	146	40	−	−	NOUN
ap-1872	147	1	=	=	PUNCT
ap-1872	147	2	[	[	PUNCT
ap-1872	147	3	0	0	NUM
ap-1872	147	4	x2	x2	NOUN
ap-1872	147	5	2	2	NUM
ap-1872	147	6	]	]	PUNCT
ap-1872	147	7	,	,	PUNCT
ap-1872	147	8	p	p	X
ap-1872	147	9	(	(	PUNCT
ap-1872	147	10	2	2	NUM
ap-1872	147	11	)	)	PUNCT
ap-1872	147	12	+	+	NOUN
ap-1872	147	13	=	=	PUNCT
ap-1872	148	1	[	[	PUNCT
ap-1872	148	2	x2	x2	NOUN
ap-1872	148	3	1	1	NUM
ap-1872	148	4	0	0	NUM
ap-1872	148	5	]	]	PUNCT
ap-1872	148	6	,	,	PUNCT
ap-1872	148	7	(	(	PUNCT
ap-1872	148	8	17	17	NUM
ap-1872	148	9	)	)	PUNCT
ap-1872	148	10	which	which	PRON
ap-1872	148	11	are	be	AUX
ap-1872	148	12	situated	situate	VERB
ap-1872	148	13	on	on	ADP
ap-1872	148	14	the	the	DET
ap-1872	148	15	±-sides	±-side	NOUN
ap-1872	148	16	of	of	ADP
ap-1872	148	17	the	the	DET
ap-1872	148	18	newton	newton	PROPN
ap-1872	148	19	hexagon	hexagon	PROPN
ap-1872	148	20	,	,	PUNCT
ap-1872	148	21	doubling	double	VERB
ap-1872	148	22	the	the	DET
ap-1872	148	23	points	point	NOUN
ap-1872	148	24	corresponding	correspond	VERB
ap-1872	148	25	to	to	ADP
ap-1872	148	26	y2,3	y2,3	PROPN
ap-1872	148	27	(	(	PUNCT
ap-1872	148	28	see	see	VERB
ap-1872	148	29	(	(	PUNCT
ap-1872	148	30	16	16	NUM
ap-1872	148	31	)	)	PUNCT
ap-1872	148	32	)	)	PUNCT
ap-1872	149	1	y	y	PROPN
ap-1872	149	2	(	(	PUNCT
ap-1872	149	3	1	1	NUM
ap-1872	149	4	)	)	SYM
ap-1872	149	5	2	2	NUM
ap-1872	149	6	=	=	SYM
ap-1872	149	7	[	[	PUNCT
ap-1872	149	8	0	0	NUM
ap-1872	149	9	x1x2	x1x2	X
ap-1872	149	10	]	]	X
ap-1872	149	11	,	,	PUNCT
ap-1872	149	12	y	y	PROPN
ap-1872	149	13	(	(	PUNCT
ap-1872	149	14	2	2	NUM
ap-1872	149	15	)	)	PUNCT
ap-1872	149	16	2	2	NUM
ap-1872	149	17	=	=	SYM
ap-1872	150	1	[	[	PUNCT
ap-1872	150	2	x2	x2	NOUN
ap-1872	150	3	2	2	NUM
ap-1872	150	4	0	0	NUM
ap-1872	150	5	]	]	PUNCT
ap-1872	150	6	,	,	PUNCT
ap-1872	150	7	y	y	PROPN
ap-1872	150	8	(	(	PUNCT
ap-1872	150	9	1	1	NUM
ap-1872	150	10	)	)	PUNCT
ap-1872	150	11	3	3	NUM
ap-1872	150	12	=	=	PUNCT
ap-1872	150	13	[	[	PUNCT
ap-1872	150	14	0	0	NUM
ap-1872	150	15	x2	x2	NOUN
ap-1872	150	16	1	1	NUM
ap-1872	150	17	]	]	PUNCT
ap-1872	150	18	,	,	PUNCT
ap-1872	150	19	y	y	PROPN
ap-1872	150	20	(	(	PUNCT
ap-1872	150	21	2	2	NUM
ap-1872	150	22	)	)	PUNCT
ap-1872	150	23	3	3	NUM
ap-1872	150	24	=	=	PUNCT
ap-1872	150	25	[	[	PUNCT
ap-1872	150	26	x1x2	x1x2	X
ap-1872	150	27	0	0	NUM
ap-1872	150	28	]	]	PUNCT
ap-1872	150	29	,	,	PUNCT
ap-1872	150	30	(	(	PUNCT
ap-1872	150	31	18	18	NUM
ap-1872	150	32	)	)	PUNCT
ap-1872	150	33	plus	plus	CCONJ
ap-1872	150	34	three	three	NUM
ap-1872	150	35	extra	extra	ADJ
ap-1872	150	36	vectors	vector	NOUN
ap-1872	150	37	on	on	ADP
ap-1872	150	38	the	the	DET
ap-1872	150	39	boundary	boundary	ADJ
ap-1872	150	40	y8	y8	PROPN
ap-1872	150	41	=	=	PUNCT
ap-1872	151	1	[	[	PUNCT
ap-1872	151	2	x3	x3	NOUN
ap-1872	151	3	2	2	NUM
ap-1872	151	4	−x1x2	−x1x2	NOUN
ap-1872	151	5	2	2	NUM
ap-1872	151	6	]	]	PUNCT
ap-1872	151	7	,	,	PUNCT
ap-1872	151	8	y9	y9	PROPN
ap-1872	151	9	=	=	PUNCT
ap-1872	152	1	[	[	PUNCT
ap-1872	152	2	x1x	x1x	PROPN
ap-1872	152	3	2	2	NUM
ap-1872	152	4	2	2	NUM
ap-1872	152	5	−x2	−x2	NOUN
ap-1872	152	6	1x2	1x2	NUM
ap-1872	152	7	]	]	PUNCT
ap-1872	152	8	,	,	PUNCT
ap-1872	152	9	y10	y10	NOUN
ap-1872	152	10	=	=	PUNCT
ap-1872	153	1	[	[	PUNCT
ap-1872	153	2	x2	x2	PROPN
ap-1872	153	3	1x2	1x2	NUM
ap-1872	153	4	−x3	−x3	PROPN
ap-1872	153	5	1	1	NUM
ap-1872	153	6	]	]	PUNCT
ap-1872	153	7	.	.	PUNCT
ap-1872	154	1	(	(	PUNCT
ap-1872	154	2	19	19	NUM
ap-1872	154	3	)	)	PUNCT
ap-1872	154	4	it	it	PRON
ap-1872	154	5	is	be	AUX
ap-1872	154	6	clear	clear	ADJ
ap-1872	154	7	that	that	SCONJ
ap-1872	154	8	v	v	X
ap-1872	154	9	(	(	PUNCT
ap-1872	154	10	2	2	NUM
ap-1872	154	11	)	)	PUNCT
ap-1872	154	12	1	1	NUM
ap-1872	154	13	⊂	⊂	PROPN
ap-1872	154	14	v	v	X
ap-1872	154	15	(	(	PUNCT
ap-1872	154	16	2	2	NUM
ap-1872	154	17	)	)	PUNCT
ap-1872	154	18	2	2	NUM
ap-1872	154	19	⊂	⊂	PROPN
ap-1872	154	20	v	v	X
ap-1872	154	21	(	(	PUNCT
ap-1872	154	22	2	2	NUM
ap-1872	154	23	)	)	PUNCT
ap-1872	154	24	3	3	NUM
ap-1872	154	25	.	.	PUNCT
ap-1872	155	1	all	all	DET
ap-1872	155	2	internal	internal	ADJ
ap-1872	155	3	points	point	NOUN
ap-1872	155	4	of	of	ADP
ap-1872	155	5	the	the	DET
ap-1872	155	6	newton	newton	PROPN
ap-1872	155	7	hexagon	hexagon	PROPN
ap-1872	155	8	are	be	AUX
ap-1872	155	9	double	double	ADJ
ap-1872	155	10	points	point	NOUN
ap-1872	155	11	,	,	PUNCT
ap-1872	155	12	while	while	SCONJ
ap-1872	155	13	the	the	DET
ap-1872	155	14	points	point	NOUN
ap-1872	155	15	on	on	ADP
ap-1872	155	16	the	the	DET
ap-1872	155	17	boundary	boundary	NOUN
ap-1872	155	18	are	be	AUX
ap-1872	155	19	single	single	ADJ
ap-1872	155	20	ones	one	NOUN
ap-1872	155	21	.	.	PUNCT
ap-1872	156	1	464	464	NUM
ap-1872	156	2	vol	vol	NOUN
ap-1872	156	3	.	.	PUNCT
ap-1872	157	1	53	53	NUM
ap-1872	157	2	no	no	NOUN
ap-1872	157	3	.	.	PUNCT
ap-1872	158	1	5/2013	5/2013	NUM
ap-1872	158	2	gln+1	gln+1	VERB
ap-1872	158	3	algebra	algebra	NOUN
ap-1872	158	4	of	of	ADP
ap-1872	158	5	matrix	matrix	NOUN
ap-1872	158	6	differential	differential	NOUN
ap-1872	158	7	operators	operator	NOUN
ap-1872	158	8	the	the	DET
ap-1872	158	9	general	general	ADJ
ap-1872	158	10	case	case	NOUN
ap-1872	158	11	.	.	PUNCT
ap-1872	159	1	the	the	DET
ap-1872	159	2	finite	finite	ADJ
ap-1872	159	3	-	-	ADJ
ap-1872	159	4	dimensional	dimensional	ADJ
ap-1872	159	5	representation	representation	NOUN
ap-1872	159	6	space	space	NOUN
ap-1872	159	7	v	v	NOUN
ap-1872	159	8	(	(	PUNCT
ap-1872	159	9	2	2	NUM
ap-1872	159	10	)	)	PUNCT
ap-1872	159	11	k	k	PROPN
ap-1872	159	12	has	have	AUX
ap-1872	159	13	dimension	dimension	NOUN
ap-1872	159	14	k(k	k(k	PROPN
ap-1872	159	15	+	+	CCONJ
ap-1872	159	16	2	2	NUM
ap-1872	159	17	)	)	PUNCT
ap-1872	159	18	and	and	CCONJ
ap-1872	159	19	is	be	AUX
ap-1872	159	20	presented	present	VERB
ap-1872	159	21	by	by	ADP
ap-1872	159	22	the	the	DET
ap-1872	159	23	newton	newton	PROPN
ap-1872	159	24	hexagon	hexagon	PROPN
ap-1872	159	25	,	,	PUNCT
ap-1872	159	26	which	which	PRON
ap-1872	159	27	contains	contain	VERB
ap-1872	159	28	(	(	PUNCT
ap-1872	159	29	k	k	PROPN
ap-1872	159	30	+	+	PROPN
ap-1872	159	31	1	1	X
ap-1872	159	32	)	)	PUNCT
ap-1872	159	33	horizontal	horizontal	ADJ
ap-1872	159	34	layers	layer	NOUN
ap-1872	159	35	.	.	PUNCT
ap-1872	160	1	the	the	DET
ap-1872	160	2	lower	low	ADJ
ap-1872	160	3	base	base	NOUN
ap-1872	160	4	has	have	VERB
ap-1872	160	5	length	length	NOUN
ap-1872	160	6	two	two	NUM
ap-1872	160	7	,	,	PUNCT
ap-1872	160	8	while	while	SCONJ
ap-1872	160	9	the	the	DET
ap-1872	160	10	upper	upper	ADJ
ap-1872	160	11	base	base	NOUN
ap-1872	160	12	has	have	VERB
ap-1872	160	13	length	length	NOUN
ap-1872	160	14	k	k	PROPN
ap-1872	160	15	(	(	PUNCT
ap-1872	160	16	see	see	VERB
ap-1872	160	17	fig	fig	NOUN
ap-1872	160	18	.	.	PUNCT
ap-1872	161	1	1	1	NUM
ap-1872	161	2	as	as	ADP
ap-1872	161	3	an	an	DET
ap-1872	161	4	illustration	illustration	NOUN
ap-1872	161	5	for	for	ADP
ap-1872	161	6	k	k	PROPN
ap-1872	161	7	=	=	PROPN
ap-1872	161	8	4	4	NUM
ap-1872	161	9	)	)	PUNCT
ap-1872	161	10	.	.	PUNCT
ap-1872	162	1	all	all	DET
ap-1872	162	2	internal	internal	ADJ
ap-1872	162	3	points	point	NOUN
ap-1872	162	4	of	of	ADP
ap-1872	162	5	the	the	DET
ap-1872	162	6	newton	newton	PROPN
ap-1872	162	7	hexagon	hexagon	PROPN
ap-1872	162	8	are	be	AUX
ap-1872	162	9	double	double	ADJ
ap-1872	162	10	points	point	NOUN
ap-1872	162	11	,	,	PUNCT
ap-1872	162	12	while	while	SCONJ
ap-1872	162	13	the	the	DET
ap-1872	162	14	points	point	NOUN
ap-1872	162	15	on	on	ADP
ap-1872	162	16	the	the	DET
ap-1872	162	17	boundary	boundary	NOUN
ap-1872	162	18	are	be	AUX
ap-1872	162	19	single	single	ADJ
ap-1872	162	20	ones	one	NOUN
ap-1872	162	21	.	.	PUNCT
ap-1872	163	1	except	except	SCONJ
ap-1872	163	2	for	for	ADP
ap-1872	163	3	k	k	PROPN
ap-1872	163	4	vectors	vector	NOUN
ap-1872	163	5	of	of	ADP
ap-1872	163	6	the	the	DET
ap-1872	163	7	last	last	ADJ
ap-1872	163	8	(	(	PUNCT
ap-1872	163	9	highest	high	ADJ
ap-1872	163	10	)	)	PUNCT
ap-1872	163	11	layer	layer	NOUN
ap-1872	163	12	of	of	ADP
ap-1872	163	13	the	the	DET
ap-1872	163	14	newton	newton	PROPN
ap-1872	163	15	hexagon	hexagon	PROPN
ap-1872	163	16	,	,	PUNCT
ap-1872	163	17	the	the	DET
ap-1872	163	18	remaining	remain	VERB
ap-1872	163	19	k(k	k(k	NOUN
ap-1872	163	20	+	+	CCONJ
ap-1872	163	21	1	1	X
ap-1872	163	22	)	)	PUNCT
ap-1872	163	23	vectors	vector	NOUN
ap-1872	163	24	span	span	VERB
ap-1872	163	25	the	the	DET
ap-1872	163	26	space	space	NOUN
ap-1872	163	27	of	of	ADP
ap-1872	163	28	all	all	DET
ap-1872	163	29	possible	possible	ADJ
ap-1872	163	30	two	two	NUM
ap-1872	163	31	-	-	PUNCT
ap-1872	163	32	component	component	NOUN
ap-1872	163	33	spinors	spinor	NOUN
ap-1872	163	34	with	with	ADP
ap-1872	163	35	components	component	NOUN
ap-1872	163	36	given	give	VERB
ap-1872	163	37	by	by	ADP
ap-1872	163	38	the	the	DET
ap-1872	163	39	inhomogeneous	inhomogeneous	ADJ
ap-1872	163	40	polynomials	polynomial	NOUN
ap-1872	163	41	in	in	ADP
ap-1872	163	42	x1	x1	PROPN
ap-1872	163	43	,	,	PUNCT
ap-1872	163	44	x2	x2	PROPN
ap-1872	163	45	of	of	ADP
ap-1872	163	46	degree	degree	NOUN
ap-1872	163	47	not	not	PART
ap-1872	163	48	higher	high	ADJ
ap-1872	163	49	than	than	ADP
ap-1872	163	50	(	(	PUNCT
ap-1872	163	51	k	k	NOUN
ap-1872	163	52	−	−	PROPN
ap-1872	163	53	1	1	NUM
ap-1872	163	54	)	)	PUNCT
ap-1872	163	55	.	.	PUNCT
ap-1872	164	1	we	we	PRON
ap-1872	164	2	denote	denote	VERB
ap-1872	164	3	this	this	DET
ap-1872	164	4	space	space	NOUN
ap-1872	164	5	as	as	ADP
ap-1872	164	6	ṽ	ṽ	PROPN
ap-1872	164	7	(	(	PUNCT
ap-1872	164	8	2	2	NUM
ap-1872	164	9	)	)	PUNCT
ap-1872	164	10	k	k	NOUN
ap-1872	164	11	⊂	⊂	PROPN
ap-1872	164	12	v	v	X
ap-1872	164	13	(	(	PUNCT
ap-1872	164	14	2	2	NUM
ap-1872	164	15	)	)	PUNCT
ap-1872	164	16	k	k	NOUN
ap-1872	164	17	.	.	PUNCT
ap-1872	165	1	the	the	DET
ap-1872	165	2	non	non	ADJ
ap-1872	165	3	-	-	ADJ
ap-1872	165	4	trivial	trivial	ADJ
ap-1872	165	5	task	task	NOUN
ap-1872	165	6	is	be	AUX
ap-1872	165	7	to	to	PART
ap-1872	165	8	describe	describe	VERB
ap-1872	165	9	k	k	PROPN
ap-1872	165	10	vectors	vector	NOUN
ap-1872	165	11	of	of	ADP
ap-1872	165	12	the	the	DET
ap-1872	165	13	last	last	ADJ
ap-1872	165	14	(	(	PUNCT
ap-1872	165	15	highest	high	ADJ
ap-1872	165	16	)	)	PUNCT
ap-1872	165	17	layer	layer	NOUN
ap-1872	165	18	of	of	ADP
ap-1872	165	19	the	the	DET
ap-1872	165	20	hexagon	hexagon	NOUN
ap-1872	165	21	.	.	PUNCT
ap-1872	166	1	after	after	ADP
ap-1872	166	2	some	some	DET
ap-1872	166	3	analysis	analysis	NOUN
ap-1872	166	4	one	one	PRON
ap-1872	166	5	can	can	AUX
ap-1872	166	6	find	find	VERB
ap-1872	166	7	that	that	SCONJ
ap-1872	166	8	they	they	PRON
ap-1872	166	9	have	have	VERB
ap-1872	166	10	the	the	DET
ap-1872	166	11	form	form	NOUN
ap-1872	166	12	yk(k+1)+i	yk(k+1)+i	NOUN
ap-1872	166	13	=	=	PUNCT
ap-1872	167	1	[	[	PUNCT
ap-1872	167	2	xk−i	xk−i	NOUN
ap-1872	167	3	2	2	NUM
ap-1872	167	4	xi1	xi1	PROPN
ap-1872	167	5	−xk−i−1	−xk−i−1	NUM
ap-1872	167	6	2	2	NUM
ap-1872	167	7	xi+1	xi+1	NUM
ap-1872	167	8	1	1	NUM
ap-1872	167	9	]	]	PUNCT
ap-1872	167	10	,	,	PUNCT
ap-1872	167	11	i	i	PRON
ap-1872	167	12	=	=	NOUN
ap-1872	167	13	0	0	NUM
ap-1872	167	14	,	,	PUNCT
ap-1872	167	15	1	1	NUM
ap-1872	167	16	,	,	PUNCT
ap-1872	167	17	2	2	NUM
ap-1872	167	18	,	,	PUNCT
ap-1872	167	19	.	.	PUNCT
ap-1872	167	20	.	.	PUNCT
ap-1872	167	21	.	.	PUNCT
ap-1872	168	1	,	,	PUNCT
ap-1872	168	2	(	(	PUNCT
ap-1872	168	3	k	k	NOUN
ap-1872	168	4	−	−	PROPN
ap-1872	168	5	1	1	NUM
ap-1872	168	6	)	)	PUNCT
ap-1872	168	7	,	,	PUNCT
ap-1872	168	8	(	(	PUNCT
ap-1872	168	9	20	20	NUM
ap-1872	168	10	)	)	PUNCT
ap-1872	168	11	hence	hence	ADV
ap-1872	168	12	they	they	PRON
ap-1872	168	13	span	span	VERB
ap-1872	168	14	a	a	DET
ap-1872	168	15	non	non	ADJ
ap-1872	168	16	-	-	ADJ
ap-1872	168	17	trivial	trivial	ADJ
ap-1872	168	18	k	k	ADJ
ap-1872	168	19	-	-	ADJ
ap-1872	168	20	dimensional	dimensional	ADJ
ap-1872	168	21	subspace	subspace	NOUN
ap-1872	168	22	of	of	ADP
ap-1872	168	23	spinors	spinor	NOUN
ap-1872	168	24	with	with	ADP
ap-1872	168	25	components	component	NOUN
ap-1872	168	26	given	give	VERB
ap-1872	168	27	by	by	ADP
ap-1872	168	28	specific	specific	ADJ
ap-1872	168	29	homogeneous	homogeneous	ADJ
ap-1872	168	30	polynomials	polynomial	NOUN
ap-1872	168	31	of	of	ADP
ap-1872	168	32	degree	degree	NOUN
ap-1872	168	33	k.	k.	PROPN
ap-1872	168	34	3.3	3.3	NUM
ap-1872	168	35	.	.	PUNCT
ap-1872	169	1	reps	rep	NOUN
ap-1872	169	2	in	in	ADP
ap-1872	169	3	3×	3×	NUM
ap-1872	169	4	3	3	NUM
ap-1872	169	5	matrices	matrix	NOUN
ap-1872	169	6	take	take	VERB
ap-1872	169	7	gl2	gl2	PROPN
ap-1872	169	8	in	in	ADP
ap-1872	169	9	three	three	NUM
ap-1872	169	10	-	-	PUNCT
ap-1872	169	11	dimensional	dimensional	ADJ
ap-1872	169	12	reps	rep	NOUN
ap-1872	169	13	by	by	ADP
ap-1872	169	14	3×	3×	NUM
ap-1872	169	15	3	3	NUM
ap-1872	169	16	matrices	matrix	NOUN
ap-1872	169	17	,	,	PUNCT
ap-1872	169	18	m11	m11	NOUN
ap-1872	169	19	=	=	PUNCT
ap-1872	170	1	2	2	ADP
ap-1872	170	2	0	0	NUM
ap-1872	170	3	0	0	NUM
ap-1872	170	4	0	0	NUM
ap-1872	170	5	1	1	NUM
ap-1872	170	6	0	0	NUM
ap-1872	170	7	0	0	NUM
ap-1872	170	8	0	0	NUM
ap-1872	170	9	0	0	NUM
ap-1872	171	1			PROPN
ap-1872	171	2	,	,	PUNCT
ap-1872	171	3	m22	m22	PROPN
ap-1872	171	4	=	=	PUNCT
ap-1872	171	5	0	0	ADP
ap-1872	171	6	0	0	NUM
ap-1872	171	7	0	0	NUM
ap-1872	171	8	0	0	NUM
ap-1872	171	9	1	1	NUM
ap-1872	171	10	0	0	NUM
ap-1872	171	11	0	0	NUM
ap-1872	171	12	0	0	NUM
ap-1872	171	13	2	2	NUM
ap-1872	171	14			PROPN
ap-1872	171	15	,	,	PUNCT
ap-1872	171	16	m12	m12	NOUN
ap-1872	171	17	=	=	SYM
ap-1872	171	18	0	0	ADV
ap-1872	171	19	√	√	ADV
ap-1872	171	20	2	2	NUM
ap-1872	171	21	0	0	NUM
ap-1872	171	22	0	0	NUM
ap-1872	171	23	0	0	NUM
ap-1872	171	24	√	√	NUM
ap-1872	171	25	2	2	NUM
ap-1872	171	26	0	0	NUM
ap-1872	171	27	0	0	NUM
ap-1872	171	28	0	0	NUM
ap-1872	172	1			PROPN
ap-1872	172	2	,	,	PUNCT
ap-1872	172	3	m21	m21	NOUN
ap-1872	172	4	=	=	PUNCT
ap-1872	172	5			PROPN
ap-1872	172	6	0	0	NUM
ap-1872	172	7	0	0	NUM
ap-1872	172	8	0√	0√	NOUN
ap-1872	173	1	2	2	NUM
ap-1872	173	2	0	0	NUM
ap-1872	173	3	0	0	NUM
ap-1872	173	4	0	0	NUM
ap-1872	173	5	√	√	NUM
ap-1872	173	6	2	2	NUM
ap-1872	173	7	0	0	NUM
ap-1872	173	8			PROPN
ap-1872	173	9	.	.	PUNCT
ap-1872	174	1	then	then	ADV
ap-1872	174	2	the	the	DET
ap-1872	174	3	generators	generator	NOUN
ap-1872	174	4	(	(	PUNCT
ap-1872	174	5	11	11	NUM
ap-1872	174	6	)	)	PUNCT
ap-1872	174	7	of	of	ADP
ap-1872	174	8	gl3	gl3	PROPN
ap-1872	174	9	are	be	AUX
ap-1872	174	10	:	:	PUNCT
ap-1872	174	11	t−	t−	PROPN
ap-1872	174	12	1	1	NUM
ap-1872	174	13	=	=	SYM
ap-1872	174	14	∂1	∂1	NOUN
ap-1872	174	15	0	0	NUM
ap-1872	174	16	0	0	NUM
ap-1872	174	17	0	0	NUM
ap-1872	174	18	∂1	∂1	NUM
ap-1872	174	19	0	0	NUM
ap-1872	174	20	0	0	NUM
ap-1872	174	21	0	0	NUM
ap-1872	174	22	∂1	∂1	ADJ
ap-1872	174	23			PROPN
ap-1872	174	24	,	,	PUNCT
ap-1872	174	25	t−	t−	PROPN
ap-1872	174	26	2	2	NUM
ap-1872	174	27	=	=	SYM
ap-1872	174	28	∂2	∂2	SYM
ap-1872	174	29	0	0	NUM
ap-1872	174	30	0	0	NUM
ap-1872	174	31	0	0	NUM
ap-1872	175	1	∂2	∂2	NOUN
ap-1872	175	2	0	0	NUM
ap-1872	175	3	0	0	NUM
ap-1872	175	4	0	0	NUM
ap-1872	175	5	∂2	∂2	PROPN
ap-1872	175	6			PROPN
ap-1872	175	7	,	,	PUNCT
ap-1872	175	8	e11	e11	NOUN
ap-1872	175	9	=	=	PUNCT
ap-1872	175	10	x1∂1	x1∂1	ADJ
ap-1872	175	11	+	+	CCONJ
ap-1872	175	12	2	2	NUM
ap-1872	175	13	0	0	NUM
ap-1872	175	14	0	0	NUM
ap-1872	175	15	0	0	NUM
ap-1872	176	1	x1∂1	x1∂1	PROPN
ap-1872	177	1	+	+	CCONJ
ap-1872	177	2	1	1	NUM
ap-1872	177	3	0	0	NUM
ap-1872	177	4	0	0	NUM
ap-1872	177	5	0	0	NUM
ap-1872	178	1	x1∂1	x1∂1	PROPN
ap-1872	178	2			PROPN
ap-1872	178	3	,	,	PUNCT
ap-1872	178	4	e12	e12	NOUN
ap-1872	178	5	=	=	NOUN
ap-1872	178	6	x1∂2	x1∂2	NOUN
ap-1872	178	7	√	√	NUM
ap-1872	178	8	2	2	NUM
ap-1872	178	9	0	0	NUM
ap-1872	178	10	0	0	NUM
ap-1872	179	1	x1∂2	x1∂2	NOUN
ap-1872	179	2	√	√	NUM
ap-1872	179	3	2	2	NUM
ap-1872	179	4	0	0	NUM
ap-1872	179	5	0	0	NUM
ap-1872	180	1	x1∂2	x1∂2	PROPN
ap-1872	180	2			PROPN
ap-1872	180	3	,	,	PUNCT
ap-1872	180	4	e21	e21	NUM
ap-1872	180	5	=	=	SYM
ap-1872	180	6	x2∂1	x2∂1	NOUN
ap-1872	180	7	0	0	NUM
ap-1872	180	8	0√	0√	NOUN
ap-1872	180	9	2	2	NUM
ap-1872	181	1	x2∂1	x2∂1	NOUN
ap-1872	181	2	0	0	NUM
ap-1872	181	3	0	0	NUM
ap-1872	181	4	√	√	NUM
ap-1872	181	5	2	2	NUM
ap-1872	181	6	x2∂1	x2∂1	PROPN
ap-1872	181	7			PROPN
ap-1872	181	8	,	,	PUNCT
ap-1872	181	9	e22	e22	NOUN
ap-1872	181	10	=	=	SYM
ap-1872	181	11	x2∂2	x2∂2	NOUN
ap-1872	181	12	0	0	NUM
ap-1872	181	13	0	0	NUM
ap-1872	181	14	0	0	NUM
ap-1872	182	1	x2∂2	x2∂2	CCONJ
ap-1872	183	1	+	+	CCONJ
ap-1872	183	2	1	1	NUM
ap-1872	183	3	0	0	NUM
ap-1872	183	4	0	0	NUM
ap-1872	183	5	0	0	NUM
ap-1872	184	1	x2∂2	x2∂2	CCONJ
ap-1872	185	1	+	+	CCONJ
ap-1872	185	2	2	2	NUM
ap-1872	185	3			PROPN
ap-1872	185	4	,	,	PUNCT
ap-1872	185	5	e0	e0	PROPN
ap-1872	185	6	=	=	PUNCT
ap-1872	185	7	a	a	VERB
ap-1872	185	8	0	0	NUM
ap-1872	185	9	0	0	NUM
ap-1872	185	10	0	0	NUM
ap-1872	185	11	a	a	DET
ap-1872	185	12	0	0	NUM
ap-1872	185	13	0	0	NUM
ap-1872	185	14	0	0	NUM
ap-1872	185	15	a	a	DET
ap-1872	185	16			PROPN
ap-1872	185	17	,	,	PUNCT
ap-1872	185	18	t+	t+	NOUN
ap-1872	185	19	1	1	NUM
ap-1872	185	20	=	=	SYM
ap-1872	185	21	x1(a−	x1(a−	PROPN
ap-1872	185	22	2	2	NUM
ap-1872	185	23	)	)	PUNCT
ap-1872	185	24	−	−	NOUN
ap-1872	185	25	√	√	NOUN
ap-1872	185	26	2x2	2x2	NUM
ap-1872	185	27	0	0	NUM
ap-1872	185	28	0	0	NUM
ap-1872	185	29	x1(a−	x1(a−	PROPN
ap-1872	185	30	1	1	NUM
ap-1872	185	31	)	)	PUNCT
ap-1872	185	32	−	−	NOUN
ap-1872	186	1	√	√	NOUN
ap-1872	186	2	2x2	2x2	NUM
ap-1872	186	3	0	0	NUM
ap-1872	186	4	0	0	NUM
ap-1872	186	5	x1a	x1a	PROPN
ap-1872	186	6			PROPN
ap-1872	186	7	,	,	PUNCT
ap-1872	186	8	t+	t+	NOUN
ap-1872	186	9	2	2	NUM
ap-1872	186	10	=	=	SYM
ap-1872	186	11			X
ap-1872	186	12	x2a	x2a	PROPN
ap-1872	186	13	0	0	NUM
ap-1872	186	14	0	0	NUM
ap-1872	186	15	−	−	NUM
ap-1872	187	1	√	√	NOUN
ap-1872	187	2	2x1	2x1	NUM
ap-1872	187	3	x2(a−	x2(a−	NUM
ap-1872	187	4	1	1	NUM
ap-1872	187	5	)	)	PUNCT
ap-1872	187	6	0	0	NUM
ap-1872	187	7	0	0	NUM
ap-1872	188	1	−	−	NUM
ap-1872	189	1	√	√	NOUN
ap-1872	189	2	2x1	2x1	NUM
ap-1872	189	3	x2(a−	x2(a−	NUM
ap-1872	189	4	2	2	NUM
ap-1872	189	5	)	)	PUNCT
ap-1872	189	6			PROPN
ap-1872	189	7	,	,	PUNCT
ap-1872	189	8	(	(	PUNCT
ap-1872	189	9	21	21	NUM
ap-1872	189	10	)	)	PUNCT
ap-1872	189	11	wherea	wherea	NOUN
ap-1872	189	12	=	=	SYM
ap-1872	189	13	k−x1∂1−x2∂2	k−x1∂1−x2∂2	NOUN
ap-1872	189	14	.	.	PUNCT
ap-1872	190	1	this	this	PRON
ap-1872	190	2	is	be	AUX
ap-1872	190	3	[	[	X
ap-1872	190	4	k	k	X
ap-1872	190	5	,	,	PUNCT
ap-1872	190	6	2]-representation	2]-representation	NUM
ap-1872	190	7	(	(	PUNCT
ap-1872	190	8	the	the	DET
ap-1872	190	9	young	young	ADJ
ap-1872	190	10	tableau	tableau	PROPN
ap-1872	190	11	has	have	AUX
ap-1872	190	12	two	two	NUM
ap-1872	190	13	rows	row	NOUN
ap-1872	190	14	of	of	ADP
ap-1872	190	15	length	length	NOUN
ap-1872	190	16	k	k	PROPN
ap-1872	190	17	and	and	CCONJ
ap-1872	190	18	2	2	NUM
ap-1872	190	19	,	,	PUNCT
ap-1872	190	20	correspondingly	correspondingly	ADV
ap-1872	190	21	)	)	PUNCT
ap-1872	190	22	and	and	CCONJ
ap-1872	190	23	their	their	PRON
ap-1872	190	24	casimir	casimir	NOUN
ap-1872	190	25	operators	operator	NOUN
ap-1872	190	26	are	be	AUX
ap-1872	190	27	:	:	PUNCT
ap-1872	190	28	c1	c1	PROPN
ap-1872	190	29	=	=	PROPN
ap-1872	191	1	k	k	PROPN
ap-1872	192	1	+	+	PROPN
ap-1872	192	2	2	2	NUM
ap-1872	192	3	,	,	PUNCT
ap-1872	192	4	c2	c2	PROPN
ap-1872	192	5	=	=	PUNCT
ap-1872	192	6	(	(	PUNCT
ap-1872	192	7	k	k	PROPN
ap-1872	192	8	+	+	CCONJ
ap-1872	192	9	1)2	1)2	NUM
ap-1872	192	10	+	+	CCONJ
ap-1872	192	11	3	3	X
ap-1872	192	12	.	.	X
ap-1872	192	13	as	as	ADP
ap-1872	192	14	an	an	DET
ap-1872	192	15	illustration	illustration	NOUN
ap-1872	192	16	let	let	VERB
ap-1872	192	17	us	we	PRON
ap-1872	192	18	explicitly	explicitly	ADV
ap-1872	192	19	show	show	VERB
ap-1872	192	20	finitedimensional	finitedimensional	ADJ
ap-1872	192	21	representation	representation	NOUN
ap-1872	192	22	spaces	space	NOUN
ap-1872	192	23	for	for	ADP
ap-1872	192	24	k	k	PROPN
ap-1872	192	25	=	=	SYM
ap-1872	192	26	2	2	NUM
ap-1872	192	27	,	,	PUNCT
ap-1872	192	28	3	3	NUM
ap-1872	192	29	.	.	PUNCT
ap-1872	193	1	the	the	DET
ap-1872	193	2	case	case	NOUN
ap-1872	193	3	k	k	X
ap-1872	194	1	=	=	SYM
ap-1872	195	1	2	2	X
ap-1872	195	2	.	.	PUNCT
ap-1872	195	3	then	then	ADV
ap-1872	195	4	the	the	DET
ap-1872	195	5	six	six	NUM
ap-1872	195	6	-	-	PUNCT
ap-1872	195	7	dimensional	dimensional	ADJ
ap-1872	195	8	representation	representation	NOUN
ap-1872	195	9	space	space	NOUN
ap-1872	195	10	v	v	NOUN
ap-1872	195	11	(	(	PUNCT
ap-1872	195	12	3	3	NUM
ap-1872	195	13	)	)	PUNCT
ap-1872	195	14	2	2	NUM
ap-1872	195	15	appears	appear	VERB
ap-1872	195	16	to	to	PART
ap-1872	195	17	be	be	AUX
ap-1872	195	18	spanned	span	VERB
ap-1872	195	19	by	by	ADP
ap-1872	195	20	:	:	PUNCT
ap-1872	195	21	p−	p−	NOUN
ap-1872	195	22	=	=	PUNCT
ap-1872	195	23	0	0	ADP
ap-1872	195	24	0	0	NUM
ap-1872	195	25	1	1	NUM
ap-1872	195	26			PROPN
ap-1872	195	27	,	,	PUNCT
ap-1872	195	28	p0	p0	NOUN
ap-1872	195	29	=	=	PUNCT
ap-1872	195	30	0	0	ADP
ap-1872	195	31	1	1	NUM
ap-1872	195	32	0	0	NUM
ap-1872	195	33			PROPN
ap-1872	195	34	,	,	PUNCT
ap-1872	195	35	p+	p+	X
ap-1872	195	36	=	=	X
ap-1872	195	37	1	1	X
ap-1872	195	38	0	0	NUM
ap-1872	195	39	0	0	NUM
ap-1872	196	1			PROPN
ap-1872	196	2	,	,	PUNCT
ap-1872	196	3	y1	y1	INTJ
ap-1872	196	4	=	=	SYM
ap-1872	196	5			PROPN
ap-1872	196	6	0	0	NUM
ap-1872	196	7	x2	x2	PROPN
ap-1872	196	8	−	−	PROPN
ap-1872	196	9	√	√	NOUN
ap-1872	196	10	2x1	2x1	NUM
ap-1872	196	11			PROPN
ap-1872	196	12	,	,	PUNCT
ap-1872	196	13	y2	y2	X
ap-1872	196	14	=	=	PUNCT
ap-1872	197	1	−√2x2	−√2x2	VERB
ap-1872	197	2	x1	x1	NOUN
ap-1872	197	3	0	0	NUM
ap-1872	198	1			PROPN
ap-1872	198	2	,	,	PUNCT
ap-1872	198	3	y3	y3	NOUN
ap-1872	198	4	=	=	SYM
ap-1872	198	5			PROPN
ap-1872	198	6	x2	x2	PROPN
ap-1872	198	7	2	2	NUM
ap-1872	198	8	−	−	NUM
ap-1872	198	9	√	√	NUM
ap-1872	198	10	2x1x2	2x1x2	NUM
ap-1872	199	1	x2	x2	NOUN
ap-1872	199	2	1	1	NUM
ap-1872	199	3			PROPN
ap-1872	199	4	.	.	PUNCT
ap-1872	200	1	(	(	PUNCT
ap-1872	200	2	22	22	NUM
ap-1872	200	3	)	)	PUNCT
ap-1872	200	4	this	this	PRON
ap-1872	200	5	corresponds	correspond	VERB
ap-1872	200	6	to	to	ADP
ap-1872	200	7	‘	'	PUNCT
ap-1872	200	8	di	di	NOUN
ap-1872	200	9	-	-	ADJ
ap-1872	200	10	antiquark	antiquark	NOUN
ap-1872	200	11	’	'	PUNCT
ap-1872	200	12	multiplet	multiplet	NOUN
ap-1872	200	13	.	.	PUNCT
ap-1872	201	1	the	the	DET
ap-1872	201	2	case	case	NOUN
ap-1872	201	3	k	k	X
ap-1872	202	1	=	=	SYM
ap-1872	203	1	3	3	X
ap-1872	203	2	.	.	PUNCT
ap-1872	203	3	then	then	ADV
ap-1872	203	4	15	15	NUM
ap-1872	203	5	-	-	PUNCT
ap-1872	203	6	dimensional	dimensional	ADJ
ap-1872	203	7	representation	representation	NOUN
ap-1872	203	8	space	space	NOUN
ap-1872	203	9	v	v	NOUN
ap-1872	203	10	(	(	PUNCT
ap-1872	203	11	3	3	NUM
ap-1872	203	12	)	)	PUNCT
ap-1872	203	13	3	3	NUM
ap-1872	203	14	appears	appear	VERB
ap-1872	203	15	to	to	PART
ap-1872	203	16	be	be	AUX
ap-1872	203	17	spanned	span	VERB
ap-1872	203	18	by	by	ADP
ap-1872	203	19	:	:	PUNCT
ap-1872	203	20	p−	p−	NOUN
ap-1872	203	21	=	=	PUNCT
ap-1872	203	22	0	0	ADP
ap-1872	203	23	0	0	NUM
ap-1872	203	24	1	1	NUM
ap-1872	203	25			PROPN
ap-1872	203	26	,	,	PUNCT
ap-1872	203	27	p0	p0	NOUN
ap-1872	203	28	=	=	PUNCT
ap-1872	203	29	0	0	ADP
ap-1872	203	30	1	1	NUM
ap-1872	203	31	0	0	NUM
ap-1872	203	32			PROPN
ap-1872	203	33	,	,	PUNCT
ap-1872	203	34	p+	p+	X
ap-1872	203	35	=	=	X
ap-1872	203	36	1	1	X
ap-1872	203	37	0	0	NUM
ap-1872	203	38	0	0	NUM
ap-1872	204	1			PROPN
ap-1872	204	2	,	,	PUNCT
ap-1872	204	3	y	y	PROPN
ap-1872	204	4	(	(	PUNCT
ap-1872	204	5	1	1	NUM
ap-1872	204	6	)	)	PUNCT
ap-1872	204	7	1	1	NUM
ap-1872	204	8	=	=	SYM
ap-1872	204	9			PROPN
ap-1872	204	10	0	0	NUM
ap-1872	204	11	x2	x2	NOUN
ap-1872	204	12	0	0	NUM
ap-1872	205	1			PROPN
ap-1872	205	2	,	,	PUNCT
ap-1872	205	3	y	y	PROPN
ap-1872	205	4	(	(	PUNCT
ap-1872	205	5	2	2	NUM
ap-1872	205	6	)	)	PUNCT
ap-1872	205	7	1	1	NUM
ap-1872	206	1	=	=	SYM
ap-1872	206	2			X
ap-1872	206	3	0	0	NUM
ap-1872	206	4	0	0	NUM
ap-1872	207	1	x1	x1	PROPN
ap-1872	207	2			PROPN
ap-1872	207	3	,	,	PUNCT
ap-1872	207	4	y	y	PROPN
ap-1872	207	5	(	(	PUNCT
ap-1872	207	6	1	1	NUM
ap-1872	207	7	)	)	SYM
ap-1872	207	8	2	2	NUM
ap-1872	207	9	=	=	SYM
ap-1872	207	10	x2	x2	NUM
ap-1872	207	11	0	0	NUM
ap-1872	207	12	0	0	NUM
ap-1872	208	1			PROPN
ap-1872	208	2	,	,	PUNCT
ap-1872	208	3	y	y	PROPN
ap-1872	208	4	(	(	PUNCT
ap-1872	208	5	2	2	NUM
ap-1872	208	6	)	)	SYM
ap-1872	208	7	2	2	NUM
ap-1872	209	1	=	=	SYM
ap-1872	209	2			PROPN
ap-1872	209	3	0	0	NUM
ap-1872	210	1	x1	x1	NOUN
ap-1872	210	2	0	0	NUM
ap-1872	211	1			PROPN
ap-1872	211	2	,	,	PUNCT
ap-1872	211	3	p	p	X
ap-1872	211	4	(	(	PUNCT
ap-1872	211	5	1	1	NUM
ap-1872	211	6	)	)	PUNCT
ap-1872	211	7	−	−	NOUN
ap-1872	212	1	=	=	SYM
ap-1872	212	2			PROPN
ap-1872	212	3	0	0	NUM
ap-1872	212	4	0	0	NUM
ap-1872	213	1	x2	x2	PROPN
ap-1872	213	2			PROPN
ap-1872	213	3	,	,	PUNCT
ap-1872	213	4	p	p	X
ap-1872	213	5	(	(	PUNCT
ap-1872	213	6	1	1	NUM
ap-1872	213	7	)	)	PUNCT
ap-1872	213	8	+	+	NOUN
ap-1872	213	9	=	=	SYM
ap-1872	213	10	x1	x1	NOUN
ap-1872	213	11	0	0	NUM
ap-1872	213	12	0	0	NUM
ap-1872	214	1			PROPN
ap-1872	214	2	,	,	PUNCT
ap-1872	214	3	y	y	PROPN
ap-1872	214	4	(	(	PUNCT
ap-1872	214	5	1	1	NUM
ap-1872	214	6	)	)	PUNCT
ap-1872	214	7	3	3	NUM
ap-1872	214	8	=	=	SYM
ap-1872	214	9	−√2x2	−√2x2	NOUN
ap-1872	214	10	2	2	NUM
ap-1872	214	11	x1x2	x1x2	SYM
ap-1872	214	12	0	0	NUM
ap-1872	215	1			PROPN
ap-1872	215	2	,	,	PUNCT
ap-1872	215	3	y	y	PROPN
ap-1872	215	4	(	(	PUNCT
ap-1872	215	5	2	2	NUM
ap-1872	215	6	)	)	PUNCT
ap-1872	215	7	3	3	NUM
ap-1872	215	8	=	=	SYM
ap-1872	215	9			PROPN
ap-1872	215	10	0	0	NUM
ap-1872	215	11	x1x2	x1x2	PUNCT
ap-1872	215	12	−	−	PROPN
ap-1872	215	13	√	√	NOUN
ap-1872	215	14	2x2	2x2	NUM
ap-1872	215	15	1	1	NUM
ap-1872	215	16			PROPN
ap-1872	215	17	,	,	PUNCT
ap-1872	215	18	y4	y4	NOUN
ap-1872	215	19	=	=	PUNCT
ap-1872	216	1			PROPN
ap-1872	216	2	0	0	NUM
ap-1872	216	3	−	−	NOUN
ap-1872	217	1	√	√	NUM
ap-1872	217	2	2x2	2x2	NUM
ap-1872	217	3	2	2	NUM
ap-1872	217	4	2x1x2	2x1x2	NUM
ap-1872	217	5			PROPN
ap-1872	217	6	,	,	PUNCT
ap-1872	217	7	y5	y5	NOUN
ap-1872	217	8	=	=	PUNCT
ap-1872	217	9			PROPN
ap-1872	217	10	2x1x2	2x1x2	NUM
ap-1872	217	11	−	−	ADP
ap-1872	217	12	√	√	NUM
ap-1872	217	13	2x2	2x2	NUM
ap-1872	217	14	1	1	NUM
ap-1872	217	15	0	0	NUM
ap-1872	217	16			PROPN
ap-1872	217	17	,	,	PUNCT
ap-1872	217	18	y6	y6	NOUN
ap-1872	217	19	=	=	PUNCT
ap-1872	217	20			NOUN
ap-1872	217	21	x3	x3	VERB
ap-1872	217	22	2	2	NUM
ap-1872	217	23	−	−	NOUN
ap-1872	217	24	√	√	NUM
ap-1872	217	25	2x1x	2x1x	NOUN
ap-1872	217	26	2	2	NUM
ap-1872	217	27	2	2	NUM
ap-1872	217	28	x2	x2	NOUN
ap-1872	217	29	1x2	1x2	NUM
ap-1872	217	30			PROPN
ap-1872	217	31	,	,	PUNCT
ap-1872	217	32	y7	y7	NOUN
ap-1872	217	33	=	=	PUNCT
ap-1872	218	1			PROPN
ap-1872	218	2	x1x	x1x	PROPN
ap-1872	218	3	2	2	NUM
ap-1872	218	4	2	2	NUM
ap-1872	218	5	−	−	NOUN
ap-1872	218	6	√	√	NUM
ap-1872	218	7	2x2	2x2	NUM
ap-1872	218	8	1x2	1x2	NUM
ap-1872	218	9	x3	x3	NOUN
ap-1872	218	10	1	1	NUM
ap-1872	218	11			PROPN
ap-1872	218	12	.	.	PUNCT
ap-1872	219	1	(	(	PUNCT
ap-1872	219	2	23	23	NUM
ap-1872	219	3	)	)	PUNCT
ap-1872	219	4	it	it	PRON
ap-1872	219	5	is	be	AUX
ap-1872	219	6	worth	worth	ADJ
ap-1872	219	7	mentioning	mention	VERB
ap-1872	219	8	that	that	PRON
ap-1872	219	9	as	as	ADP
ap-1872	219	10	a	a	DET
ap-1872	219	11	consequence	consequence	NOUN
ap-1872	219	12	of	of	ADP
ap-1872	219	13	a	a	DET
ap-1872	219	14	particular	particular	ADJ
ap-1872	219	15	realization	realization	NOUN
ap-1872	219	16	of	of	ADP
ap-1872	219	17	the	the	DET
ap-1872	219	18	generators	generator	NOUN
ap-1872	219	19	(	(	PUNCT
ap-1872	219	20	11	11	NUM
ap-1872	219	21	)	)	PUNCT
ap-1872	219	22	of	of	ADP
ap-1872	219	23	the	the	DET
ap-1872	219	24	gl3	gl3	PROPN
ap-1872	219	25	algebra	algebra	NOUN
ap-1872	219	26	there	there	ADV
ap-1872	219	27	exist	exist	VERB
ap-1872	219	28	a	a	DET
ap-1872	219	29	certain	certain	ADJ
ap-1872	219	30	relations	relation	NOUN
ap-1872	219	31	between	between	ADP
ap-1872	219	32	generators	generator	NOUN
ap-1872	219	33	other	other	ADJ
ap-1872	219	34	than	than	ADP
ap-1872	219	35	those	those	PRON
ap-1872	219	36	given	give	VERB
ap-1872	219	37	by	by	ADP
ap-1872	219	38	the	the	DET
ap-1872	219	39	casimir	casimir	NOUN
ap-1872	219	40	operators	operator	NOUN
ap-1872	219	41	.	.	PUNCT
ap-1872	220	1	the	the	DET
ap-1872	220	2	first	first	ADJ
ap-1872	220	3	observation	observation	NOUN
ap-1872	220	4	is	be	AUX
ap-1872	220	5	that	that	SCONJ
ap-1872	220	6	there	there	PRON
ap-1872	220	7	are	be	VERB
ap-1872	220	8	no	no	DET
ap-1872	220	9	linear	linear	ADJ
ap-1872	220	10	relations	relation	NOUN
ap-1872	220	11	between	between	ADP
ap-1872	220	12	generators	generator	NOUN
ap-1872	220	13	of	of	ADP
ap-1872	220	14	such	such	DET
ap-1872	220	15	a	a	DET
ap-1872	220	16	type	type	NOUN
ap-1872	220	17	.	.	PUNCT
ap-1872	221	1	some	some	DET
ap-1872	221	2	time	time	NOUN
ap-1872	221	3	ago	ago	ADV
ap-1872	221	4	nine	nine	NUM
ap-1872	221	5	quadratic	quadratic	ADJ
ap-1872	221	6	relations	relation	NOUN
ap-1872	221	7	were	be	AUX
ap-1872	221	8	found	find	VERB
ap-1872	221	9	465	465	NUM
ap-1872	221	10	yu	yu	PROPN
ap-1872	221	11	.	.	PUNCT
ap-1872	221	12	f.	f.	PROPN
ap-1872	221	13	smirnov	smirnov	PROPN
ap-1872	221	14	,	,	PUNCT
ap-1872	221	15	a.	a.	NOUN
ap-1872	221	16	v.	v.	PROPN
ap-1872	221	17	turbiner	turbiner	PROPN
ap-1872	221	18	acta	acta	PROPN
ap-1872	221	19	polytechnica	polytechnica	PROPN
ap-1872	221	20	ms0	ms0	NOUN
ap-1872	221	21	1/2	1/2	NUM
ap-1872	221	22	1	1	NUM
ap-1872	221	23	3/2	3/2	NUM
ap-1872	221	24	2	2	NUM
ap-1872	221	25	5/2	5/2	NUM
ap-1872	221	26	3	3	NUM
ap-1872	221	27	l/2	l/2	NUM
ap-1872	221	28	figure	figure	NOUN
ap-1872	221	29	2	2	NUM
ap-1872	221	30	.	.	PUNCT
ap-1872	221	31	verma	verma	PROPN
ap-1872	221	32	module	module	NOUN
ap-1872	221	33	with	with	ADP
ap-1872	221	34	the	the	DET
ap-1872	221	35	lowest	low	ADJ
ap-1872	221	36	weight	weight	NOUN
ap-1872	221	37	(	(	PUNCT
ap-1872	221	38	057	057	NUM
ap-1872	221	39	)	)	PUNCT
ap-1872	221	40	for	for	ADP
ap-1872	221	41	s	s	NOUN
ap-1872	221	42	=	=	SYM
ap-1872	221	43	5/2	5/2	NUM
ap-1872	221	44	.	.	PUNCT
ap-1872	222	1	between	between	ADP
ap-1872	222	2	gl3	gl3	PROPN
ap-1872	222	3	generators	generator	NOUN
ap-1872	222	4	taken	take	VERB
ap-1872	222	5	in	in	ADP
ap-1872	222	6	scalar	scalar	ADJ
ap-1872	222	7	representation	representation	NOUN
ap-1872	222	8	(	(	PUNCT
ap-1872	222	9	12	12	NUM
ap-1872	222	10	)	)	PUNCT
ap-1872	222	11	other	other	ADJ
ap-1872	222	12	than	than	ADP
ap-1872	222	13	casimir	casimir	NOUN
ap-1872	222	14	operators	operator	NOUN
ap-1872	222	15	[	[	X
ap-1872	222	16	8	8	NUM
ap-1872	222	17	]	]	PUNCT
ap-1872	222	18	.	.	PUNCT
ap-1872	223	1	surprisingly	surprisingly	ADV
ap-1872	223	2	,	,	PUNCT
ap-1872	223	3	certain	certain	ADJ
ap-1872	223	4	modifications	modification	NOUN
ap-1872	223	5	of	of	ADP
ap-1872	223	6	these	these	DET
ap-1872	223	7	relations	relation	NOUN
ap-1872	223	8	also	also	ADV
ap-1872	223	9	exist	exist	VERB
ap-1872	223	10	for	for	ADP
ap-1872	223	11	[	[	X
ap-1872	223	12	kn	kn	X
ap-1872	223	13	]	]	X
ap-1872	223	14	mixed	mixed	ADJ
ap-1872	223	15	representations	representation	NOUN
ap-1872	223	16	(	(	PUNCT
ap-1872	223	17	11	11	NUM
ap-1872	223	18	)	)	PUNCT
ap-1872	223	19	,	,	PUNCT
ap-1872	223	20	−	−	PROPN
ap-1872	223	21	t+	t+	PUNCT
ap-1872	223	22	1	1	NUM
ap-1872	223	23	e22	e22	NOUN
ap-1872	223	24	+	+	CCONJ
ap-1872	223	25	t+	t+	NOUN
ap-1872	223	26	2	2	NUM
ap-1872	223	27	e12	e12	NOUN
ap-1872	223	28	=	=	SYM
ap-1872	223	29	x1	x1	PROPN
ap-1872	223	30	[	[	PUNCT
ap-1872	223	31	m22x1∂1	m22x1∂1	NUM
ap-1872	223	32	+	+	NOUN
ap-1872	223	33	m11x2∂2	m11x2∂2	NOUN
ap-1872	223	34	+	+	CCONJ
ap-1872	223	35	(	(	PUNCT
ap-1872	223	36	m11	m11	NOUN
ap-1872	223	37	−	−	PROPN
ap-1872	223	38	k)m22	k)m22	X
ap-1872	223	39	−m21m12	−m21m12	PROPN
ap-1872	223	40	]	]	PUNCT
ap-1872	223	41	−	−	PROPN
ap-1872	224	1	x2(x1∂1	x2(x1∂1	PROPN
ap-1872	224	2	−	−	PROPN
ap-1872	225	1	k	k	INTJ
ap-1872	226	1	−	−	PROPN
ap-1872	226	2	1)m12	1)m12	NUM
ap-1872	226	3	−m21x	−m21x	PROPN
ap-1872	226	4	2	2	NUM
ap-1872	226	5	1∂2	1∂2	NUM
ap-1872	226	6	≡	≡	PROPN
ap-1872	226	7	−t̃+	−t̃+	PROPN
ap-1872	226	8	1	1	NUM
ap-1872	226	9	,	,	PUNCT
ap-1872	226	10	(	(	PUNCT
ap-1872	226	11	24	24	NUM
ap-1872	226	12	)	)	PUNCT
ap-1872	226	13	−	−	NOUN
ap-1872	226	14	t+	t+	PUNCT
ap-1872	226	15	2	2	NUM
ap-1872	226	16	e11	e11	NOUN
ap-1872	226	17	+	+	CCONJ
ap-1872	226	18	t+	t+	NOUN
ap-1872	226	19	1	1	NUM
ap-1872	226	20	e21	e21	PROPN
ap-1872	226	21	=	=	SYM
ap-1872	226	22	x2	x2	PROPN
ap-1872	226	23	[	[	PUNCT
ap-1872	226	24	m22x1∂1	m22x1∂1	NUM
ap-1872	226	25	+	+	NOUN
ap-1872	226	26	m11x2∂2	m11x2∂2	NOUN
ap-1872	226	27	+	+	SYM
ap-1872	226	28	(	(	PUNCT
ap-1872	226	29	m22	m22	PROPN
ap-1872	226	30	−	−	PROPN
ap-1872	226	31	k)m11	k)m11	AUX
ap-1872	226	32	−m12m21	−m12m21	NOUN
ap-1872	226	33	]	]	PUNCT
ap-1872	226	34	−	−	PUNCT
ap-1872	227	1	x1(x2∂2	x1(x2∂2	NOUN
ap-1872	227	2	−	−	PROPN
ap-1872	228	1	k	k	INTJ
ap-1872	228	2	−	−	PROPN
ap-1872	228	3	1)m21	1)m21	NUM
ap-1872	228	4	−m12x	−m12x	NOUN
ap-1872	228	5	2	2	NUM
ap-1872	228	6	2∂1	2∂1	NUM
ap-1872	228	7	≡	≡	PROPN
ap-1872	228	8	−t̃+	−t̃+	PROPN
ap-1872	228	9	2	2	NUM
ap-1872	228	10	,	,	PUNCT
ap-1872	228	11	(	(	PUNCT
ap-1872	228	12	25	25	NUM
ap-1872	228	13	)	)	PUNCT
ap-1872	228	14	−	−	PROPN
ap-1872	229	1	e12(e0	e12(e0	PROPN
ap-1872	229	2	+	+	CCONJ
ap-1872	229	3	1	1	NUM
ap-1872	229	4	)	)	PUNCT
ap-1872	229	5	+	+	CCONJ
ap-1872	229	6	t+	t+	NOUN
ap-1872	229	7	1	1	NUM
ap-1872	229	8	t	t	NOUN
ap-1872	229	9	−	−	NOUN
ap-1872	229	10	2	2	NUM
ap-1872	229	11	=	=	SYM
ap-1872	229	12	m12(x1∂1	m12(x1∂1	NOUN
ap-1872	229	13	−	−	PROPN
ap-1872	229	14	k	k	NOUN
ap-1872	230	1	−	−	PROPN
ap-1872	230	2	1)−m11x1∂2	1)−m11x1∂2	PROPN
ap-1872	230	3	≡	≡	PROPN
ap-1872	230	4	−ẽ12	−ẽ12	PROPN
ap-1872	230	5	,	,	PUNCT
ap-1872	230	6	(	(	PUNCT
ap-1872	230	7	26	26	NUM
ap-1872	230	8	)	)	PUNCT
ap-1872	230	9	−	−	PROPN
ap-1872	230	10	e21(e0	e21(e0	NOUN
ap-1872	230	11	+	+	CCONJ
ap-1872	230	12	1	1	NUM
ap-1872	230	13	)	)	PUNCT
ap-1872	230	14	+	+	CCONJ
ap-1872	230	15	t+	t+	NOUN
ap-1872	230	16	2	2	NUM
ap-1872	230	17	t	t	NOUN
ap-1872	230	18	−	−	NOUN
ap-1872	230	19	1	1	NUM
ap-1872	230	20	=	=	SYM
ap-1872	230	21	m21(x2∂2	m21(x2∂2	NOUN
ap-1872	230	22	−	−	PROPN
ap-1872	231	1	k	k	NOUN
ap-1872	232	1	−	−	PROPN
ap-1872	232	2	1)−m22x2∂1	1)−m22x2∂1	NUM
ap-1872	232	3	≡	≡	PROPN
ap-1872	232	4	−ẽ21	−ẽ21	PROPN
ap-1872	232	5	,	,	PUNCT
ap-1872	232	6	(	(	PUNCT
ap-1872	232	7	27	27	NUM
ap-1872	232	8	)	)	PUNCT
ap-1872	232	9	t+	t+	PUNCT
ap-1872	232	10	1	1	NUM
ap-1872	232	11	t	t	NOUN
ap-1872	232	12	−	−	NOUN
ap-1872	232	13	1	1	NUM
ap-1872	232	14	−	−	PROPN
ap-1872	232	15	e11(1	e11(1	ADJ
ap-1872	232	16	+	+	CCONJ
ap-1872	232	17	e0	e0	PROPN
ap-1872	232	18	)	)	PUNCT
ap-1872	232	19	=	=	PUNCT
ap-1872	232	20	m11x2∂2	m11x2∂2	X
ap-1872	232	21	−m12x2∂1	−m12x2∂1	X
ap-1872	232	22	−	−	PROPN
ap-1872	232	23	(	(	PUNCT
ap-1872	232	24	k	k	PROPN
ap-1872	232	25	+	+	PROPN
ap-1872	232	26	1)m11	1)m11	NUM
ap-1872	232	27	≡	≡	PROPN
ap-1872	232	28	−ẽ11	−ẽ11	PROPN
ap-1872	232	29	,	,	PUNCT
ap-1872	232	30	(	(	PUNCT
ap-1872	232	31	28	28	NUM
ap-1872	232	32	)	)	PUNCT
ap-1872	232	33	t+	t+	NOUN
ap-1872	232	34	2	2	NUM
ap-1872	232	35	t	t	NOUN
ap-1872	232	36	−	−	NOUN
ap-1872	232	37	2	2	NUM
ap-1872	232	38	−	−	NOUN
ap-1872	232	39	e22(1	e22(1	NOUN
ap-1872	232	40	+	+	CCONJ
ap-1872	232	41	e0	e0	PROPN
ap-1872	232	42	)	)	PUNCT
ap-1872	232	43	=	=	PUNCT
ap-1872	233	1	m22x1∂1	m22x1∂1	NUM
ap-1872	233	2	−m21x1∂2	−m21x1∂2	X
ap-1872	233	3	−	−	PROPN
ap-1872	234	1	(	(	PUNCT
ap-1872	234	2	k	k	PROPN
ap-1872	234	3	+	+	PROPN
ap-1872	234	4	1)m22	1)m22	PROPN
ap-1872	234	5	≡	≡	PROPN
ap-1872	234	6	−ẽ22	−ẽ22	PROPN
ap-1872	234	7	,	,	PUNCT
ap-1872	234	8	(	(	PUNCT
ap-1872	234	9	29	29	NUM
ap-1872	234	10	)	)	PUNCT
ap-1872	234	11	e12e21	e12e21	VERB
ap-1872	234	12	−	−	PROPN
ap-1872	234	13	e11e22	e11e22	NOUN
ap-1872	234	14	−	−	NOUN
ap-1872	234	15	e11	e11	NOUN
ap-1872	234	16	=	=	PUNCT
ap-1872	234	17	m12x2∂1	m12x2∂1	NOUN
ap-1872	234	18	+	+	NOUN
ap-1872	234	19	m21x1∂2	m21x1∂2	NOUN
ap-1872	234	20	−m22x1∂1	−m22x1∂1	PUNCT
ap-1872	234	21	−m11x2∂2	−m11x2∂2	ADP
ap-1872	234	22	+	+	NOUN
ap-1872	234	23	m12m21	m12m21	PROPN
ap-1872	234	24	−m11m22	−m11m22	NOUN
ap-1872	234	25	−m11	−m11	NUM
ap-1872	234	26	≡	≡	PROPN
ap-1872	234	27	−ê11	−ê11	PROPN
ap-1872	234	28	,	,	PUNCT
ap-1872	234	29	(	(	PUNCT
ap-1872	234	30	30	30	X
ap-1872	234	31	)	)	PUNCT
ap-1872	234	32	e22	e22	PROPN
ap-1872	234	33	t	t	NOUN
ap-1872	234	34	−	−	NUM
ap-1872	234	35	1	1	NUM
ap-1872	234	36	−	−	PROPN
ap-1872	234	37	e21	e21	PROPN
ap-1872	234	38	t	t	NOUN
ap-1872	234	39	−	−	NUM
ap-1872	234	40	2	2	NUM
ap-1872	234	41	=	=	NOUN
ap-1872	234	42	m22∂1	m22∂1	NOUN
ap-1872	234	43	−m21∂2	−m21∂2	ADP
ap-1872	234	44	≡	≡	PROPN
ap-1872	234	45	t̃−	t̃−	PROPN
ap-1872	234	46	1	1	NUM
ap-1872	234	47	,	,	PUNCT
ap-1872	234	48	(	(	PUNCT
ap-1872	234	49	31	31	NUM
ap-1872	234	50	)	)	PUNCT
ap-1872	234	51	e12	e12	NOUN
ap-1872	234	52	t	t	NOUN
ap-1872	234	53	−	−	PROPN
ap-1872	234	54	1	1	NUM
ap-1872	234	55	−	−	NOUN
ap-1872	234	56	e11	e11	X
ap-1872	234	57	t	t	NOUN
ap-1872	234	58	−	−	PROPN
ap-1872	234	59	2	2	NUM
ap-1872	234	60	=	=	SYM
ap-1872	234	61	m12∂1	m12∂1	NOUN
ap-1872	234	62	−m11∂2	−m11∂2	NUM
ap-1872	234	63	≡	≡	PROPN
ap-1872	234	64	−t̃−	−t̃−	PROPN
ap-1872	234	65	2	2	NUM
ap-1872	234	66	.	.	PUNCT
ap-1872	235	1	(	(	PUNCT
ap-1872	235	2	32	32	NUM
ap-1872	235	3	)	)	PUNCT
ap-1872	235	4	not	not	PART
ap-1872	235	5	all	all	DET
ap-1872	235	6	these	these	DET
ap-1872	235	7	relations	relation	NOUN
ap-1872	235	8	are	be	AUX
ap-1872	235	9	independent	independent	ADJ
ap-1872	235	10	.	.	PUNCT
ap-1872	236	1	it	it	PRON
ap-1872	236	2	can	can	AUX
ap-1872	236	3	be	be	AUX
ap-1872	236	4	shown	show	VERB
ap-1872	236	5	that	that	SCONJ
ap-1872	236	6	one	one	NUM
ap-1872	236	7	relation	relation	NOUN
ap-1872	236	8	is	be	AUX
ap-1872	236	9	linearly	linearly	ADV
ap-1872	236	10	dependent	dependent	ADJ
ap-1872	236	11	,	,	PUNCT
ap-1872	236	12	since	since	SCONJ
ap-1872	236	13	the	the	DET
ap-1872	236	14	sum	sum	NOUN
ap-1872	236	15	of	of	ADP
ap-1872	236	16	(	(	PUNCT
ap-1872	236	17	28)+	28)+	NUM
ap-1872	236	18	(	(	PUNCT
ap-1872	236	19	29)+	29)+	NUM
ap-1872	236	20	(	(	PUNCT
ap-1872	236	21	30	30	NUM
ap-1872	236	22	)	)	PUNCT
ap-1872	236	23	gives	give	VERB
ap-1872	236	24	the	the	DET
ap-1872	236	25	second	second	ADJ
ap-1872	236	26	casimir	casimir	NOUN
ap-1872	236	27	operator	operator	NOUN
ap-1872	236	28	c2	c2	PROPN
ap-1872	236	29	.	.	PUNCT
ap-1872	237	1	in	in	ADP
ap-1872	237	2	scalar	scalar	ADJ
ap-1872	237	3	case	case	NOUN
ap-1872	237	4	,	,	PUNCT
ap-1872	237	5	at	at	ADP
ap-1872	237	6	least	least	ADJ
ap-1872	237	7	,	,	PUNCT
ap-1872	237	8	we	we	PRON
ap-1872	237	9	can	can	AUX
ap-1872	237	10	assign	assign	VERB
ap-1872	237	11	a	a	DET
ap-1872	237	12	natural	natural	ADJ
ap-1872	237	13	(	(	PUNCT
ap-1872	237	14	vectorial	vectorial	ADJ
ap-1872	237	15	)	)	PUNCT
ap-1872	237	16	grading	grade	VERB
ap-1872	237	17	to	to	ADP
ap-1872	237	18	the	the	DET
ap-1872	237	19	generators	generator	NOUN
ap-1872	237	20	.	.	PUNCT
ap-1872	238	1	the	the	DET
ap-1872	238	2	above	above	ADJ
ap-1872	238	3	relations	relation	NOUN
ap-1872	238	4	also	also	ADV
ap-1872	238	5	reflect	reflect	VERB
ap-1872	238	6	a	a	DET
ap-1872	238	7	certain	certain	ADJ
ap-1872	238	8	decomposition	decomposition	NOUN
ap-1872	238	9	of	of	ADP
ap-1872	238	10	the	the	DET
ap-1872	238	11	gradings	grading	NOUN
ap-1872	238	12	,	,	PUNCT
ap-1872	238	13	(	(	PUNCT
ap-1872	238	14	1	1	NUM
ap-1872	238	15	,	,	PUNCT
ap-1872	238	16	0)(0	0)(0	NUM
ap-1872	238	17	,	,	PUNCT
ap-1872	238	18	0	0	NUM
ap-1872	238	19	)	)	PUNCT
ap-1872	238	20	=	=	SYM
ap-1872	238	21	(	(	PUNCT
ap-1872	238	22	0	0	NUM
ap-1872	238	23	,	,	PUNCT
ap-1872	238	24	1)(1,−1	1)(1,−1	NUM
ap-1872	238	25	)	)	PUNCT
ap-1872	238	26	(	(	PUNCT
ap-1872	238	27	0	0	NUM
ap-1872	238	28	,	,	PUNCT
ap-1872	238	29	1)(0	1)(0	NUM
ap-1872	238	30	,	,	PUNCT
ap-1872	238	31	0	0	NUM
ap-1872	238	32	)	)	PUNCT
ap-1872	238	33	=	=	NOUN
ap-1872	238	34	(	(	PUNCT
ap-1872	238	35	1	1	NUM
ap-1872	238	36	,	,	PUNCT
ap-1872	238	37	0)(−1	0)(−1	PROPN
ap-1872	238	38	,	,	PUNCT
ap-1872	238	39	0	0	NUM
ap-1872	238	40	)	)	PUNCT
ap-1872	238	41	for	for	ADP
ap-1872	238	42	the	the	DET
ap-1872	238	43	first	first	ADJ
ap-1872	238	44	two	two	NUM
ap-1872	238	45	relations	relation	NOUN
ap-1872	238	46	,	,	PUNCT
ap-1872	238	47	(	(	PUNCT
ap-1872	238	48	1,−1)(0	1,−1)(0	NUM
ap-1872	238	49	,	,	PUNCT
ap-1872	238	50	0	0	NUM
ap-1872	238	51	)	)	PUNCT
ap-1872	238	52	=	=	NOUN
ap-1872	238	53	(	(	PUNCT
ap-1872	238	54	1	1	NUM
ap-1872	238	55	,	,	PUNCT
ap-1872	238	56	0)(0,−1	0)(0,−1	NOUN
ap-1872	238	57	)	)	PUNCT
ap-1872	238	58	(	(	PUNCT
ap-1872	238	59	−1	−1	NOUN
ap-1872	238	60	,	,	PUNCT
ap-1872	238	61	1)(0	1)(0	NUM
ap-1872	238	62	,	,	PUNCT
ap-1872	238	63	0	0	NUM
ap-1872	238	64	)	)	PUNCT
ap-1872	238	65	=	=	SYM
ap-1872	238	66	(	(	PUNCT
ap-1872	238	67	0	0	NUM
ap-1872	238	68	,	,	PUNCT
ap-1872	238	69	1)(−1	1)(−1	NUM
ap-1872	238	70	,	,	PUNCT
ap-1872	238	71	0	0	NUM
ap-1872	238	72	)	)	PUNCT
ap-1872	238	73	for	for	ADP
ap-1872	238	74	the	the	DET
ap-1872	238	75	second	second	ADJ
ap-1872	238	76	two	two	NUM
ap-1872	238	77	,	,	PUNCT
ap-1872	238	78	(	(	PUNCT
ap-1872	238	79	1	1	NUM
ap-1872	238	80	,	,	PUNCT
ap-1872	238	81	0)(−1	0)(−1	PROPN
ap-1872	238	82	,	,	PUNCT
ap-1872	238	83	0	0	NUM
ap-1872	238	84	)	)	PUNCT
ap-1872	238	85	=	=	SYM
ap-1872	238	86	(	(	PUNCT
ap-1872	238	87	0	0	NUM
ap-1872	238	88	,	,	PUNCT
ap-1872	238	89	0)(0	0)(0	NUM
ap-1872	238	90	,	,	PUNCT
ap-1872	238	91	0	0	NUM
ap-1872	238	92	)	)	PUNCT
ap-1872	238	93	(	(	PUNCT
ap-1872	238	94	0	0	NUM
ap-1872	238	95	,	,	PUNCT
ap-1872	238	96	1)(0,−1	1)(0,−1	NUM
ap-1872	238	97	)	)	PUNCT
ap-1872	239	1	=	=	SYM
ap-1872	239	2	(	(	PUNCT
ap-1872	239	3	0	0	NUM
ap-1872	239	4	,	,	PUNCT
ap-1872	239	5	0)(0	0)(0	NUM
ap-1872	239	6	,	,	PUNCT
ap-1872	239	7	0	0	NUM
ap-1872	239	8	)	)	PUNCT
ap-1872	239	9	(	(	PUNCT
ap-1872	239	10	1,−1)(−1	1,−1)(−1	NUM
ap-1872	239	11	,	,	PUNCT
ap-1872	239	12	1	1	NUM
ap-1872	239	13	)	)	PUNCT
ap-1872	239	14	=	=	SYM
ap-1872	239	15	(	(	PUNCT
ap-1872	239	16	0	0	NUM
ap-1872	239	17	,	,	PUNCT
ap-1872	239	18	0)(0	0)(0	NUM
ap-1872	239	19	,	,	PUNCT
ap-1872	239	20	0	0	NUM
ap-1872	239	21	)	)	PUNCT
ap-1872	239	22	for	for	ADP
ap-1872	239	23	three	three	NUM
ap-1872	239	24	before	before	ADP
ap-1872	239	25	the	the	DET
ap-1872	239	26	last	last	ADJ
ap-1872	239	27	two	two	NUM
ap-1872	239	28	,	,	PUNCT
ap-1872	239	29	and	and	CCONJ
ap-1872	239	30	(	(	PUNCT
ap-1872	239	31	0	0	NUM
ap-1872	239	32	,	,	PUNCT
ap-1872	239	33	0)(−1	0)(−1	PROPN
ap-1872	239	34	,	,	PUNCT
ap-1872	239	35	0	0	NUM
ap-1872	239	36	)	)	PUNCT
ap-1872	239	37	=	=	PRON
ap-1872	239	38	(	(	PUNCT
ap-1872	239	39	−1	−1	NOUN
ap-1872	239	40	,	,	PUNCT
ap-1872	239	41	1)(0,−1	1)(0,−1	NUM
ap-1872	239	42	)	)	PUNCT
ap-1872	239	43	(	(	PUNCT
ap-1872	239	44	0	0	NUM
ap-1872	239	45	,	,	PUNCT
ap-1872	239	46	0)(0,−1	0)(0,−1	NOUN
ap-1872	239	47	)	)	PUNCT
ap-1872	240	1	=	=	SYM
ap-1872	240	2	(	(	PUNCT
ap-1872	240	3	1,−1)(−1	1,−1)(−1	NUM
ap-1872	240	4	,	,	PUNCT
ap-1872	240	5	1	1	NUM
ap-1872	240	6	)	)	PUNCT
ap-1872	240	7	for	for	ADP
ap-1872	240	8	the	the	DET
ap-1872	240	9	last	last	ADJ
ap-1872	240	10	two	two	NUM
ap-1872	240	11	.	.	PUNCT
ap-1872	241	1	4	4	X
ap-1872	241	2	.	.	X
ap-1872	241	3	algebra	algebra	NOUN
ap-1872	241	4	g(m	g(m	VERB
ap-1872	241	5	)	)	PUNCT
ap-1872	241	6	in	in	ADP
ap-1872	241	7	mixed	mixed	ADJ
ap-1872	241	8	representation	representation	NOUN
ap-1872	241	9	the	the	DET
ap-1872	241	10	basic	basic	ADJ
ap-1872	241	11	property	property	NOUN
ap-1872	241	12	which	which	PRON
ap-1872	241	13	was	be	AUX
ap-1872	241	14	used	use	VERB
ap-1872	241	15	to	to	PART
ap-1872	241	16	construct	construct	VERB
ap-1872	241	17	the	the	DET
ap-1872	241	18	mixed	mixed	ADJ
ap-1872	241	19	representation	representation	NOUN
ap-1872	241	20	of	of	ADP
ap-1872	241	21	the	the	DET
ap-1872	241	22	algebra	algebra	NOUN
ap-1872	241	23	gln+1	gln+1	PRON
ap-1872	241	24	is	be	AUX
ap-1872	241	25	the	the	DET
ap-1872	241	26	existence	existence	NOUN
ap-1872	241	27	of	of	ADP
ap-1872	241	28	the	the	DET
ap-1872	241	29	weyl	weyl	VERB
ap-1872	241	30	-	-	ADJ
ap-1872	241	31	cartan	cartan	ADJ
ap-1872	241	32	decomposition	decomposition	NOUN
ap-1872	241	33	gln+1	gln+1	NOUN
ap-1872	241	34	=	=	SYM
ap-1872	241	35	l⊕	l⊕	X
ap-1872	241	36	(	(	PUNCT
ap-1872	241	37	gln	gln	PROPN
ap-1872	241	38	⊕	⊕	PROPN
ap-1872	241	39	i)⊕	i)⊕	PROPN
ap-1872	241	40	u	u	NOUN
ap-1872	241	41	with	with	ADP
ap-1872	241	42	property	property	NOUN
ap-1872	241	43	(	(	PUNCT
ap-1872	241	44	6	6	NUM
ap-1872	241	45	)	)	PUNCT
ap-1872	241	46	.	.	PUNCT
ap-1872	242	1	one	one	PRON
ap-1872	242	2	can	can	AUX
ap-1872	242	3	pose	pose	VERB
ap-1872	242	4	a	a	DET
ap-1872	242	5	question	question	NOUN
ap-1872	242	6	about	about	ADP
ap-1872	242	7	the	the	DET
ap-1872	242	8	existence	existence	NOUN
ap-1872	242	9	of	of	ADP
ap-1872	242	10	other	other	ADJ
ap-1872	242	11	algebras	algebra	NOUN
ap-1872	242	12	than	than	ADP
ap-1872	242	13	gln+1	gln+1	VERB
ap-1872	242	14	for	for	ADP
ap-1872	242	15	which	which	PRON
ap-1872	242	16	the	the	DET
ap-1872	242	17	weyl	weyl	VERB
ap-1872	242	18	-	-	ADJ
ap-1872	242	19	cartan	cartan	ADJ
ap-1872	242	20	decomposition	decomposition	NOUN
ap-1872	242	21	with	with	ADP
ap-1872	242	22	property	property	NOUN
ap-1872	242	23	(	(	PUNCT
ap-1872	242	24	6	6	NUM
ap-1872	242	25	)	)	PUNCT
ap-1872	242	26	holds	hold	VERB
ap-1872	242	27	.	.	PUNCT
ap-1872	243	1	the	the	DET
ap-1872	243	2	answer	answer	NOUN
ap-1872	243	3	is	be	AUX
ap-1872	243	4	affirmative	affirmative	ADJ
ap-1872	243	5	.	.	PUNCT
ap-1872	244	1	let	let	VERB
ap-1872	244	2	us	we	PRON
ap-1872	244	3	consider	consider	VERB
ap-1872	244	4	the	the	DET
ap-1872	244	5	important	important	ADJ
ap-1872	244	6	particular	particular	ADJ
ap-1872	244	7	case	case	NOUN
ap-1872	244	8	of	of	ADP
ap-1872	244	9	the	the	DET
ap-1872	244	10	cartan	cartan	ADJ
ap-1872	244	11	466	466	NUM
ap-1872	244	12	vol	vol	NOUN
ap-1872	244	13	.	.	PUNCT
ap-1872	245	1	53	53	NUM
ap-1872	245	2	no	no	NOUN
ap-1872	245	3	.	.	PUNCT
ap-1872	246	1	5/2013	5/2013	NUM
ap-1872	246	2	gln+1	gln+1	VERB
ap-1872	246	3	algebra	algebra	NOUN
ap-1872	246	4	of	of	ADP
ap-1872	246	5	matrix	matrix	NOUN
ap-1872	246	6	differential	differential	NOUN
ap-1872	246	7	operators	operator	NOUN
ap-1872	246	8	algebra	algebra	VERB
ap-1872	246	9	gl2	gl2	PROPN
ap-1872	246	10	⊕	⊕	PROPN
ap-1872	246	11	i	i	PRON
ap-1872	246	12	,	,	PUNCT
ap-1872	246	13	and	and	CCONJ
ap-1872	246	14	construct	construct	VERB
ap-1872	246	15	a	a	DET
ap-1872	246	16	realization	realization	NOUN
ap-1872	246	17	of	of	ADP
ap-1872	246	18	a	a	DET
ap-1872	246	19	new	new	ADJ
ap-1872	246	20	algebra	algebra	NOUN
ap-1872	246	21	denoted	denote	VERB
ap-1872	246	22	g(m	g(m	NOUN
ap-1872	246	23	)	)	PUNCT
ap-1872	246	24	with	with	ADP
ap-1872	246	25	the	the	DET
ap-1872	246	26	property	property	NOUN
ap-1872	246	27	g(m	g(m	VERB
ap-1872	246	28	)	)	PUNCT
ap-1872	246	29	=	=	SYM
ap-1872	246	30	lm+1	lm+1	PRON
ap-1872	246	31	o	o	NOUN
ap-1872	246	32	(	(	PUNCT
ap-1872	246	33	gl2	gl2	PROPN
ap-1872	246	34	⊕	⊕	PROPN
ap-1872	246	35	i	i	NOUN
ap-1872	246	36	)	)	PUNCT
ap-1872	246	37	n	n	PRON
ap-1872	246	38	um+1	um+1	PROPN
ap-1872	246	39	,	,	PUNCT
ap-1872	246	40	(	(	PUNCT
ap-1872	246	41	33	33	NUM
ap-1872	246	42	)	)	PUNCT
ap-1872	246	43	where	where	SCONJ
ap-1872	246	44	lm(um	lm(um	NOUN
ap-1872	246	45	)	)	PUNCT
ap-1872	246	46	is	be	AUX
ap-1872	246	47	the	the	DET
ap-1872	246	48	commutative	commutative	ADJ
ap-1872	246	49	algebra	algebra	NOUN
ap-1872	246	50	of	of	ADP
ap-1872	246	51	the	the	DET
ap-1872	246	52	lowering	lower	VERB
ap-1872	246	53	(	(	PUNCT
ap-1872	246	54	raising	raise	VERB
ap-1872	246	55	)	)	PUNCT
ap-1872	246	56	generators	generator	NOUN
ap-1872	246	57	with	with	ADP
ap-1872	246	58	the	the	DET
ap-1872	246	59	property	property	NOUN
ap-1872	246	60	[	[	X
ap-1872	246	61	lm	lm	INTJ
ap-1872	246	62	,	,	PUNCT
ap-1872	246	63	um	um	INTJ
ap-1872	246	64	]	]	PUNCT
ap-1872	246	65	=	=	PUNCT
ap-1872	246	66	pm−1(gl2⊕	pm−1(gl2⊕	PROPN
ap-1872	246	67	i	i	NOUN
ap-1872	246	68	)	)	PUNCT
ap-1872	246	69	with	with	ADP
ap-1872	246	70	pm−1	pm−1	PROPN
ap-1872	246	71	as	as	ADP
ap-1872	246	72	a	a	DET
ap-1872	246	73	polynomial	polynomial	NOUN
ap-1872	246	74	of	of	ADP
ap-1872	246	75	degree	degree	NOUN
ap-1872	246	76	(	(	PUNCT
ap-1872	246	77	m	m	NOUN
ap-1872	246	78	−	−	NOUN
ap-1872	246	79	1	1	NUM
ap-1872	246	80	)	)	PUNCT
ap-1872	246	81	in	in	ADP
ap-1872	246	82	generators	generator	NOUN
ap-1872	246	83	of	of	ADP
ap-1872	246	84	gl2	gl2	PROPN
ap-1872	246	85	⊕	⊕	PROPN
ap-1872	246	86	i.	i.	PROPN
ap-1872	246	87	thus	thus	ADV
ap-1872	246	88	,	,	PUNCT
ap-1872	246	89	it	it	PRON
ap-1872	246	90	realizes	realize	VERB
ap-1872	246	91	a	a	DET
ap-1872	246	92	property	property	NOUN
ap-1872	246	93	of	of	ADP
ap-1872	246	94	the	the	DET
ap-1872	246	95	generalized	generalized	ADJ
ap-1872	246	96	gauss	gauss	ADJ
ap-1872	246	97	decomposition	decomposition	NOUN
ap-1872	246	98	.	.	PUNCT
ap-1872	247	1	the	the	DET
ap-1872	247	2	emerging	emerge	VERB
ap-1872	247	3	algebra	algebra	NOUN
ap-1872	247	4	is	be	AUX
ap-1872	247	5	a	a	DET
ap-1872	247	6	polynomial	polynomial	ADJ
ap-1872	247	7	algebra	algebra	NOUN
ap-1872	247	8	.	.	PUNCT
ap-1872	248	1	it	it	PRON
ap-1872	248	2	is	be	AUX
ap-1872	248	3	worth	worth	ADJ
ap-1872	248	4	emphasizing	emphasize	VERB
ap-1872	248	5	that	that	SCONJ
ap-1872	248	6	the	the	DET
ap-1872	248	7	realization	realization	NOUN
ap-1872	248	8	we	we	PRON
ap-1872	248	9	are	be	AUX
ap-1872	248	10	going	go	VERB
ap-1872	248	11	to	to	PART
ap-1872	248	12	construct	construct	VERB
ap-1872	248	13	appears	appear	VERB
ap-1872	248	14	at	at	ADP
ap-1872	248	15	dim(lk	dim(lk	NOUN
ap-1872	248	16	)	)	PUNCT
ap-1872	248	17	=	=	SYM
ap-1872	248	18	dim(um	dim(um	NOUN
ap-1872	248	19	)	)	PUNCT
ap-1872	248	20	=	=	VERB
ap-1872	248	21	m.	m.	NOUN
ap-1872	248	22	for	for	ADP
ap-1872	248	23	m	m	PROPN
ap-1872	248	24	=	=	NOUN
ap-1872	248	25	1	1	NUM
ap-1872	248	26	the	the	DET
ap-1872	248	27	algebra	algebra	NOUN
ap-1872	248	28	g(1	g(1	NOUN
ap-1872	248	29	)	)	PUNCT
ap-1872	248	30	=	=	PUNCT
ap-1872	249	1	gl3	gl3	ADV
ap-1872	249	2	,	,	PUNCT
ap-1872	249	3	see	see	VERB
ap-1872	249	4	(	(	PUNCT
ap-1872	249	5	6	6	NUM
ap-1872	249	6	)	)	PUNCT
ap-1872	249	7	.	.	PUNCT
ap-1872	250	1	our	our	PRON
ap-1872	250	2	final	final	ADJ
ap-1872	250	3	goal	goal	NOUN
ap-1872	250	4	is	be	AUX
ap-1872	250	5	to	to	PART
ap-1872	250	6	build	build	VERB
ap-1872	250	7	the	the	DET
ap-1872	250	8	realization	realization	NOUN
ap-1872	250	9	of	of	ADP
ap-1872	250	10	(	(	PUNCT
ap-1872	250	11	33	33	NUM
ap-1872	250	12	)	)	PUNCT
ap-1872	250	13	in	in	ADP
ap-1872	250	14	terms	term	NOUN
ap-1872	250	15	of	of	ADP
ap-1872	250	16	finite	finite	ADJ
ap-1872	250	17	order	order	NOUN
ap-1872	250	18	differential	differential	NOUN
ap-1872	250	19	operators	operator	NOUN
ap-1872	250	20	acting	act	VERB
ap-1872	250	21	on	on	ADP
ap-1872	250	22	the	the	DET
ap-1872	250	23	plane	plane	NOUN
ap-1872	250	24	r2	r2	NOUN
ap-1872	250	25	.	.	PUNCT
ap-1872	251	1	the	the	DET
ap-1872	251	2	simplest	simple	ADJ
ap-1872	251	3	realization	realization	NOUN
ap-1872	251	4	of	of	ADP
ap-1872	251	5	the	the	DET
ap-1872	251	6	algebra	algebra	NOUN
ap-1872	251	7	gl2	gl2	PROPN
ap-1872	251	8	by	by	ADP
ap-1872	251	9	differential	differential	ADJ
ap-1872	251	10	operators	operator	NOUN
ap-1872	251	11	in	in	ADP
ap-1872	251	12	two	two	NUM
ap-1872	251	13	variables	variable	NOUN
ap-1872	251	14	is	be	AUX
ap-1872	251	15	the	the	DET
ap-1872	251	16	vector	vector	NOUN
ap-1872	251	17	field	field	NOUN
ap-1872	251	18	representation	representation	NOUN
ap-1872	251	19	,	,	PUNCT
ap-1872	251	20	see	see	VERB
ap-1872	251	21	(	(	PUNCT
ap-1872	251	22	1	1	NUM
ap-1872	251	23	)	)	PUNCT
ap-1872	251	24	at	at	ADP
ap-1872	251	25	n	n	NOUN
ap-1872	251	26	=	=	SYM
ap-1872	251	27	2	2	NUM
ap-1872	251	28	.	.	X
ap-1872	252	1	exactly	exactly	ADV
ap-1872	252	2	this	this	DET
ap-1872	252	3	representation	representation	NOUN
ap-1872	252	4	was	be	AUX
ap-1872	252	5	used	use	VERB
ap-1872	252	6	to	to	PART
ap-1872	252	7	construct	construct	VERB
ap-1872	252	8	the	the	DET
ap-1872	252	9	representation	representation	NOUN
ap-1872	252	10	of	of	ADP
ap-1872	252	11	the	the	DET
ap-1872	252	12	gl3	gl3	PROPN
ap-1872	252	13	algebra	algebra	NOUN
ap-1872	252	14	acting	act	VERB
ap-1872	252	15	of	of	ADP
ap-1872	252	16	r2	r2	PROPN
ap-1872	252	17	,	,	PUNCT
ap-1872	252	18	see	see	VERB
ap-1872	252	19	(	(	PUNCT
ap-1872	252	20	11	11	NUM
ap-1872	252	21	)	)	PUNCT
ap-1872	252	22	,	,	PUNCT
ap-1872	252	23	(	(	PUNCT
ap-1872	252	24	12	12	NUM
ap-1872	252	25	)	)	PUNCT
ap-1872	252	26	.	.	PUNCT
ap-1872	253	1	in	in	ADP
ap-1872	253	2	this	this	DET
ap-1872	253	3	case	case	NOUN
ap-1872	253	4	dim(lm	dim(lm	NOUN
ap-1872	253	5	)	)	PUNCT
ap-1872	253	6	=	=	SYM
ap-1872	253	7	dim(um	dim(um	NOUN
ap-1872	253	8	)	)	PUNCT
ap-1872	253	9	=	=	SYM
ap-1872	254	1	2	2	X
ap-1872	254	2	.	.	X
ap-1872	254	3	we	we	PRON
ap-1872	254	4	are	be	AUX
ap-1872	254	5	unable	unable	ADJ
ap-1872	254	6	to	to	PART
ap-1872	254	7	find	find	VERB
ap-1872	254	8	other	other	ADJ
ap-1872	254	9	algebras	algebra	NOUN
ap-1872	254	10	with	with	ADP
ap-1872	254	11	dim(lm	dim(lm	NOUN
ap-1872	254	12	)	)	PUNCT
ap-1872	254	13	=	=	SYM
ap-1872	254	14	dim(um	dim(um	NOUN
ap-1872	254	15	)	)	PUNCT
ap-1872	254	16	>	>	X
ap-1872	255	1	2	2	X
ap-1872	255	2	.	.	PUNCT
ap-1872	255	3	however	however	ADV
ap-1872	255	4	,	,	PUNCT
ap-1872	255	5	there	there	PRON
ap-1872	255	6	exists	exist	VERB
ap-1872	255	7	another	another	DET
ap-1872	255	8	representation	representation	NOUN
ap-1872	255	9	of	of	ADP
ap-1872	255	10	the	the	DET
ap-1872	255	11	algebra	algebra	NOUN
ap-1872	255	12	gl2	gl2	PROPN
ap-1872	255	13	by	by	ADP
ap-1872	255	14	the	the	DET
ap-1872	255	15	first	first	ADJ
ap-1872	255	16	order	order	NOUN
ap-1872	255	17	differential	differential	NOUN
ap-1872	255	18	operators	operator	NOUN
ap-1872	255	19	in	in	ADP
ap-1872	255	20	two	two	NUM
ap-1872	255	21	variables	variable	NOUN
ap-1872	255	22	,	,	PUNCT
ap-1872	255	23	j̃12	j̃12	NOUN
ap-1872	255	24	=	=	SYM
ap-1872	255	25	∂x	∂x	PROPN
ap-1872	255	26	,	,	PUNCT
ap-1872	255	27	j̃	j̃	PROPN
ap-1872	255	28	(	(	PUNCT
ap-1872	255	29	k	k	NOUN
ap-1872	255	30	)	)	PUNCT
ap-1872	255	31	11	11	NUM
ap-1872	255	32	=	=	PUNCT
ap-1872	256	1	−x∂x	−x∂x	X
ap-1872	257	1	+	+	X
ap-1872	257	2	k	k	PROPN
ap-1872	257	3	3	3	NUM
ap-1872	257	4	,	,	PUNCT
ap-1872	257	5	j̃	j̃	PROPN
ap-1872	257	6	(	(	PUNCT
ap-1872	257	7	k	k	NOUN
ap-1872	257	8	)	)	PUNCT
ap-1872	257	9	22	22	NUM
ap-1872	258	1	=	=	PUNCT
ap-1872	258	2	−x∂x	−x∂x	X
ap-1872	258	3	+	+	CCONJ
ap-1872	258	4	sy∂y	sy∂y	NOUN
ap-1872	258	5	,	,	PUNCT
ap-1872	258	6	j̃	j̃	PROPN
ap-1872	258	7	(	(	PUNCT
ap-1872	258	8	k	k	NOUN
ap-1872	258	9	)	)	PUNCT
ap-1872	258	10	21	21	NUM
ap-1872	258	11	=	=	SYM
ap-1872	258	12	x2∂x	x2∂x	NOUN
ap-1872	258	13	+	+	CCONJ
ap-1872	258	14	sxy∂y	sxy∂y	PROPN
ap-1872	258	15	−	−	PROPN
ap-1872	258	16	kx	kx	PROPN
ap-1872	258	17	,	,	PUNCT
ap-1872	258	18	(	(	PUNCT
ap-1872	258	19	34	34	NUM
ap-1872	258	20	)	)	PUNCT
ap-1872	258	21	(	(	PUNCT
ap-1872	258	22	see	see	VERB
ap-1872	258	23	s.	s.	PROPN
ap-1872	258	24	lie	lie	PROPN
ap-1872	258	25	,	,	PUNCT
ap-1872	258	26	[	[	X
ap-1872	258	27	9	9	NUM
ap-1872	258	28	]	]	PUNCT
ap-1872	258	29	at	at	ADP
ap-1872	258	30	k	k	PROPN
ap-1872	258	31	=	=	SYM
ap-1872	258	32	0	0	NUM
ap-1872	258	33	and	and	CCONJ
ap-1872	258	34	a.	a.	PROPN
ap-1872	258	35	gonzález	gonzález	PROPN
ap-1872	258	36	-	-	PUNCT
ap-1872	258	37	lopéz	lopéz	PROPN
ap-1872	258	38	et	et	PROPN
ap-1872	258	39	al	al	PROPN
ap-1872	258	40	,	,	PUNCT
ap-1872	258	41	[	[	X
ap-1872	258	42	10	10	NUM
ap-1872	258	43	]	]	X
ap-1872	258	44	at	at	ADP
ap-1872	258	45	k	k	PROPN
ap-1872	258	46	6=	6=	PROPN
ap-1872	258	47	0	0	NUM
ap-1872	258	48	(	(	PUNCT
ap-1872	258	49	case	case	NOUN
ap-1872	258	50	24	24	NUM
ap-1872	258	51	)	)	PUNCT
ap-1872	258	52	)	)	PUNCT
ap-1872	258	53	,	,	PUNCT
ap-1872	258	54	where	where	SCONJ
ap-1872	258	55	s	s	X
ap-1872	258	56	,	,	PUNCT
ap-1872	258	57	k	k	PROPN
ap-1872	258	58	are	be	AUX
ap-1872	258	59	arbitrary	arbitrary	ADJ
ap-1872	258	60	numbers	number	NOUN
ap-1872	258	61	.	.	PUNCT
ap-1872	259	1	these	these	DET
ap-1872	259	2	generators	generator	NOUN
ap-1872	259	3	obey	obey	VERB
ap-1872	259	4	the	the	DET
ap-1872	259	5	standard	standard	ADJ
ap-1872	259	6	commutation	commutation	NOUN
ap-1872	259	7	relations	relation	NOUN
ap-1872	259	8	(	(	PUNCT
ap-1872	259	9	2	2	NUM
ap-1872	259	10	)	)	PUNCT
ap-1872	259	11	of	of	ADP
ap-1872	259	12	the	the	DET
ap-1872	259	13	algebra	algebra	NOUN
ap-1872	259	14	gl2	gl2	PROPN
ap-1872	259	15	in	in	ADP
ap-1872	259	16	the	the	DET
ap-1872	259	17	vector	vector	NOUN
ap-1872	259	18	field	field	NOUN
ap-1872	259	19	representation	representation	NOUN
ap-1872	259	20	(	(	PUNCT
ap-1872	259	21	1	1	NUM
ap-1872	259	22	)	)	PUNCT
ap-1872	259	23	.	.	PUNCT
ap-1872	260	1	it	it	PRON
ap-1872	260	2	is	be	AUX
ap-1872	260	3	evident	evident	ADJ
ap-1872	260	4	that	that	SCONJ
ap-1872	260	5	the	the	DET
ap-1872	260	6	sum	sum	NOUN
ap-1872	260	7	of	of	ADP
ap-1872	260	8	the	the	DET
ap-1872	260	9	two	two	NUM
ap-1872	260	10	representations	representation	NOUN
ap-1872	260	11	,	,	PUNCT
ap-1872	260	12	j̃ij	j̃ij	PROPN
ap-1872	260	13	and	and	CCONJ
ap-1872	260	14	the	the	DET
ap-1872	260	15	matrix	matrix	NOUN
ap-1872	260	16	representation	representation	NOUN
ap-1872	260	17	mij	mij	NOUN
ap-1872	260	18	,	,	PUNCT
ap-1872	260	19	is	be	AUX
ap-1872	260	20	also	also	ADV
ap-1872	260	21	a	a	DET
ap-1872	260	22	representation	representation	NOUN
ap-1872	260	23	,	,	PUNCT
ap-1872	261	1	jij	jij	PROPN
ap-1872	261	2	≡	≡	PROPN
ap-1872	261	3	j̃ij	j̃ij	PROPN
ap-1872	262	1	+	+	PUNCT
ap-1872	262	2	mij	mij	NOUN
ap-1872	262	3	∈	∈	PROPN
ap-1872	262	4	gl2	gl2	PROPN
ap-1872	262	5	.	.	PUNCT
ap-1872	263	1	(	(	PUNCT
ap-1872	263	2	35	35	NUM
ap-1872	263	3	)	)	PUNCT
ap-1872	263	4	(	(	PUNCT
ap-1872	263	5	cf	cf	NOUN
ap-1872	263	6	.	.	PUNCT
ap-1872	264	1	(	(	PUNCT
ap-1872	264	2	5	5	NUM
ap-1872	264	3	)	)	PUNCT
ap-1872	264	4	)	)	PUNCT
ap-1872	264	5	.	.	PUNCT
ap-1872	265	1	it	it	PRON
ap-1872	265	2	is	be	AUX
ap-1872	265	3	worth	worth	ADJ
ap-1872	265	4	mentioning	mention	VERB
ap-1872	265	5	that	that	SCONJ
ap-1872	265	6	the	the	DET
ap-1872	265	7	gl2	gl2	PROPN
ap-1872	265	8	algebra	algebra	PROPN
ap-1872	265	9	commutation	commutation	NOUN
ap-1872	265	10	relations	relation	NOUN
ap-1872	265	11	for	for	ADP
ap-1872	265	12	mpm	mpm	NOUN
ap-1872	265	13	are	be	AUX
ap-1872	265	14	taken	take	VERB
ap-1872	265	15	in	in	ADP
ap-1872	265	16	a	a	DET
ap-1872	265	17	canonical	canonical	ADJ
ap-1872	265	18	form	form	NOUN
ap-1872	265	19	(	(	PUNCT
ap-1872	265	20	4	4	NUM
ap-1872	265	21	)	)	PUNCT
ap-1872	265	22	.	.	PUNCT
ap-1872	266	1	the	the	DET
ap-1872	266	2	unity	unity	NOUN
ap-1872	266	3	generator	generator	NOUN
ap-1872	266	4	i	i	PRON
ap-1872	266	5	in	in	ADP
ap-1872	266	6	(	(	PUNCT
ap-1872	266	7	33	33	NUM
ap-1872	266	8	)	)	PUNCT
ap-1872	266	9	is	be	AUX
ap-1872	266	10	written	write	VERB
ap-1872	266	11	in	in	ADP
ap-1872	266	12	the	the	DET
ap-1872	266	13	form	form	NOUN
ap-1872	266	14	of	of	ADP
ap-1872	266	15	a	a	DET
ap-1872	266	16	generalized	generalize	VERB
ap-1872	266	17	euler	euler	VERB
ap-1872	266	18	-	-	PUNCT
ap-1872	266	19	cartan	cartan	PROPN
ap-1872	266	20	operator	operator	NOUN
ap-1872	266	21	j	j	PROPN
ap-1872	266	22	(	(	PUNCT
ap-1872	266	23	k	k	NOUN
ap-1872	266	24	)	)	PUNCT
ap-1872	266	25	0	0	NUM
ap-1872	267	1	=	=	SYM
ap-1872	267	2	x∂x	x∂x	PUNCT
ap-1872	268	1	+	+	NOUN
ap-1872	268	2	sy∂y	sy∂y	VERB
ap-1872	268	3	−	−	PROPN
ap-1872	268	4	k.	k.	NOUN
ap-1872	268	5	(	(	PUNCT
ap-1872	268	6	36	36	NUM
ap-1872	268	7	)	)	PUNCT
ap-1872	268	8	now	now	ADV
ap-1872	268	9	let	let	VERB
ap-1872	268	10	us	we	PRON
ap-1872	268	11	assume	assume	VERB
ap-1872	268	12	that	that	SCONJ
ap-1872	268	13	s	s	VERB
ap-1872	268	14	is	be	AUX
ap-1872	268	15	non	non	ADJ
ap-1872	268	16	-	-	ADJ
ap-1872	268	17	negative	negative	ADJ
ap-1872	268	18	integer	integer	NOUN
ap-1872	268	19	,	,	PUNCT
ap-1872	268	20	s	s	PART
ap-1872	268	21	=	=	NOUN
ap-1872	268	22	m	m	PROPN
ap-1872	268	23	,	,	PUNCT
ap-1872	268	24	m	m	VERB
ap-1872	268	25	=	=	NOUN
ap-1872	268	26	0	0	NUM
ap-1872	268	27	,	,	PUNCT
ap-1872	268	28	1	1	NUM
ap-1872	268	29	,	,	PUNCT
ap-1872	268	30	2	2	NUM
ap-1872	268	31	,	,	PUNCT
ap-1872	268	32	.	.	PUNCT
ap-1872	268	33	.	.	PUNCT
ap-1872	269	1	..	..	PUNCT
ap-1872	269	2	evidently	evidently	ADV
ap-1872	269	3	,	,	PUNCT
ap-1872	269	4	the	the	DET
ap-1872	269	5	lowering	lower	VERB
ap-1872	269	6	generators	generator	NOUN
ap-1872	269	7	(	(	PUNCT
ap-1872	269	8	of	of	ADP
ap-1872	269	9	negative	negative	ADJ
ap-1872	269	10	grading	grading	NOUN
ap-1872	269	11	)	)	PUNCT
ap-1872	269	12	from	from	ADP
ap-1872	269	13	lm+1	lm+1	PRON
ap-1872	269	14	can	can	AUX
ap-1872	269	15	be	be	AUX
ap-1872	269	16	given	give	VERB
ap-1872	269	17	by	by	ADP
ap-1872	269	18	t−	t−	PROPN
ap-1872	269	19	i	i	PROPN
ap-1872	269	20	=	=	SYM
ap-1872	269	21	xi∂y	xi∂y	PROPN
ap-1872	269	22	,	,	PUNCT
ap-1872	269	23	i	i	NOUN
ap-1872	269	24	=	=	NOUN
ap-1872	269	25	0	0	NUM
ap-1872	269	26	,	,	PUNCT
ap-1872	269	27	1	1	NUM
ap-1872	269	28	,	,	PUNCT
ap-1872	269	29	.	.	PUNCT
ap-1872	269	30	.	.	PUNCT
ap-1872	269	31	.	.	PUNCT
ap-1872	270	1	,	,	PUNCT
ap-1872	270	2	m	m	PROPN
ap-1872	270	3	,	,	PUNCT
ap-1872	270	4	(	(	PUNCT
ap-1872	270	5	37	37	NUM
ap-1872	270	6	)	)	PUNCT
ap-1872	270	7	forming	form	VERB
ap-1872	270	8	commutative	commutative	ADJ
ap-1872	270	9	algebra	algebra	NOUN
ap-1872	270	10	[	[	X
ap-1872	270	11	t−	t−	PROPN
ap-1872	270	12	i	i	PROPN
ap-1872	270	13	,	,	PUNCT
ap-1872	270	14	t	t	PROPN
ap-1872	271	1	−	−	PROPN
ap-1872	271	2	j	j	PROPN
ap-1872	271	3	]	]	X
ap-1872	272	1	=	=	PUNCT
ap-1872	272	2	0	0	X
ap-1872	272	3	.	.	PUNCT
ap-1872	273	1	(	(	PUNCT
ap-1872	273	2	38	38	NUM
ap-1872	273	3	)	)	PUNCT
ap-1872	273	4	(	(	PUNCT
ap-1872	273	5	cf	cf	NOUN
ap-1872	273	6	.	.	PUNCT
ap-1872	274	1	[	[	X
ap-1872	274	2	9	9	NUM
ap-1872	274	3	,	,	PUNCT
ap-1872	274	4	10	10	NUM
ap-1872	274	5	]	]	NUM
ap-1872	274	6	)	)	PUNCT
ap-1872	274	7	.	.	PUNCT
ap-1872	275	1	eventually	eventually	ADV
ap-1872	275	2	,	,	PUNCT
ap-1872	275	3	the	the	DET
ap-1872	275	4	generators	generator	NOUN
ap-1872	275	5	of	of	ADP
ap-1872	275	6	the	the	DET
ap-1872	275	7	algebra	algebra	NOUN
ap-1872	275	8	(	(	PUNCT
ap-1872	275	9	gl2	gl2	PROPN
ap-1872	275	10	⊕	⊕	PROPN
ap-1872	275	11	i	i	NOUN
ap-1872	275	12	)	)	PUNCT
ap-1872	275	13	n	n	CCONJ
ap-1872	275	14	lm+1	lm+1	PRON
ap-1872	275	15	take	take	VERB
ap-1872	275	16	the	the	DET
ap-1872	275	17	form	form	NOUN
ap-1872	275	18	j12	j12	NOUN
ap-1872	275	19	=	=	SYM
ap-1872	275	20	∂x	∂x	PROPN
ap-1872	276	1	+	+	NUM
ap-1872	276	2	m12	m12	PROPN
ap-1872	276	3	,	,	PUNCT
ap-1872	276	4	j	j	PROPN
ap-1872	276	5	(	(	PUNCT
ap-1872	276	6	k	k	NOUN
ap-1872	276	7	)	)	PUNCT
ap-1872	276	8	11	11	NUM
ap-1872	277	1	=	=	PUNCT
ap-1872	277	2	−x∂x	−x∂x	X
ap-1872	278	1	+	+	X
ap-1872	278	2	k	k	PROPN
ap-1872	278	3	3	3	NUM
ap-1872	278	4	+	+	NOUN
ap-1872	278	5	m11	m11	NOUN
ap-1872	278	6	,	,	PUNCT
ap-1872	278	7	j	j	PROPN
ap-1872	278	8	(	(	PUNCT
ap-1872	278	9	k	k	NOUN
ap-1872	278	10	)	)	PUNCT
ap-1872	278	11	22	22	NUM
ap-1872	279	1	=	=	PUNCT
ap-1872	279	2	−x∂x	−x∂x	VERB
ap-1872	280	1	+	+	ADJ
ap-1872	280	2	my∂y	my∂y	PROPN
ap-1872	280	3	+	+	PROPN
ap-1872	280	4	m22	m22	PROPN
ap-1872	280	5	,	,	PUNCT
ap-1872	280	6	j	j	PROPN
ap-1872	280	7	(	(	PUNCT
ap-1872	280	8	k	k	NOUN
ap-1872	280	9	)	)	PUNCT
ap-1872	280	10	21	21	NUM
ap-1872	280	11	=	=	SYM
ap-1872	280	12	x2∂x	x2∂x	PROPN
ap-1872	281	1	+	+	PROPN
ap-1872	281	2	mxy∂y	mxy∂y	NOUN
ap-1872	281	3	−	−	NOUN
ap-1872	281	4	kx+m21	kx+m21	PROPN
ap-1872	281	5	,	,	PUNCT
ap-1872	281	6	(	(	PUNCT
ap-1872	281	7	39	39	NUM
ap-1872	281	8	)	)	PUNCT
ap-1872	281	9	with	with	ADP
ap-1872	281	10	j	j	PROPN
ap-1872	281	11	(	(	PUNCT
ap-1872	281	12	k	k	NOUN
ap-1872	281	13	)	)	PUNCT
ap-1872	281	14	0	0	NUM
ap-1872	282	1	and	and	CCONJ
ap-1872	282	2	t−	t−	PROPN
ap-1872	282	3	i	i	PRON
ap-1872	282	4	given	give	VERB
ap-1872	282	5	by	by	ADP
ap-1872	282	6	(	(	PUNCT
ap-1872	282	7	36	36	NUM
ap-1872	282	8	)	)	PUNCT
ap-1872	282	9	and	and	CCONJ
ap-1872	282	10	(	(	PUNCT
ap-1872	282	11	37	37	NUM
ap-1872	282	12	)	)	PUNCT
ap-1872	282	13	,	,	PUNCT
ap-1872	282	14	respectively	respectively	ADV
ap-1872	282	15	.	.	PUNCT
ap-1872	283	1	let	let	VERB
ap-1872	283	2	us	we	PRON
ap-1872	283	3	consider	consider	VERB
ap-1872	283	4	two	two	NUM
ap-1872	283	5	particular	particular	ADJ
ap-1872	283	6	cases	case	NOUN
ap-1872	283	7	of	of	ADP
ap-1872	283	8	the	the	DET
ap-1872	283	9	general	general	ADJ
ap-1872	283	10	construction	construction	NOUN
ap-1872	283	11	of	of	ADP
ap-1872	283	12	the	the	DET
ap-1872	283	13	raising	raise	VERB
ap-1872	283	14	generators	generator	NOUN
ap-1872	283	15	for	for	ADP
ap-1872	283	16	the	the	DET
ap-1872	283	17	commutative	commutative	ADJ
ap-1872	283	18	algebra	algebra	PROPN
ap-1872	283	19	u	u	NOUN
ap-1872	283	20	.	.	PUNCT
ap-1872	284	1	case	case	NOUN
ap-1872	284	2	1	1	NUM
ap-1872	284	3	.	.	X
ap-1872	285	1	for	for	ADP
ap-1872	285	2	the	the	DET
ap-1872	285	3	first	first	ADJ
ap-1872	285	4	case	case	NOUN
ap-1872	285	5	we	we	PRON
ap-1872	285	6	take	take	VERB
ap-1872	285	7	the	the	DET
ap-1872	285	8	trivial	trivial	ADJ
ap-1872	285	9	matrix	matrix	NOUN
ap-1872	285	10	representation	representation	NOUN
ap-1872	285	11	of	of	ADP
ap-1872	285	12	the	the	DET
ap-1872	285	13	gl2	gl2	PROPN
ap-1872	285	14	,	,	PUNCT
ap-1872	285	15	m11	m11	NOUN
ap-1872	285	16	=	=	SYM
ap-1872	285	17	m12	m12	NOUN
ap-1872	285	18	=	=	SYM
ap-1872	285	19	m21	m21	PROPN
ap-1872	285	20	=	=	PUNCT
ap-1872	285	21	m22	m22	PROPN
ap-1872	285	22	=	=	SYM
ap-1872	285	23	0	0	PROPN
ap-1872	285	24	.	.	PUNCT
ap-1872	286	1	one	one	PRON
ap-1872	286	2	can	can	AUX
ap-1872	286	3	check	check	VERB
ap-1872	286	4	that	that	DET
ap-1872	286	5	one	one	NUM
ap-1872	286	6	of	of	ADP
ap-1872	286	7	the	the	DET
ap-1872	286	8	raising	raise	VERB
ap-1872	286	9	generators	generator	NOUN
ap-1872	286	10	is	be	AUX
ap-1872	286	11	given	give	VERB
ap-1872	286	12	by	by	ADP
ap-1872	286	13	u0	u0	ADJ
ap-1872	286	14	=	=	NOUN
ap-1872	286	15	y∂mx	y∂mx	NOUN
ap-1872	286	16	,	,	PUNCT
ap-1872	286	17	(	(	PUNCT
ap-1872	286	18	40	40	NUM
ap-1872	286	19	)	)	PUNCT
ap-1872	286	20	while	while	SCONJ
ap-1872	286	21	all	all	DET
ap-1872	286	22	other	other	ADJ
ap-1872	286	23	raising	raise	VERB
ap-1872	286	24	generators	generator	NOUN
ap-1872	286	25	are	be	AUX
ap-1872	286	26	multiple	multiple	ADJ
ap-1872	286	27	commutators	commutator	NOUN
ap-1872	286	28	of	of	ADP
ap-1872	286	29	j	j	PROPN
ap-1872	286	30	(	(	PUNCT
ap-1872	286	31	k	k	NOUN
ap-1872	286	32	)	)	PUNCT
ap-1872	286	33	21	21	NUM
ap-1872	286	34	with	with	ADP
ap-1872	286	35	u0	u0	PROPN
ap-1872	286	36	,	,	PUNCT
ap-1872	286	37	ui	ui	PROPN
ap-1872	286	38	≡	≡	PROPN
ap-1872	287	1	[	[	X
ap-1872	287	2	j	j	X
ap-1872	287	3	(	(	PUNCT
ap-1872	287	4	k	k	NOUN
ap-1872	287	5	)	)	PUNCT
ap-1872	287	6	21	21	NUM
ap-1872	287	7	,	,	PUNCT
ap-1872	287	8	[	[	X
ap-1872	287	9	j	j	X
ap-1872	287	10	(	(	PUNCT
ap-1872	287	11	k	k	NOUN
ap-1872	287	12	)	)	PUNCT
ap-1872	287	13	21	21	NUM
ap-1872	287	14	,	,	PUNCT
ap-1872	287	15	[	[	X
ap-1872	287	16	·	·	PUNCT
ap-1872	287	17	·	·	PUNCT
ap-1872	287	18	·	·	PUNCT
ap-1872	287	19	j	j	X
ap-1872	287	20	(	(	PUNCT
ap-1872	287	21	k	k	NOUN
ap-1872	287	22	)	)	PUNCT
ap-1872	287	23	21	21	NUM
ap-1872	287	24	,	,	PUNCT
ap-1872	287	25	t0	t0	PROPN
ap-1872	287	26	]	]	PUNCT
ap-1872	287	27	·	·	PUNCT
ap-1872	287	28	·	·	PUNCT
ap-1872	287	29	·	·	PUNCT
ap-1872	287	30	]	]	PUNCT
ap-1872	288	1	]	]	X
ap-1872	288	2	︸	︸	X
ap-1872	288	3	︷︷	︷︷	NOUN
ap-1872	288	4	︸	︸	X
ap-1872	289	1	i	i	NOUN
ap-1872	289	2	=	=	SYM
ap-1872	289	3	y∂m−i	y∂m−i	X
ap-1872	289	4	x	x	X
ap-1872	289	5	j	j	PROPN
ap-1872	289	6	(	(	PUNCT
ap-1872	289	7	k	k	NOUN
ap-1872	289	8	)	)	PUNCT
ap-1872	289	9	0	0	PUNCT
ap-1872	290	1	(	(	PUNCT
ap-1872	290	2	j	j	PROPN
ap-1872	290	3	(	(	PUNCT
ap-1872	290	4	k	k	NOUN
ap-1872	290	5	)	)	PUNCT
ap-1872	290	6	0	0	PUNCT
ap-1872	291	1	+	+	CCONJ
ap-1872	291	2	1	1	NUM
ap-1872	291	3	)	)	PUNCT
ap-1872	291	4	.	.	PUNCT
ap-1872	291	5	.	.	PUNCT
ap-1872	291	6	.	.	PUNCT
ap-1872	292	1	(	(	PUNCT
ap-1872	292	2	j	j	PROPN
ap-1872	292	3	(	(	PUNCT
ap-1872	292	4	k	k	NOUN
ap-1872	292	5	)	)	PUNCT
ap-1872	292	6	0	0	PUNCT
ap-1872	293	1	+	+	CCONJ
ap-1872	293	2	i−	i−	PROPN
ap-1872	293	3	1	1	NUM
ap-1872	293	4	)	)	PUNCT
ap-1872	293	5	,	,	PUNCT
ap-1872	293	6	(	(	PUNCT
ap-1872	293	7	41	41	NUM
ap-1872	293	8	)	)	PUNCT
ap-1872	293	9	at	at	ADP
ap-1872	293	10	i	i	NOUN
ap-1872	293	11	=	=	NOUN
ap-1872	293	12	1	1	NUM
ap-1872	293	13	,	,	PUNCT
ap-1872	293	14	.	.	PUNCT
ap-1872	293	15	.	.	PUNCT
ap-1872	294	1	.m	.m	PROPN
ap-1872	294	2	.	.	PUNCT
ap-1872	295	1	all	all	PRON
ap-1872	295	2	of	of	ADP
ap-1872	295	3	them	they	PRON
ap-1872	295	4	are	be	AUX
ap-1872	295	5	differential	differential	ADJ
ap-1872	295	6	operators	operator	NOUN
ap-1872	295	7	of	of	ADP
ap-1872	295	8	fixed	fix	VERB
ap-1872	295	9	degree	degree	NOUN
ap-1872	295	10	m.	m.	NOUN
ap-1872	295	11	the	the	DET
ap-1872	295	12	procedure	procedure	NOUN
ap-1872	295	13	for	for	ADP
ap-1872	295	14	construction	construction	NOUN
ap-1872	295	15	of	of	ADP
ap-1872	295	16	the	the	DET
ap-1872	295	17	operators	operator	NOUN
ap-1872	295	18	ui	ui	PROPN
ap-1872	295	19	has	have	VERB
ap-1872	295	20	the	the	DET
ap-1872	295	21	property	property	NOUN
ap-1872	295	22	of	of	ADP
ap-1872	295	23	nilpotency	nilpotency	NOUN
ap-1872	295	24	:	:	PUNCT
ap-1872	295	25	ui	ui	PROPN
ap-1872	295	26	=	=	NOUN
ap-1872	295	27	0	0	PROPN
ap-1872	295	28	,	,	PUNCT
ap-1872	295	29	i	i	PRON
ap-1872	295	30	>	>	X
ap-1872	295	31	m.	m.	NOUN
ap-1872	295	32	in	in	ADP
ap-1872	295	33	particular	particular	ADJ
ap-1872	295	34	,	,	PUNCT
ap-1872	295	35	for	for	ADP
ap-1872	295	36	m	m	PROPN
ap-1872	295	37	=	=	SYM
ap-1872	295	38	1	1	NUM
ap-1872	295	39	,	,	PUNCT
ap-1872	295	40	u0	u0	ADJ
ap-1872	295	41	=	=	PUNCT
ap-1872	295	42	y∂x	y∂x	NOUN
ap-1872	295	43	,	,	PUNCT
ap-1872	295	44	u1	u1	PROPN
ap-1872	295	45	=	=	SYM
ap-1872	295	46	yj	yj	PROPN
ap-1872	295	47	(	(	PUNCT
ap-1872	295	48	k	k	NOUN
ap-1872	295	49	)	)	PUNCT
ap-1872	295	50	0	0	NUM
ap-1872	296	1	=	=	SYM
ap-1872	296	2	y(x∂x	y(x∂x	PROPN
ap-1872	297	1	+	+	CCONJ
ap-1872	297	2	y∂y	y∂y	NOUN
ap-1872	297	3	−	−	PROPN
ap-1872	297	4	k	k	NOUN
ap-1872	297	5	)	)	PUNCT
ap-1872	297	6	.	.	PUNCT
ap-1872	298	1	inspecting	inspect	VERB
ap-1872	298	2	the	the	DET
ap-1872	298	3	generators	generator	NOUN
ap-1872	298	4	t−	t−	PROPN
ap-1872	298	5	0,1	0,1	NUM
ap-1872	298	6	,	,	PUNCT
ap-1872	298	7	jij	jij	PROPN
ap-1872	298	8	,	,	PUNCT
ap-1872	298	9	j	j	PROPN
ap-1872	298	10	(	(	PUNCT
ap-1872	298	11	n	n	CCONJ
ap-1872	298	12	)	)	PUNCT
ap-1872	298	13	,	,	PUNCT
ap-1872	298	14	u0,1	u0,1	NOUN
ap-1872	298	15	one	one	NOUN
ap-1872	298	16	can	can	AUX
ap-1872	298	17	see	see	VERB
ap-1872	298	18	that	that	SCONJ
ap-1872	298	19	they	they	PRON
ap-1872	298	20	span	span	VERB
ap-1872	298	21	the	the	DET
ap-1872	298	22	algebra	algebra	NOUN
ap-1872	298	23	gl3	gl3	ADV
ap-1872	298	24	,	,	PUNCT
ap-1872	298	25	see	see	VERB
ap-1872	298	26	(	(	PUNCT
ap-1872	298	27	12	12	NUM
ap-1872	298	28	)	)	PUNCT
ap-1872	298	29	.	.	PUNCT
ap-1872	299	1	hence	hence	ADV
ap-1872	299	2	,	,	PUNCT
ap-1872	299	3	the	the	DET
ap-1872	299	4	algebra	algebra	PROPN
ap-1872	299	5	g(1	g(1	NOUN
ap-1872	299	6	)	)	PUNCT
ap-1872	299	7	≡	≡	PROPN
ap-1872	299	8	gl3	gl3	PROPN
ap-1872	299	9	.	.	PUNCT
ap-1872	300	1	if	if	SCONJ
ap-1872	300	2	parameter	parameter	PROPN
ap-1872	300	3	k	k	PROPN
ap-1872	300	4	takes	take	VERB
ap-1872	300	5	non	non	ADJ
ap-1872	300	6	-	-	ADJ
ap-1872	300	7	negative	negative	ADJ
ap-1872	300	8	integer	integer	NOUN
ap-1872	300	9	the	the	DET
ap-1872	300	10	algebra	algebra	NOUN
ap-1872	300	11	g(m	g(m	VERB
ap-1872	300	12	)	)	PUNCT
ap-1872	300	13	spanned	span	VERB
ap-1872	300	14	by	by	ADP
ap-1872	300	15	the	the	DET
ap-1872	300	16	generators	generator	NOUN
ap-1872	300	17	(	(	PUNCT
ap-1872	300	18	39	39	NUM
ap-1872	300	19	)	)	PUNCT
ap-1872	300	20	,	,	PUNCT
ap-1872	300	21	(	(	PUNCT
ap-1872	300	22	40	40	NUM
ap-1872	300	23	)	)	PUNCT
ap-1872	300	24	,	,	PUNCT
ap-1872	300	25	(	(	PUNCT
ap-1872	300	26	41	41	NUM
ap-1872	300	27	)	)	PUNCT
ap-1872	300	28	appears	appear	VERB
ap-1872	300	29	in	in	ADP
ap-1872	300	30	finite	finite	ADJ
ap-1872	300	31	-	-	ADJ
ap-1872	300	32	dimensional	dimensional	ADJ
ap-1872	300	33	representation	representation	NOUN
ap-1872	300	34	.	.	PUNCT
ap-1872	301	1	its	its	PRON
ap-1872	301	2	finitedimensional	finitedimensional	ADJ
ap-1872	301	3	representation	representation	NOUN
ap-1872	301	4	space	space	NOUN
ap-1872	301	5	is	be	AUX
ap-1872	301	6	a	a	DET
ap-1872	301	7	triangular	triangular	ADJ
ap-1872	301	8	space	space	NOUN
ap-1872	301	9	of	of	ADP
ap-1872	301	10	polynomials	polynomial	NOUN
ap-1872	301	11	pk,0	pk,0	PROPN
ap-1872	301	12	=	=	SYM
ap-1872	301	13	〈	〈	PROPN
ap-1872	301	14	xp1yp2	xp1yp2	X
ap-1872	301	15	∣∣	∣∣	NUM
ap-1872	301	16	0	0	X
ap-1872	301	17	≤	≤	PROPN
ap-1872	301	18	p1	p1	PROPN
ap-1872	301	19	+	+	PROPN
ap-1872	301	20	mp2	mp2	PROPN
ap-1872	301	21	≤	≤	NOUN
ap-1872	301	22	k	k	PROPN
ap-1872	301	23	〉	〉	NOUN
ap-1872	301	24	,	,	PUNCT
ap-1872	301	25	k	k	PROPN
ap-1872	301	26	=	=	SYM
ap-1872	301	27	0	0	NUM
ap-1872	301	28	,	,	PUNCT
ap-1872	301	29	1	1	NUM
ap-1872	301	30	,	,	PUNCT
ap-1872	301	31	2	2	NUM
ap-1872	301	32	,	,	PUNCT
ap-1872	301	33	.	.	PUNCT
ap-1872	301	34	.	.	PUNCT
ap-1872	301	35	.	.	PUNCT
ap-1872	301	36	.	.	PUNCT
ap-1872	302	1	(	(	PUNCT
ap-1872	302	2	42	42	NUM
ap-1872	302	3	)	)	PUNCT
ap-1872	302	4	namely	namely	ADV
ap-1872	302	5	in	in	ADP
ap-1872	302	6	this	this	DET
ap-1872	302	7	representation	representation	NOUN
ap-1872	302	8	,	,	PUNCT
ap-1872	302	9	the	the	DET
ap-1872	302	10	algebra	algebra	NOUN
ap-1872	302	11	g(m	g(m	VERB
ap-1872	302	12	)	)	PUNCT
ap-1872	302	13	appears	appear	VERB
ap-1872	302	14	as	as	ADP
ap-1872	302	15	a	a	DET
ap-1872	302	16	hidden	hidden	ADJ
ap-1872	302	17	algebra	algebra	NOUN
ap-1872	302	18	of	of	ADP
ap-1872	302	19	the	the	DET
ap-1872	302	20	3	3	NUM
ap-1872	302	21	-	-	PUNCT
ap-1872	302	22	body	body	NOUN
ap-1872	302	23	g2	g2	PROPN
ap-1872	302	24	trigonometric	trigonometric	ADJ
ap-1872	302	25	model	model	NOUN
ap-1872	303	1	[	[	X
ap-1872	303	2	6	6	NUM
ap-1872	303	3	]	]	PUNCT
ap-1872	303	4	at	at	ADP
ap-1872	303	5	m	m	PROPN
ap-1872	303	6	=	=	SYM
ap-1872	303	7	2	2	NUM
ap-1872	303	8	and	and	CCONJ
ap-1872	303	9	of	of	ADP
ap-1872	303	10	the	the	DET
ap-1872	303	11	so	so	ADV
ap-1872	303	12	-	-	PUNCT
ap-1872	303	13	called	call	VERB
ap-1872	303	14	ttw	ttw	PROPN
ap-1872	303	15	model	model	NOUN
ap-1872	303	16	at	at	ADP
ap-1872	303	17	integer	integer	PROPN
ap-1872	303	18	m	m	PROPN
ap-1872	303	19	,	,	PUNCT
ap-1872	303	20	in	in	ADP
ap-1872	303	21	particular	particular	ADJ
ap-1872	303	22	,	,	PUNCT
ap-1872	303	23	of	of	ADP
ap-1872	303	24	the	the	DET
ap-1872	303	25	dihedral	dihedral	ADJ
ap-1872	303	26	i2(m	i2(m	NOUN
ap-1872	303	27	)	)	PUNCT
ap-1872	303	28	rational	rational	ADJ
ap-1872	303	29	model	model	NOUN
ap-1872	304	1	[	[	X
ap-1872	304	2	11	11	NUM
ap-1872	304	3	]	]	SYM
ap-1872	304	4	.	.	PUNCT
ap-1872	304	5	467	467	NUM
ap-1872	304	6	yu	yu	PROPN
ap-1872	304	7	.	.	PUNCT
ap-1872	304	8	f.	f.	PROPN
ap-1872	304	9	smirnov	smirnov	PROPN
ap-1872	304	10	,	,	PUNCT
ap-1872	304	11	a.	a.	NOUN
ap-1872	304	12	v.	v.	PROPN
ap-1872	304	13	turbiner	turbiner	PROPN
ap-1872	304	14	acta	acta	PROPN
ap-1872	304	15	polytechnica	polytechnica	PROPN
ap-1872	304	16	case	case	NOUN
ap-1872	304	17	2	2	X
ap-1872	304	18	.	.	PUNCT
ap-1872	305	1	the	the	DET
ap-1872	305	2	second	second	ADJ
ap-1872	305	3	case	case	NOUN
ap-1872	305	4	is	be	AUX
ap-1872	305	5	a	a	DET
ap-1872	305	6	certain	certain	ADJ
ap-1872	305	7	evident	evident	ADJ
ap-1872	305	8	extension	extension	NOUN
ap-1872	305	9	when	when	SCONJ
ap-1872	305	10	generators	generator	NOUN
ap-1872	305	11	mij	mij	VERB
ap-1872	305	12	are	be	AUX
ap-1872	305	13	of	of	ADP
ap-1872	305	14	an	an	DET
ap-1872	305	15	arbitrary	arbitrary	ADJ
ap-1872	305	16	matrix	matrix	NOUN
ap-1872	305	17	representation	representation	NOUN
ap-1872	305	18	of	of	ADP
ap-1872	305	19	the	the	DET
ap-1872	305	20	algebra	algebra	PROPN
ap-1872	305	21	gl2	gl2	PROPN
ap-1872	305	22	.	.	PUNCT
ap-1872	306	1	raising	raise	VERB
ap-1872	306	2	generators	generator	NOUN
ap-1872	306	3	(	(	PUNCT
ap-1872	306	4	40	40	NUM
ap-1872	306	5	)	)	PUNCT
ap-1872	306	6	,	,	PUNCT
ap-1872	306	7	(	(	PUNCT
ap-1872	306	8	41	41	NUM
ap-1872	306	9	)	)	PUNCT
ap-1872	306	10	remain	remain	VERB
ap-1872	306	11	raising	raise	VERB
ap-1872	306	12	generators	generator	NOUN
ap-1872	306	13	even	even	ADV
ap-1872	306	14	if	if	SCONJ
ap-1872	306	15	cartan	cartan	ADJ
ap-1872	306	16	generators	generator	NOUN
ap-1872	306	17	are	be	AUX
ap-1872	306	18	given	give	VERB
ap-1872	306	19	by	by	ADP
ap-1872	306	20	(	(	PUNCT
ap-1872	306	21	39	39	NUM
ap-1872	306	22	)	)	PUNCT
ap-1872	306	23	with	with	ADP
ap-1872	306	24	arbitrary	arbitrary	ADJ
ap-1872	306	25	mij	mij	NOUN
ap-1872	306	26	∈	∈	PROPN
ap-1872	306	27	gl2	gl2	PROPN
ap-1872	306	28	.	.	PUNCT
ap-1872	307	1	however	however	ADV
ap-1872	307	2	,	,	PUNCT
ap-1872	307	3	the	the	DET
ap-1872	307	4	algebra	algebra	NOUN
ap-1872	307	5	is	be	AUX
ap-1872	307	6	not	not	PART
ap-1872	307	7	closed	closed	ADJ
ap-1872	307	8	:	:	PUNCT
ap-1872	308	1	[	[	X
ap-1872	308	2	t	t	X
ap-1872	308	3	,	,	PUNCT
ap-1872	308	4	u	u	NOUN
ap-1872	308	5	]	]	PUNCT
ap-1872	308	6	6=	6=	ADP
ap-1872	308	7	p	p	X
ap-1872	308	8	(	(	PUNCT
ap-1872	308	9	gl2⊕i	gl2⊕i	NOUN
ap-1872	308	10	)	)	PUNCT
ap-1872	308	11	.	.	PUNCT
ap-1872	309	1	it	it	PRON
ap-1872	309	2	can	can	AUX
ap-1872	309	3	be	be	AUX
ap-1872	309	4	fixed	fix	VERB
ap-1872	309	5	,	,	PUNCT
ap-1872	309	6	at	at	ADP
ap-1872	309	7	least	least	ADJ
ap-1872	309	8	,	,	PUNCT
ap-1872	309	9	for	for	ADP
ap-1872	309	10	the	the	DET
ap-1872	309	11	case	case	NOUN
ap-1872	309	12	m	m	NOUN
ap-1872	309	13	=	=	NOUN
ap-1872	310	1	1	1	X
ap-1872	310	2	.	.	X
ap-1872	310	3	ifmij	ifmij	PROPN
ap-1872	310	4	are	be	AUX
ap-1872	310	5	generators	generator	NOUN
ap-1872	310	6	of	of	ADP
ap-1872	310	7	gl2	gl2	PROPN
ap-1872	310	8	subalgebra	subalgebra	NOUN
ap-1872	310	9	of	of	ADP
ap-1872	310	10	gl3	gl3	PROPN
ap-1872	310	11	.	.	PUNCT
ap-1872	311	1	by	by	ADP
ap-1872	311	2	adding	add	VERB
ap-1872	311	3	to	to	ADP
ap-1872	311	4	t	t	PROPN
ap-1872	311	5	,	,	PUNCT
ap-1872	311	6	u	u	NOUN
ap-1872	311	7	generators	generator	NOUN
ap-1872	311	8	(	(	PUNCT
ap-1872	311	9	38	38	NUM
ap-1872	311	10	)	)	PUNCT
ap-1872	311	11	,	,	PUNCT
ap-1872	311	12	(	(	PUNCT
ap-1872	311	13	40	40	NUM
ap-1872	311	14	)	)	PUNCT
ap-1872	311	15	,	,	PUNCT
ap-1872	311	16	(	(	PUNCT
ap-1872	311	17	41	41	NUM
ap-1872	311	18	)	)	PUNCT
ap-1872	311	19	the	the	DET
ap-1872	311	20	appropriate	appropriate	ADJ
ap-1872	311	21	matrix	matrix	NOUN
ap-1872	311	22	generators	generator	NOUN
ap-1872	311	23	from	from	ADP
ap-1872	311	24	gl3	gl3	PROPN
ap-1872	311	25	,	,	PUNCT
ap-1872	311	26	the	the	DET
ap-1872	311	27	algebra	algebra	NOUN
ap-1872	311	28	gets	get	VERB
ap-1872	311	29	closed	closed	ADJ
ap-1872	311	30	.	.	PUNCT
ap-1872	312	1	we	we	PRON
ap-1872	312	2	end	end	VERB
ap-1872	312	3	up	up	ADP
ap-1872	312	4	with	with	ADP
ap-1872	312	5	the	the	DET
ap-1872	312	6	gl3	gl3	ADJ
ap-1872	312	7	algebra	algebra	NOUN
ap-1872	312	8	of	of	ADP
ap-1872	312	9	matrix	matrix	NOUN
ap-1872	312	10	differential	differential	NOUN
ap-1872	312	11	operators	operator	NOUN
ap-1872	312	12	other	other	ADJ
ap-1872	312	13	than	than	ADP
ap-1872	312	14	(	(	PUNCT
ap-1872	312	15	11	11	NUM
ap-1872	312	16	)	)	PUNCT
ap-1872	312	17	.	.	PUNCT
ap-1872	313	1	we	we	PRON
ap-1872	313	2	are	be	AUX
ap-1872	313	3	not	not	PART
ap-1872	313	4	aware	aware	ADJ
ap-1872	313	5	of	of	ADP
ap-1872	313	6	a	a	DET
ap-1872	313	7	solution	solution	NOUN
ap-1872	313	8	to	to	ADP
ap-1872	313	9	this	this	DET
ap-1872	313	10	problem	problem	NOUN
ap-1872	313	11	for	for	ADP
ap-1872	313	12	the	the	DET
ap-1872	313	13	case	case	NOUN
ap-1872	313	14	of	of	ADP
ap-1872	313	15	m	m	PROPN
ap-1872	313	16	6=	6=	NUM
ap-1872	313	17	1	1	NUM
ap-1872	313	18	except	except	SCONJ
ap-1872	313	19	for	for	ADP
ap-1872	313	20	the	the	DET
ap-1872	313	21	case	case	NOUN
ap-1872	313	22	of	of	ADP
ap-1872	313	23	trivial	trivial	ADJ
ap-1872	313	24	matrix	matrix	NOUN
ap-1872	313	25	representation	representation	NOUN
ap-1872	313	26	,	,	PUNCT
ap-1872	313	27	see	see	VERB
ap-1872	313	28	case	case	NOUN
ap-1872	313	29	1	1	NUM
ap-1872	313	30	.	.	SYM
ap-1872	313	31	5	5	NUM
ap-1872	313	32	.	.	X
ap-1872	313	33	extension	extension	NOUN
ap-1872	313	34	of	of	ADP
ap-1872	313	35	the	the	DET
ap-1872	313	36	3	3	NUM
ap-1872	313	37	-	-	PUNCT
ap-1872	313	38	body	body	NOUN
ap-1872	313	39	calogero	calogero	NOUN
ap-1872	313	40	model	model	NOUN
ap-1872	313	41	the	the	DET
ap-1872	313	42	first	first	ADJ
ap-1872	313	43	algebraic	algebraic	ADJ
ap-1872	313	44	form	form	NOUN
ap-1872	313	45	for	for	ADP
ap-1872	313	46	the	the	DET
ap-1872	313	47	3	3	NUM
ap-1872	313	48	-	-	PUNCT
ap-1872	313	49	body	body	NOUN
ap-1872	313	50	calogero	calogero	NOUN
ap-1872	313	51	hamiltonian	hamiltonian	NOUN
ap-1872	314	1	[	[	X
ap-1872	314	2	12	12	NUM
ap-1872	314	3	]	]	PUNCT
ap-1872	314	4	appears	appear	VERB
ap-1872	314	5	after	after	ADP
ap-1872	314	6	gauge	gauge	NOUN
ap-1872	314	7	rotation	rotation	NOUN
ap-1872	314	8	with	with	ADP
ap-1872	314	9	the	the	DET
ap-1872	314	10	ground	ground	NOUN
ap-1872	314	11	state	state	NOUN
ap-1872	314	12	function	function	NOUN
ap-1872	314	13	,	,	PUNCT
ap-1872	314	14	separation	separation	NOUN
ap-1872	314	15	of	of	ADP
ap-1872	314	16	the	the	DET
ap-1872	314	17	center	center	NOUN
ap-1872	314	18	-	-	PUNCT
ap-1872	314	19	ofmass	ofmass	NOUN
ap-1872	314	20	and	and	CCONJ
ap-1872	314	21	changing	change	VERB
ap-1872	314	22	the	the	DET
ap-1872	314	23	variables	variable	NOUN
ap-1872	314	24	to	to	ADP
ap-1872	314	25	elementary	elementary	ADJ
ap-1872	314	26	symmetric	symmetric	ADJ
ap-1872	314	27	polynomials	polynomial	NOUN
ap-1872	314	28	of	of	ADP
ap-1872	314	29	the	the	DET
ap-1872	314	30	translationally	translationally	ADJ
ap-1872	314	31	-	-	PUNCT
ap-1872	314	32	symmetric	symmetric	ADJ
ap-1872	314	33	coordinates	coordinate	NOUN
ap-1872	314	34	[	[	X
ap-1872	314	35	5	5	NUM
ap-1872	314	36	]	]	PUNCT
ap-1872	314	37	,	,	PUNCT
ap-1872	314	38	hcal	hcal	ADJ
ap-1872	314	39	=	=	SYM
ap-1872	314	40	−2τ2∂	−2τ2∂	NOUN
ap-1872	314	41	2	2	NUM
ap-1872	314	42	τ2τ2	τ2τ2	PUNCT
ap-1872	314	43	−	−	PROPN
ap-1872	314	44	6τ3∂	6τ3∂	NUM
ap-1872	314	45	2	2	NUM
ap-1872	314	46	τ2τ3	τ2τ3	NOUN
ap-1872	314	47	+	+	NOUN
ap-1872	314	48	2	2	NUM
ap-1872	314	49	3τ	3τ	NUM
ap-1872	314	50	2	2	NUM
ap-1872	314	51	2	2	NUM
ap-1872	314	52	∂	∂	NUM
ap-1872	314	53	2	2	NUM
ap-1872	314	54	τ3τ3	τ3τ3	SYM
ap-1872	314	55	−	−	PROPN
ap-1872	314	56	[	[	PUNCT
ap-1872	314	57	4ωτ2	4ωτ2	NUM
ap-1872	314	58	+	+	SYM
ap-1872	314	59	2(1	2(1	NUM
ap-1872	314	60	+	+	CCONJ
ap-1872	314	61	3ν	3ν	NUM
ap-1872	314	62	)	)	PUNCT
ap-1872	314	63	]	]	PUNCT
ap-1872	315	1	∂τ2	∂τ2	PROPN
ap-1872	316	1	−	−	PROPN
ap-1872	316	2	6ωτ3∂τ3	6ωτ3∂τ3	NOUN
ap-1872	316	3	.	.	PUNCT
ap-1872	317	1	(	(	PUNCT
ap-1872	317	2	43	43	NUM
ap-1872	317	3	)	)	PUNCT
ap-1872	317	4	these	these	DET
ap-1872	317	5	new	new	ADJ
ap-1872	317	6	coordinates	coordinate	NOUN
ap-1872	317	7	are	be	AUX
ap-1872	317	8	polynomial	polynomial	ADJ
ap-1872	317	9	invariants	invariant	NOUN
ap-1872	317	10	of	of	ADP
ap-1872	317	11	the	the	DET
ap-1872	317	12	a2	a2	PROPN
ap-1872	317	13	weyl	weyl	PROPN
ap-1872	317	14	group	group	NOUN
ap-1872	317	15	.	.	PUNCT
ap-1872	318	1	its	its	PRON
ap-1872	318	2	eigenvalues	eigenvalue	NOUN
ap-1872	318	3	are	be	AUX
ap-1872	318	4	−	−	PROPN
ap-1872	318	5	εp	εp	NOUN
ap-1872	318	6	=	=	NOUN
ap-1872	318	7	2ω(2p1	2ω(2p1	NOUN
ap-1872	318	8	+	+	CCONJ
ap-1872	318	9	3p2	3p2	NUM
ap-1872	318	10	)	)	PUNCT
ap-1872	318	11	,	,	PUNCT
ap-1872	318	12	p1,2	p1,2	PROPN
ap-1872	318	13	=	=	SYM
ap-1872	318	14	0	0	NUM
ap-1872	318	15	,	,	PUNCT
ap-1872	318	16	1	1	NUM
ap-1872	318	17	,	,	PUNCT
ap-1872	318	18	.	.	PUNCT
ap-1872	318	19	.	.	PUNCT
ap-1872	318	20	.	.	PUNCT
ap-1872	318	21	.	.	PUNCT
ap-1872	319	1	(	(	PUNCT
ap-1872	319	2	44	44	NUM
ap-1872	319	3	)	)	PUNCT
ap-1872	319	4	as	as	SCONJ
ap-1872	319	5	is	be	AUX
ap-1872	319	6	shown	show	VERB
ap-1872	319	7	in	in	ADP
ap-1872	319	8	ruhl	ruhl	NOUN
ap-1872	319	9	and	and	CCONJ
ap-1872	319	10	turbiner	turbiner	NOUN
ap-1872	320	1	[	[	X
ap-1872	320	2	5	5	NUM
ap-1872	320	3	]	]	PUNCT
ap-1872	320	4	,	,	PUNCT
ap-1872	320	5	the	the	DET
ap-1872	320	6	operator	operator	NOUN
ap-1872	320	7	(	(	PUNCT
ap-1872	320	8	43	43	NUM
ap-1872	320	9	)	)	PUNCT
ap-1872	320	10	can	can	AUX
ap-1872	320	11	be	be	AUX
ap-1872	320	12	rewritten	rewrite	VERB
ap-1872	320	13	in	in	ADP
ap-1872	320	14	a	a	DET
ap-1872	320	15	lie	lie	NOUN
ap-1872	320	16	-	-	PUNCT
ap-1872	320	17	algebraic	algebraic	ADJ
ap-1872	320	18	form	form	NOUN
ap-1872	320	19	in	in	ADP
ap-1872	320	20	terms	term	NOUN
ap-1872	320	21	of	of	ADP
ap-1872	320	22	gl(3)-algebra	gl(3)-algebra	NOUN
ap-1872	320	23	generators	generator	NOUN
ap-1872	320	24	of	of	ADP
ap-1872	320	25	the	the	DET
ap-1872	320	26	representation	representation	NOUN
ap-1872	320	27	[	[	X
ap-1872	320	28	k	k	X
ap-1872	320	29	,	,	PUNCT
ap-1872	320	30	0	0	NUM
ap-1872	320	31	]	]	PUNCT
ap-1872	320	32	.	.	PUNCT
ap-1872	321	1	the	the	DET
ap-1872	321	2	corresponding	corresponding	ADJ
ap-1872	321	3	expression	expression	NOUN
ap-1872	321	4	is	be	AUX
ap-1872	321	5	hcal	hcal	ADJ
ap-1872	321	6	=	=	SYM
ap-1872	321	7	−2e11	−2e11	PROPN
ap-1872	321	8	t	t	NOUN
ap-1872	321	9	−	−	NUM
ap-1872	321	10	1	1	NUM
ap-1872	321	11	−	−	NOUN
ap-1872	321	12	6e22	6e22	NUM
ap-1872	321	13	t	t	NOUN
ap-1872	321	14	−	−	NOUN
ap-1872	321	15	1	1	NUM
ap-1872	321	16	+	+	SYM
ap-1872	321	17	2	2	NUM
ap-1872	321	18	3e12e12	3e12e12	NOUN
ap-1872	321	19	−	−	NOUN
ap-1872	321	20	4ωe11	4ωe11	INTJ
ap-1872	321	21	−	−	PROPN
ap-1872	321	22	2(1	2(1	NUM
ap-1872	321	23	+	+	CCONJ
ap-1872	321	24	3ν)t−	3ν)t−	NUM
ap-1872	321	25	1	1	NUM
ap-1872	321	26	−	−	NUM
ap-1872	321	27	6ωe22	6ωe22	NUM
ap-1872	321	28	.	.	PUNCT
ap-1872	322	1	(	(	PUNCT
ap-1872	322	2	45	45	NUM
ap-1872	322	3	)	)	PUNCT
ap-1872	322	4	now	now	ADV
ap-1872	322	5	we	we	PRON
ap-1872	322	6	can	can	AUX
ap-1872	322	7	substitute	substitute	VERB
ap-1872	322	8	the	the	DET
ap-1872	322	9	generators	generator	NOUN
ap-1872	322	10	of	of	ADP
ap-1872	322	11	the	the	DET
ap-1872	322	12	representation	representation	NOUN
ap-1872	322	13	[	[	X
ap-1872	322	14	k	k	X
ap-1872	322	15	,	,	PUNCT
ap-1872	322	16	n	n	CCONJ
ap-1872	322	17	]	]	PUNCT
ap-1872	322	18	in	in	ADP
ap-1872	322	19	the	the	DET
ap-1872	322	20	form	form	NOUN
ap-1872	322	21	(	(	PUNCT
ap-1872	322	22	11	11	NUM
ap-1872	322	23	)	)	PUNCT
ap-1872	322	24	h̃cal	h̃cal	ADJ
ap-1872	322	25	=	=	SYM
ap-1872	322	26	−2τ2∂	−2τ2∂	NOUN
ap-1872	322	27	2	2	NUM
ap-1872	322	28	τ2τ2	τ2τ2	PUNCT
ap-1872	322	29	−	−	PROPN
ap-1872	322	30	6τ3∂	6τ3∂	NUM
ap-1872	322	31	2	2	NUM
ap-1872	322	32	τ2τ3	τ2τ3	NOUN
ap-1872	322	33	+	+	NOUN
ap-1872	322	34	2	2	NUM
ap-1872	322	35	3τ	3τ	NUM
ap-1872	322	36	2	2	NUM
ap-1872	322	37	2	2	NUM
ap-1872	322	38	∂	∂	NUM
ap-1872	322	39	2	2	NUM
ap-1872	322	40	τ3τ3	τ3τ3	PUNCT
ap-1872	322	41	−	−	PROPN
ap-1872	322	42	2	2	NUM
ap-1872	322	43	[	[	PUNCT
ap-1872	322	44	2ωτ2	2ωτ2	NUM
ap-1872	322	45	+	+	CCONJ
ap-1872	322	46	(	(	PUNCT
ap-1872	322	47	1	1	NUM
ap-1872	322	48	+	+	NUM
ap-1872	322	49	3ν	3ν	NUM
ap-1872	322	50	)	)	PUNCT
ap-1872	323	1	+	+	CCONJ
ap-1872	323	2	(	(	PUNCT
ap-1872	323	3	n−	n−	NOUN
ap-1872	323	4	2m22	2m22	NUM
ap-1872	323	5	)	)	PUNCT
ap-1872	323	6	]	]	PUNCT
ap-1872	324	1	∂τ2	∂τ2	PROPN
ap-1872	324	2	−	−	PROPN
ap-1872	324	3	(	(	PUNCT
ap-1872	324	4	6ωτ3	6ωτ3	NUM
ap-1872	324	5	−	−	NUM
ap-1872	324	6	4	4	NUM
ap-1872	324	7	3m12τ2	3m12τ2	NUM
ap-1872	324	8	)	)	PUNCT
ap-1872	325	1	∂τ3	∂τ3	NOUN
ap-1872	325	2	+	+	CCONJ
ap-1872	325	3	2	2	NUM
ap-1872	325	4	3m12m12	3m12m12	NOUN
ap-1872	325	5	−	−	PROPN
ap-1872	325	6	4ωn−	4ωn−	NOUN
ap-1872	325	7	2ωm22	2ωm22	PROPN
ap-1872	325	8	.	.	PUNCT
ap-1872	326	1	(	(	PUNCT
ap-1872	326	2	46	46	NUM
ap-1872	326	3	)	)	PUNCT
ap-1872	326	4	this	this	PRON
ap-1872	326	5	is	be	AUX
ap-1872	326	6	an	an	DET
ap-1872	326	7	n×	n×	PROPN
ap-1872	326	8	n	n	NOUN
ap-1872	326	9	matrix	matrix	NOUN
ap-1872	326	10	differential	differential	NOUN
ap-1872	326	11	operator	operator	NOUN
ap-1872	326	12	.	.	PUNCT
ap-1872	327	1	it	it	PRON
ap-1872	327	2	contains	contain	VERB
ap-1872	327	3	infinitely	infinitely	ADV
ap-1872	327	4	many	many	ADJ
ap-1872	327	5	finite	finite	ADJ
ap-1872	327	6	-	-	ADJ
ap-1872	327	7	dimensional	dimensional	ADJ
ap-1872	327	8	invariant	invariant	ADJ
ap-1872	327	9	subspaces	subspace	NOUN
ap-1872	327	10	which	which	PRON
ap-1872	327	11	are	be	AUX
ap-1872	327	12	nothing	nothing	PRON
ap-1872	327	13	but	but	CCONJ
ap-1872	327	14	finite	finite	ADJ
ap-1872	327	15	-	-	ADJ
ap-1872	327	16	dimensional	dimensional	ADJ
ap-1872	327	17	representation	representation	NOUN
ap-1872	327	18	spaces	space	NOUN
ap-1872	327	19	of	of	ADP
ap-1872	327	20	the	the	DET
ap-1872	327	21	algebra	algebra	NOUN
ap-1872	327	22	gl(3	gl(3	VERB
ap-1872	327	23	)	)	PUNCT
ap-1872	327	24	.	.	PUNCT
ap-1872	328	1	this	this	DET
ap-1872	328	2	operator	operator	NOUN
ap-1872	328	3	remains	remain	VERB
ap-1872	328	4	exactly	exactly	ADV
ap-1872	328	5	-	-	PUNCT
ap-1872	328	6	solvable	solvable	ADJ
ap-1872	328	7	with	with	ADP
ap-1872	328	8	the	the	DET
ap-1872	328	9	same	same	ADJ
ap-1872	328	10	spectra	spectra	NOUN
ap-1872	328	11	as	as	ADP
ap-1872	328	12	the	the	DET
ap-1872	328	13	scalar	scalar	ADJ
ap-1872	328	14	calogero	calogero	PROPN
ap-1872	328	15	operator	operator	NOUN
ap-1872	328	16	.	.	PUNCT
ap-1872	329	1	this	this	DET
ap-1872	329	2	operator	operator	NOUN
ap-1872	329	3	probably	probably	ADV
ap-1872	329	4	remains	remain	VERB
ap-1872	329	5	completely	completely	ADV
ap-1872	329	6	integrable	integrable	ADJ
ap-1872	329	7	.	.	PUNCT
ap-1872	330	1	a	a	DET
ap-1872	330	2	higher	high	ADJ
ap-1872	330	3	-	-	PUNCT
ap-1872	330	4	than	than	ADP
ap-1872	330	5	-	-	PUNCT
ap-1872	330	6	second	second	NOUN
ap-1872	330	7	-	-	PUNCT
ap-1872	330	8	order	order	NOUN
ap-1872	330	9	integral	integral	NOUN
ap-1872	330	10	is	be	AUX
ap-1872	330	11	the	the	DET
ap-1872	330	12	differential	differential	ADJ
ap-1872	330	13	operator	operator	NOUN
ap-1872	330	14	of	of	ADP
ap-1872	330	15	the	the	DET
ap-1872	330	16	sixth	sixth	ADJ
ap-1872	330	17	order	order	NOUN
ap-1872	330	18	(	(	PUNCT
ap-1872	330	19	ω	ω	NUM
ap-1872	330	20	6=	6=	NUM
ap-1872	330	21	0	0	NUM
ap-1872	330	22	)	)	PUNCT
ap-1872	330	23	or	or	CCONJ
ap-1872	330	24	of	of	ADP
ap-1872	330	25	the	the	DET
ap-1872	330	26	third	third	ADJ
ap-1872	330	27	order	order	NOUN
ap-1872	330	28	(	(	PUNCT
ap-1872	330	29	ω	ω	NOUN
ap-1872	330	30	=	=	NOUN
ap-1872	330	31	0	0	NUM
ap-1872	330	32	)	)	PUNCT
ap-1872	330	33	,	,	PUNCT
ap-1872	330	34	which	which	PRON
ap-1872	330	35	takes	take	VERB
ap-1872	330	36	an	an	DET
ap-1872	330	37	algebraic	algebraic	ADJ
ap-1872	330	38	form	form	NOUN
ap-1872	330	39	after	after	ADP
ap-1872	330	40	gauging	gauge	VERB
ap-1872	330	41	away	away	ADP
ap-1872	330	42	the	the	DET
ap-1872	330	43	ground	ground	NOUN
ap-1872	330	44	state	state	NOUN
ap-1872	330	45	function	function	NOUN
ap-1872	330	46	in	in	ADP
ap-1872	330	47	τ	τ	PROPN
ap-1872	330	48	coordinates	coordinate	NOUN
ap-1872	330	49	.	.	PUNCT
ap-1872	331	1	it	it	PRON
ap-1872	331	2	can	can	AUX
ap-1872	331	3	be	be	AUX
ap-1872	331	4	rewritten	rewrite	VERB
ap-1872	331	5	in	in	ADP
ap-1872	331	6	terms	term	NOUN
ap-1872	331	7	of	of	ADP
ap-1872	331	8	the	the	DET
ap-1872	331	9	gl(3)algebra	gl(3)algebra	NOUN
ap-1872	331	10	generators	generator	NOUN
ap-1872	331	11	of	of	ADP
ap-1872	331	12	the	the	DET
ap-1872	331	13	representation	representation	NOUN
ap-1872	331	14	[	[	X
ap-1872	331	15	k	k	X
ap-1872	331	16	,	,	PUNCT
ap-1872	331	17	0	0	NUM
ap-1872	331	18	]	]	PUNCT
ap-1872	331	19	,	,	PUNCT
ap-1872	331	20	which	which	PRON
ap-1872	331	21	then	then	ADV
ap-1872	331	22	can	can	AUX
ap-1872	331	23	be	be	AUX
ap-1872	331	24	replaced	replace	VERB
ap-1872	331	25	by	by	ADP
ap-1872	331	26	the	the	DET
ap-1872	331	27	generators	generator	NOUN
ap-1872	331	28	of	of	ADP
ap-1872	331	29	the	the	DET
ap-1872	331	30	representation	representation	NOUN
ap-1872	331	31	[	[	X
ap-1872	331	32	k	k	X
ap-1872	331	33	,	,	PUNCT
ap-1872	331	34	n	n	CCONJ
ap-1872	331	35	]	]	PUNCT
ap-1872	331	36	.	.	PUNCT
ap-1872	332	1	under	under	ADP
ap-1872	332	2	such	such	DET
ap-1872	332	3	a	a	DET
ap-1872	332	4	replacement	replacement	NOUN
ap-1872	332	5	the	the	DET
ap-1872	332	6	spectra	spectra	NOUN
ap-1872	332	7	of	of	ADP
ap-1872	332	8	the	the	DET
ap-1872	332	9	integral	integral	ADJ
ap-1872	332	10	remain	remain	VERB
ap-1872	332	11	unchanged	unchanged	ADJ
ap-1872	332	12	and	and	CCONJ
ap-1872	332	13	algebraic	algebraic	ADJ
ap-1872	332	14	.	.	PUNCT
ap-1872	333	1	6	6	NUM
ap-1872	333	2	.	.	X
ap-1872	333	3	extension	extension	NOUN
ap-1872	333	4	of	of	ADP
ap-1872	333	5	the	the	DET
ap-1872	333	6	3	3	NUM
ap-1872	333	7	-	-	PUNCT
ap-1872	333	8	body	body	NOUN
ap-1872	333	9	sutherland	sutherland	NOUN
ap-1872	333	10	model	model	NOUN
ap-1872	333	11	the	the	DET
ap-1872	333	12	first	first	ADJ
ap-1872	333	13	algebraic	algebraic	ADJ
ap-1872	333	14	form	form	NOUN
ap-1872	333	15	for	for	ADP
ap-1872	333	16	the	the	DET
ap-1872	333	17	3	3	NUM
ap-1872	333	18	-	-	PUNCT
ap-1872	333	19	body	body	NOUN
ap-1872	333	20	sutherland	sutherland	NOUN
ap-1872	333	21	hamiltonian	hamiltonian	NOUN
ap-1872	334	1	[	[	X
ap-1872	334	2	13	13	NUM
ap-1872	334	3	]	]	PUNCT
ap-1872	334	4	appears	appear	VERB
ap-1872	334	5	after	after	ADP
ap-1872	334	6	gauge	gauge	NOUN
ap-1872	334	7	rotation	rotation	NOUN
ap-1872	334	8	with	with	ADP
ap-1872	334	9	the	the	DET
ap-1872	334	10	ground	ground	NOUN
ap-1872	334	11	state	state	NOUN
ap-1872	334	12	function	function	NOUN
ap-1872	334	13	,	,	PUNCT
ap-1872	334	14	separation	separation	NOUN
ap-1872	334	15	of	of	ADP
ap-1872	334	16	the	the	DET
ap-1872	334	17	center	center	NOUN
ap-1872	334	18	-	-	PUNCT
ap-1872	334	19	of	of	ADP
ap-1872	334	20	-	-	PUNCT
ap-1872	334	21	mass	mass	NOUN
ap-1872	334	22	and	and	CCONJ
ap-1872	334	23	changing	change	VERB
ap-1872	334	24	the	the	DET
ap-1872	334	25	variables	variable	NOUN
ap-1872	334	26	to	to	ADP
ap-1872	334	27	elementary	elementary	ADJ
ap-1872	334	28	symmetric	symmetric	ADJ
ap-1872	334	29	polynomials	polynomial	NOUN
ap-1872	334	30	of	of	ADP
ap-1872	334	31	the	the	DET
ap-1872	334	32	exponentials	exponential	NOUN
ap-1872	334	33	of	of	ADP
ap-1872	334	34	translationallysymmetric	translationallysymmetric	ADJ
ap-1872	334	35	coordinates	coordinate	NOUN
ap-1872	334	36	[	[	X
ap-1872	334	37	5	5	NUM
ap-1872	334	38	]	]	PUNCT
ap-1872	334	39	,	,	PUNCT
ap-1872	334	40	hsuth	hsuth	NOUN
ap-1872	334	41	=	=	SYM
ap-1872	334	42	−	−	PROPN
ap-1872	334	43	(	(	PUNCT
ap-1872	334	44	2η2	2η2	NUM
ap-1872	334	45	+	+	CCONJ
ap-1872	334	46	α2	α2	ADJ
ap-1872	334	47	2	2	NUM
ap-1872	334	48	η2	η2	VERB
ap-1872	334	49	2	2	NUM
ap-1872	334	50	−	−	NOUN
ap-1872	334	51	α4	α4	NOUN
ap-1872	334	52	24	24	NUM
ap-1872	334	53	η	η	PROPN
ap-1872	334	54	2	2	NUM
ap-1872	334	55	3	3	NUM
ap-1872	334	56	)	)	PUNCT
ap-1872	334	57	∂2	∂2	NOUN
ap-1872	334	58	η2η2	η2η2	X
ap-1872	334	59	−	−	NOUN
ap-1872	334	60	(	(	PUNCT
ap-1872	334	61	6	6	NUM
ap-1872	334	62	+	+	NUM
ap-1872	334	63	4α2	4α2	NUM
ap-1872	334	64	3	3	NUM
ap-1872	334	65	η2	η2	PROPN
ap-1872	334	66	)	)	PUNCT
ap-1872	334	67	η3∂	η3∂	PROPN
ap-1872	334	68	2	2	NUM
ap-1872	334	69	η2η3	η2η3	NOUN
ap-1872	334	70	+	+	X
ap-1872	334	71	(	(	PUNCT
ap-1872	334	72	2	2	NUM
ap-1872	334	73	3η	3η	NUM
ap-1872	334	74	2	2	NUM
ap-1872	334	75	2	2	NUM
ap-1872	334	76	−	−	NOUN
ap-1872	334	77	α2	α2	ADJ
ap-1872	334	78	2	2	NUM
ap-1872	334	79	η2	η2	ADJ
ap-1872	334	80	3	3	NUM
ap-1872	334	81	)	)	PUNCT
ap-1872	334	82	∂2	∂2	NOUN
ap-1872	334	83	η3η3	η3η3	NOUN
ap-1872	334	84	−	−	NOUN
ap-1872	334	85	[	[	PUNCT
ap-1872	334	86	2(1	2(1	NUM
ap-1872	334	87	+	+	NOUN
ap-1872	334	88	3ν)+2	3ν)+2	NUM
ap-1872	334	89	(	(	PUNCT
ap-1872	334	90	ν+	ν+	NOUN
ap-1872	334	91	1	1	NUM
ap-1872	334	92	3	3	NUM
ap-1872	334	93	)	)	PUNCT
ap-1872	334	94	α2η2	α2η2	X
ap-1872	334	95	]	]	PUNCT
ap-1872	334	96	∂η2−2	∂η2−2	X
ap-1872	334	97	(	(	PUNCT
ap-1872	334	98	ν+	ν+	NOUN
ap-1872	334	99	1	1	NUM
ap-1872	334	100	3	3	NUM
ap-1872	334	101	)	)	PUNCT
ap-1872	334	102	α2η3∂η3	α2η3∂η3	X
ap-1872	334	103	,	,	PUNCT
ap-1872	334	104	(	(	PUNCT
ap-1872	334	105	47	47	NUM
ap-1872	334	106	)	)	PUNCT
ap-1872	334	107	where	where	SCONJ
ap-1872	334	108	α	α	NOUN
ap-1872	334	109	is	be	AUX
ap-1872	334	110	the	the	DET
ap-1872	334	111	inverse	inverse	ADJ
ap-1872	334	112	radius	radius	NOUN
ap-1872	334	113	of	of	ADP
ap-1872	334	114	the	the	DET
ap-1872	334	115	circle	circle	NOUN
ap-1872	334	116	on	on	ADP
ap-1872	334	117	which	which	PRON
ap-1872	334	118	the	the	DET
ap-1872	334	119	bodies	body	NOUN
ap-1872	334	120	are	be	AUX
ap-1872	334	121	situated	situate	VERB
ap-1872	334	122	.	.	PUNCT
ap-1872	335	1	these	these	DET
ap-1872	335	2	new	new	ADJ
ap-1872	335	3	coordinates	coordinate	NOUN
ap-1872	335	4	are	be	AUX
ap-1872	335	5	fundamental	fundamental	ADJ
ap-1872	335	6	trigonometric	trigonometric	ADJ
ap-1872	335	7	invariants	invariant	NOUN
ap-1872	335	8	of	of	ADP
ap-1872	335	9	the	the	DET
ap-1872	335	10	a2	a2	PROPN
ap-1872	335	11	weyl	weyl	PROPN
ap-1872	335	12	group	group	NOUN
ap-1872	335	13	.	.	PUNCT
ap-1872	336	1	as	as	SCONJ
ap-1872	336	2	shown	show	VERB
ap-1872	336	3	in	in	ADP
ap-1872	336	4	[	[	X
ap-1872	336	5	5	5	NUM
ap-1872	336	6	]	]	PUNCT
ap-1872	336	7	,	,	PUNCT
ap-1872	336	8	operator	operator	NOUN
ap-1872	336	9	(	(	PUNCT
ap-1872	336	10	47	47	NUM
ap-1872	336	11	)	)	PUNCT
ap-1872	336	12	can	can	AUX
ap-1872	336	13	be	be	AUX
ap-1872	336	14	rewritten	rewrite	VERB
ap-1872	336	15	in	in	ADP
ap-1872	336	16	a	a	DET
ap-1872	336	17	lie	lie	NOUN
ap-1872	336	18	-	-	PUNCT
ap-1872	336	19	algebraic	algebraic	ADJ
ap-1872	336	20	form	form	NOUN
ap-1872	336	21	in	in	ADP
ap-1872	336	22	terms	term	NOUN
ap-1872	336	23	of	of	ADP
ap-1872	336	24	the	the	DET
ap-1872	336	25	gl(3)-algebra	gl(3)-algebra	ADJ
ap-1872	336	26	generators	generator	NOUN
ap-1872	336	27	of	of	ADP
ap-1872	336	28	the	the	DET
ap-1872	336	29	representation	representation	NOUN
ap-1872	336	30	[	[	X
ap-1872	336	31	k	k	X
ap-1872	336	32	,	,	PUNCT
ap-1872	336	33	0	0	NUM
ap-1872	336	34	]	]	PUNCT
ap-1872	336	35	,	,	PUNCT
ap-1872	336	36	hsuth	hsuth	NOUN
ap-1872	336	37	=	=	SYM
ap-1872	336	38	−2e11	−2e11	PROPN
ap-1872	336	39	t	t	NOUN
ap-1872	336	40	−	−	NUM
ap-1872	336	41	1	1	NUM
ap-1872	336	42	−	−	NOUN
ap-1872	336	43	6e22	6e22	NUM
ap-1872	336	44	t	t	NOUN
ap-1872	336	45	−	−	NOUN
ap-1872	336	46	1	1	NUM
ap-1872	336	47	+	+	SYM
ap-1872	336	48	2	2	NUM
ap-1872	336	49	3e12e12	3e12e12	NOUN
ap-1872	336	50	−2(1	−2(1	NOUN
ap-1872	337	1	+	+	ADP
ap-1872	337	2	3ν)t−	3ν)t−	NUM
ap-1872	337	3	1	1	NUM
ap-1872	337	4	+	+	NUM
ap-1872	337	5	α4	α4	NOUN
ap-1872	337	6	24e21e21−	24e21e21−	NUM
ap-1872	337	7	α2	α2	NOUN
ap-1872	337	8	6	6	NUM
ap-1872	337	9	[	[	PUNCT
ap-1872	337	10	3e11e11	3e11e11	ADJ
ap-1872	337	11	+8e11e22	+8e11e22	NOUN
ap-1872	337	12	+	+	CCONJ
ap-1872	337	13	3e22e22	3e22e22	NOUN
ap-1872	337	14	+	+	CCONJ
ap-1872	337	15	(	(	PUNCT
ap-1872	337	16	1	1	NUM
ap-1872	337	17	+	+	SYM
ap-1872	337	18	12ν)(e11	12ν)(e11	NUM
ap-1872	337	19	+	+	SYM
ap-1872	337	20	e22	e22	NOUN
ap-1872	337	21	)	)	PUNCT
ap-1872	337	22	]	]	PUNCT
ap-1872	337	23	.	.	PUNCT
ap-1872	338	1	(	(	PUNCT
ap-1872	338	2	48	48	NUM
ap-1872	338	3	)	)	PUNCT
ap-1872	338	4	now	now	ADV
ap-1872	338	5	we	we	PRON
ap-1872	338	6	can	can	AUX
ap-1872	338	7	substitute	substitute	VERB
ap-1872	338	8	the	the	DET
ap-1872	338	9	generators	generator	NOUN
ap-1872	338	10	of	of	ADP
ap-1872	338	11	the	the	DET
ap-1872	338	12	representation	representation	NOUN
ap-1872	338	13	[	[	X
ap-1872	338	14	k	k	X
ap-1872	338	15	,	,	PUNCT
ap-1872	338	16	n	n	CCONJ
ap-1872	338	17	]	]	PUNCT
ap-1872	338	18	in	in	ADP
ap-1872	338	19	the	the	DET
ap-1872	338	20	form	form	NOUN
ap-1872	338	21	(	(	PUNCT
ap-1872	338	22	11	11	NUM
ap-1872	338	23	)	)	PUNCT
ap-1872	338	24	h̃suth	h̃suth	NOUN
ap-1872	338	25	=	=	PUNCT
ap-1872	339	1	−	−	PROPN
ap-1872	339	2	(	(	PUNCT
ap-1872	339	3	2η2	2η2	NUM
ap-1872	339	4	+	+	CCONJ
ap-1872	339	5	α2	α2	ADJ
ap-1872	339	6	2	2	NUM
ap-1872	339	7	η2	η2	VERB
ap-1872	339	8	2	2	NUM
ap-1872	339	9	−	−	NOUN
ap-1872	339	10	α4	α4	NOUN
ap-1872	339	11	24	24	NUM
ap-1872	339	12	η	η	PROPN
ap-1872	339	13	2	2	NUM
ap-1872	339	14	3	3	NUM
ap-1872	339	15	)	)	PUNCT
ap-1872	339	16	∂2	∂2	NOUN
ap-1872	339	17	η2η2	η2η2	X
ap-1872	339	18	−	−	NOUN
ap-1872	340	1	(	(	PUNCT
ap-1872	341	1	6	6	NUM
ap-1872	341	2	+	+	NUM
ap-1872	341	3	4α2	4α2	NUM
ap-1872	341	4	3	3	NUM
ap-1872	341	5	η2	η2	PROPN
ap-1872	341	6	)	)	PUNCT
ap-1872	341	7	η3∂	η3∂	PROPN
ap-1872	341	8	2	2	NUM
ap-1872	341	9	η2η3	η2η3	NOUN
ap-1872	341	10	+	+	X
ap-1872	341	11	(	(	PUNCT
ap-1872	341	12	2	2	NUM
ap-1872	341	13	3η	3η	NUM
ap-1872	341	14	2	2	NUM
ap-1872	341	15	2	2	NUM
ap-1872	341	16	−	−	NOUN
ap-1872	341	17	α2	α2	ADJ
ap-1872	341	18	2	2	NUM
ap-1872	341	19	η2	η2	ADJ
ap-1872	341	20	3	3	NUM
ap-1872	341	21	)	)	PUNCT
ap-1872	341	22	∂2	∂2	NOUN
ap-1872	341	23	η3η3	η3η3	NOUN
ap-1872	341	24	−	−	PROPN
ap-1872	341	25	2	2	NUM
ap-1872	341	26	[	[	PUNCT
ap-1872	341	27	(	(	PUNCT
ap-1872	341	28	1	1	NUM
ap-1872	341	29	+	+	NUM
ap-1872	341	30	3ν	3ν	NUM
ap-1872	341	31	)	)	PUNCT
ap-1872	342	1	+	+	CCONJ
ap-1872	342	2	(	(	PUNCT
ap-1872	342	3	ν	ν	X
ap-1872	342	4	+	+	NOUN
ap-1872	342	5	1	1	NUM
ap-1872	342	6	3	3	NUM
ap-1872	342	7	)	)	PUNCT
ap-1872	342	8	α2η2	α2η2	X
ap-1872	343	1	+	+	CCONJ
ap-1872	343	2	(	(	PUNCT
ap-1872	343	3	n−	n−	NOUN
ap-1872	343	4	2m22	2m22	NUM
ap-1872	343	5	)	)	PUNCT
ap-1872	343	6	]	]	PUNCT
ap-1872	344	1	∂η2	∂η2	VERB
ap-1872	344	2	+	+	CCONJ
ap-1872	344	3	α4	α4	NOUN
ap-1872	344	4	24m21η3∂η2	24m21η3∂η2	NUM
ap-1872	344	5	+	+	CCONJ
ap-1872	344	6	[	[	PUNCT
ap-1872	344	7	2	2	NUM
ap-1872	344	8	(	(	PUNCT
ap-1872	344	9	ν	ν	NOUN
ap-1872	344	10	+	+	NOUN
ap-1872	344	11	1	1	NUM
ap-1872	344	12	3	3	NUM
ap-1872	344	13	)	)	PUNCT
ap-1872	344	14	α2η3	α2η3	NOUN
ap-1872	344	15	−	−	ADP
ap-1872	344	16	4	4	NUM
ap-1872	344	17	3m12η2	3m12η2	PROPN
ap-1872	344	18	]	]	PUNCT
ap-1872	344	19	∂η3	∂η3	PROPN
ap-1872	344	20	−	−	NUM
ap-1872	344	21	α2	α2	ADJ
ap-1872	344	22	3	3	NUM
ap-1872	344	23	[	[	PUNCT
ap-1872	344	24	3n(η2∂η2	3n(η2∂η2	NUM
ap-1872	344	25	+	+	CCONJ
ap-1872	344	26	η3∂η3	η3∂η3	PROPN
ap-1872	344	27	)	)	PUNCT
ap-1872	345	1	+	+	NOUN
ap-1872	345	2	m11η3∂η3	m11η3∂η3	NOUN
ap-1872	345	3	+	+	NOUN
ap-1872	345	4	m22η2∂η2	m22η2∂η2	NOUN
ap-1872	345	5	]	]	X
ap-1872	345	6	+	+	CCONJ
ap-1872	345	7	2	2	NUM
ap-1872	345	8	3m12m12	3m12m12	NOUN
ap-1872	345	9	+	+	NUM
ap-1872	345	10	α4	α4	NOUN
ap-1872	345	11	24m21m21	24m21m21	NOUN
ap-1872	345	12	−	−	PROPN
ap-1872	345	13	α2	α2	ADJ
ap-1872	345	14	6	6	NUM
ap-1872	345	15	[	[	PUNCT
ap-1872	345	16	2m11m22	2m11m22	NOUN
ap-1872	345	17	+	+	CCONJ
ap-1872	345	18	(	(	PUNCT
ap-1872	345	19	1	1	NUM
ap-1872	345	20	+	+	NUM
ap-1872	345	21	12ν	12ν	NOUN
ap-1872	345	22	+	+	X
ap-1872	345	23	3n)n	3n)n	NUM
ap-1872	345	24	]	]	PUNCT
ap-1872	345	25	.	.	PUNCT
ap-1872	346	1	(	(	PUNCT
ap-1872	346	2	49	49	NUM
ap-1872	346	3	)	)	PUNCT
ap-1872	346	4	468	468	NUM
ap-1872	346	5	vol	vol	NOUN
ap-1872	346	6	.	.	PUNCT
ap-1872	347	1	53	53	NUM
ap-1872	347	2	no	no	NOUN
ap-1872	347	3	.	.	PUNCT
ap-1872	348	1	5/2013	5/2013	NUM
ap-1872	348	2	gln+1	gln+1	VERB
ap-1872	348	3	algebra	algebra	NOUN
ap-1872	348	4	of	of	ADP
ap-1872	348	5	matrix	matrix	NOUN
ap-1872	348	6	differential	differential	NOUN
ap-1872	348	7	operators	operator	NOUN
ap-1872	348	8	this	this	PRON
ap-1872	348	9	is	be	AUX
ap-1872	348	10	an	an	DET
ap-1872	348	11	n×	n×	PROPN
ap-1872	348	12	n	n	NOUN
ap-1872	348	13	matrix	matrix	NOUN
ap-1872	348	14	differential	differential	NOUN
ap-1872	348	15	operator	operator	NOUN
ap-1872	348	16	.	.	PUNCT
ap-1872	349	1	it	it	PRON
ap-1872	349	2	contains	contain	VERB
ap-1872	349	3	infinitely	infinitely	ADV
ap-1872	349	4	-	-	PUNCT
ap-1872	349	5	many	many	ADJ
ap-1872	349	6	finite	finite	ADJ
ap-1872	349	7	-	-	ADJ
ap-1872	349	8	dimensional	dimensional	ADJ
ap-1872	349	9	invariant	invariant	ADJ
ap-1872	349	10	subspaces	subspace	NOUN
ap-1872	349	11	which	which	PRON
ap-1872	349	12	are	be	AUX
ap-1872	349	13	nothing	nothing	PRON
ap-1872	349	14	but	but	CCONJ
ap-1872	349	15	finite	finite	ADJ
ap-1872	349	16	-	-	ADJ
ap-1872	349	17	dimensional	dimensional	ADJ
ap-1872	349	18	representation	representation	NOUN
ap-1872	349	19	spaces	space	NOUN
ap-1872	349	20	of	of	ADP
ap-1872	349	21	the	the	DET
ap-1872	349	22	algebra	algebra	NOUN
ap-1872	349	23	gl(3	gl(3	VERB
ap-1872	349	24	)	)	PUNCT
ap-1872	349	25	.	.	PUNCT
ap-1872	350	1	this	this	DET
ap-1872	350	2	operator	operator	NOUN
ap-1872	350	3	remains	remain	VERB
ap-1872	350	4	exactly	exactly	ADV
ap-1872	350	5	-	-	PUNCT
ap-1872	350	6	solvable	solvable	ADJ
ap-1872	350	7	with	with	ADP
ap-1872	350	8	the	the	DET
ap-1872	350	9	same	same	ADJ
ap-1872	350	10	spectra	spectra	NOUN
ap-1872	350	11	as	as	ADP
ap-1872	350	12	the	the	DET
ap-1872	350	13	scalar	scalar	ADJ
ap-1872	350	14	sutherland	sutherland	NOUN
ap-1872	350	15	operator	operator	NOUN
ap-1872	350	16	.	.	PUNCT
ap-1872	351	1	the	the	DET
ap-1872	351	2	operator	operator	NOUN
ap-1872	351	3	(	(	PUNCT
ap-1872	351	4	49	49	NUM
ap-1872	351	5	)	)	PUNCT
ap-1872	351	6	probably	probably	ADV
ap-1872	351	7	remains	remain	VERB
ap-1872	351	8	completely	completely	ADV
ap-1872	351	9	integrable	integrable	ADJ
ap-1872	351	10	.	.	PUNCT
ap-1872	352	1	a	a	DET
ap-1872	352	2	non	non	ADJ
ap-1872	352	3	-	-	ADJ
ap-1872	352	4	trivial	trivial	ADJ
ap-1872	352	5	integral	integral	NOUN
ap-1872	352	6	is	be	AUX
ap-1872	352	7	the	the	DET
ap-1872	352	8	differential	differential	ADJ
ap-1872	352	9	operator	operator	NOUN
ap-1872	352	10	of	of	ADP
ap-1872	352	11	the	the	DET
ap-1872	352	12	third	third	ADJ
ap-1872	352	13	order	order	NOUN
ap-1872	352	14	,	,	PUNCT
ap-1872	352	15	it	it	PRON
ap-1872	352	16	takes	take	VERB
ap-1872	352	17	the	the	DET
ap-1872	352	18	algebraic	algebraic	ADJ
ap-1872	352	19	form	form	NOUN
ap-1872	352	20	after	after	ADP
ap-1872	352	21	gauging	gauge	VERB
ap-1872	352	22	away	away	ADP
ap-1872	352	23	the	the	DET
ap-1872	352	24	ground	ground	NOUN
ap-1872	352	25	state	state	NOUN
ap-1872	352	26	function	function	NOUN
ap-1872	352	27	in	in	ADP
ap-1872	352	28	η	η	PROPN
ap-1872	352	29	coordinates	coordinate	NOUN
ap-1872	352	30	.	.	PUNCT
ap-1872	353	1	it	it	PRON
ap-1872	353	2	can	can	AUX
ap-1872	353	3	be	be	AUX
ap-1872	353	4	rewritten	rewrite	VERB
ap-1872	353	5	in	in	ADP
ap-1872	353	6	terms	term	NOUN
ap-1872	353	7	of	of	ADP
ap-1872	353	8	the	the	DET
ap-1872	353	9	gl(3)algebra	gl(3)algebra	NOUN
ap-1872	353	10	generators	generator	NOUN
ap-1872	353	11	of	of	ADP
ap-1872	353	12	the	the	DET
ap-1872	353	13	representation	representation	NOUN
ap-1872	353	14	[	[	X
ap-1872	353	15	k	k	X
ap-1872	353	16	,	,	PUNCT
ap-1872	353	17	0	0	NUM
ap-1872	353	18	]	]	PUNCT
ap-1872	353	19	,	,	PUNCT
ap-1872	353	20	which	which	PRON
ap-1872	353	21	then	then	ADV
ap-1872	353	22	can	can	AUX
ap-1872	353	23	be	be	AUX
ap-1872	353	24	replaced	replace	VERB
ap-1872	353	25	by	by	ADP
ap-1872	353	26	the	the	DET
ap-1872	353	27	generators	generator	NOUN
ap-1872	353	28	of	of	ADP
ap-1872	353	29	the	the	DET
ap-1872	353	30	representation	representation	NOUN
ap-1872	353	31	[	[	X
ap-1872	353	32	k	k	X
ap-1872	353	33	,	,	PUNCT
ap-1872	353	34	n	n	CCONJ
ap-1872	353	35	]	]	PUNCT
ap-1872	353	36	.	.	PUNCT
ap-1872	354	1	under	under	ADP
ap-1872	354	2	such	such	DET
ap-1872	354	3	a	a	DET
ap-1872	354	4	replacement	replacement	NOUN
ap-1872	354	5	the	the	DET
ap-1872	354	6	spectra	spectra	NOUN
ap-1872	354	7	of	of	ADP
ap-1872	354	8	the	the	DET
ap-1872	354	9	integral	integral	ADJ
ap-1872	354	10	remain	remain	VERB
ap-1872	354	11	unchanged	unchanged	ADJ
ap-1872	354	12	and	and	CCONJ
ap-1872	354	13	algebraic	algebraic	ADJ
ap-1872	354	14	.	.	PUNCT
ap-1872	355	1	7	7	X
ap-1872	355	2	.	.	X
ap-1872	355	3	conclusions	conclusion	NOUN
ap-1872	355	4	the	the	DET
ap-1872	355	5	algebra	algebra	PROPN
ap-1872	355	6	gln	gln	NOUN
ap-1872	355	7	of	of	ADP
ap-1872	355	8	differential	differential	NOUN
ap-1872	355	9	operators	operator	NOUN
ap-1872	355	10	plays	play	VERB
ap-1872	355	11	the	the	DET
ap-1872	355	12	role	role	NOUN
ap-1872	355	13	of	of	ADP
ap-1872	355	14	a	a	DET
ap-1872	355	15	hidden	hide	VERB
ap-1872	355	16	algebra	algebra	NOUN
ap-1872	355	17	for	for	ADP
ap-1872	355	18	all	all	DET
ap-1872	355	19	an	an	DET
ap-1872	355	20	,	,	PUNCT
ap-1872	355	21	bn	bn	NOUN
ap-1872	355	22	,	,	PUNCT
ap-1872	355	23	cn	cn	PROPN
ap-1872	355	24	,	,	PUNCT
ap-1872	355	25	dn	dn	PROPN
ap-1872	355	26	,	,	PUNCT
ap-1872	355	27	bcn	bcn	PROPN
ap-1872	355	28	calogero	calogero	PROPN
ap-1872	355	29	-	-	PUNCT
ap-1872	355	30	moser	moser	PROPN
ap-1872	355	31	hamiltonians	hamiltonians	PROPN
ap-1872	355	32	,	,	PUNCT
ap-1872	355	33	both	both	PRON
ap-1872	355	34	rational	rational	ADJ
ap-1872	355	35	and	and	CCONJ
ap-1872	355	36	trigonometric	trigonometric	ADJ
ap-1872	355	37	,	,	PUNCT
ap-1872	355	38	with	with	SCONJ
ap-1872	355	39	the	the	DET
ap-1872	355	40	weyl	weyl	VERB
ap-1872	355	41	symmetry	symmetry	NOUN
ap-1872	355	42	of	of	ADP
ap-1872	355	43	classical	classical	ADJ
ap-1872	355	44	root	root	NOUN
ap-1872	355	45	spaces	space	NOUN
ap-1872	355	46	(	(	PUNCT
ap-1872	355	47	see	see	VERB
ap-1872	355	48	[	[	X
ap-1872	355	49	14	14	NUM
ap-1872	355	50	]	]	PUNCT
ap-1872	355	51	and	and	CCONJ
ap-1872	355	52	references	reference	NOUN
ap-1872	355	53	therein	therein	ADV
ap-1872	355	54	)	)	PUNCT
ap-1872	355	55	.	.	PUNCT
ap-1872	356	1	we	we	PRON
ap-1872	356	2	have	have	AUX
ap-1872	356	3	described	describe	VERB
ap-1872	356	4	a	a	DET
ap-1872	356	5	procedure	procedure	NOUN
ap-1872	356	6	which	which	PRON
ap-1872	356	7	,	,	PUNCT
ap-1872	356	8	in	in	ADP
ap-1872	356	9	our	our	PRON
ap-1872	356	10	opinion	opinion	NOUN
ap-1872	356	11	,	,	PUNCT
ap-1872	356	12	should	should	AUX
ap-1872	356	13	carry	carry	VERB
ap-1872	356	14	the	the	DET
ap-1872	356	15	name	name	NOUN
ap-1872	356	16	of	of	ADP
ap-1872	356	17	the	the	DET
ap-1872	356	18	havlicek	havlicek	NOUN
ap-1872	356	19	procedure	procedure	NOUN
ap-1872	356	20	,	,	PUNCT
ap-1872	356	21	to	to	PART
ap-1872	356	22	construct	construct	VERB
ap-1872	356	23	the	the	DET
ap-1872	356	24	algebra	algebra	PROPN
ap-1872	356	25	gln	gln	NOUN
ap-1872	356	26	of	of	ADP
ap-1872	356	27	the	the	DET
ap-1872	356	28	matrix	matrix	NOUN
ap-1872	356	29	differential	differential	NOUN
ap-1872	356	30	operators	operator	NOUN
ap-1872	356	31	.	.	PUNCT
ap-1872	357	1	the	the	DET
ap-1872	357	2	procedure	procedure	NOUN
ap-1872	357	3	is	be	AUX
ap-1872	357	4	based	base	VERB
ap-1872	357	5	on	on	ADP
ap-1872	357	6	a	a	DET
ap-1872	357	7	mixed	mixed	ADJ
ap-1872	357	8	,	,	PUNCT
ap-1872	357	9	matrix	matrix	NOUN
ap-1872	357	10	-	-	PUNCT
ap-1872	357	11	differential	differential	NOUN
ap-1872	357	12	operator	operator	NOUN
ap-1872	357	13	realization	realization	NOUN
ap-1872	357	14	of	of	ADP
ap-1872	357	15	the	the	DET
ap-1872	357	16	gauss	gauss	ADJ
ap-1872	357	17	decomposition	decomposition	NOUN
ap-1872	357	18	diagram	diagram	NOUN
ap-1872	357	19	.	.	PUNCT
ap-1872	358	1	as	as	ADP
ap-1872	358	2	for	for	ADP
ap-1872	358	3	hamiltonian	hamiltonian	ADJ
ap-1872	358	4	reduction	reduction	NOUN
ap-1872	358	5	models	model	NOUN
ap-1872	358	6	with	with	ADP
ap-1872	358	7	the	the	DET
ap-1872	358	8	exceptional	exceptional	ADJ
ap-1872	358	9	weyl	weyl	VERB
ap-1872	358	10	symmetry	symmetry	NOUN
ap-1872	358	11	group	group	NOUN
ap-1872	358	12	g2	g2	PROPN
ap-1872	358	13	,	,	PUNCT
ap-1872	358	14	f4	f4	PROPN
ap-1872	358	15	,	,	PUNCT
ap-1872	358	16	e6,7,8	e6,7,8	PROPN
ap-1872	358	17	,	,	PUNCT
ap-1872	358	18	both	both	PRON
ap-1872	358	19	rational	rational	ADJ
ap-1872	358	20	and	and	CCONJ
ap-1872	358	21	trigonometric	trigonometric	ADJ
ap-1872	358	22	,	,	PUNCT
ap-1872	358	23	there	there	PRON
ap-1872	358	24	exist	exist	VERB
ap-1872	358	25	hidden	hidden	ADJ
ap-1872	358	26	algebras	algebra	NOUN
ap-1872	358	27	of	of	ADP
ap-1872	358	28	differential	differential	ADJ
ap-1872	358	29	operators	operator	NOUN
ap-1872	358	30	(	(	PUNCT
ap-1872	358	31	see	see	VERB
ap-1872	358	32	[	[	X
ap-1872	358	33	14	14	NUM
ap-1872	358	34	]	]	PUNCT
ap-1872	358	35	and	and	CCONJ
ap-1872	358	36	references	reference	NOUN
ap-1872	358	37	therein	therein	ADV
ap-1872	358	38	)	)	PUNCT
ap-1872	358	39	.	.	PUNCT
ap-1872	359	1	all	all	DET
ap-1872	359	2	these	these	DET
ap-1872	359	3	algebras	algebra	NOUN
ap-1872	359	4	are	be	AUX
ap-1872	359	5	infinite	infinite	ADJ
ap-1872	359	6	-	-	PUNCT
ap-1872	359	7	dimensional	dimensional	ADJ
ap-1872	359	8	but	but	CCONJ
ap-1872	359	9	finitely	finitely	ADV
ap-1872	359	10	-	-	PUNCT
ap-1872	359	11	generated	generate	VERB
ap-1872	359	12	.	.	PUNCT
ap-1872	360	1	for	for	ADP
ap-1872	360	2	generating	generate	VERB
ap-1872	360	3	elements	element	NOUN
ap-1872	360	4	of	of	ADP
ap-1872	360	5	these	these	DET
ap-1872	360	6	algebras	algebra	NOUN
ap-1872	360	7	an	an	DET
ap-1872	360	8	analogue	analogue	NOUN
ap-1872	360	9	of	of	ADP
ap-1872	360	10	the	the	DET
ap-1872	360	11	weyl	weyl	VERB
ap-1872	360	12	-	-	ADJ
ap-1872	360	13	cartan	cartan	ADJ
ap-1872	360	14	decomposition	decomposition	NOUN
ap-1872	360	15	exists	exist	VERB
ap-1872	360	16	but	but	CCONJ
ap-1872	360	17	in	in	ADP
ap-1872	360	18	the	the	DET
ap-1872	360	19	gauss	gauss	ADJ
ap-1872	360	20	decomposition	decomposition	NOUN
ap-1872	360	21	diagram	diagram	NOUN
ap-1872	360	22	,	,	PUNCT
ap-1872	360	23	a	a	DET
ap-1872	360	24	commutator	commutator	NOUN
ap-1872	360	25	of	of	ADP
ap-1872	360	26	the	the	DET
ap-1872	360	27	lowering	lowering	NOUN
ap-1872	360	28	and	and	CCONJ
ap-1872	360	29	raising	raise	VERB
ap-1872	360	30	generators	generator	NOUN
ap-1872	360	31	is	be	AUX
ap-1872	360	32	a	a	DET
ap-1872	360	33	polynomial	polynomial	NOUN
ap-1872	360	34	of	of	ADP
ap-1872	360	35	the	the	DET
ap-1872	360	36	higher	high	ADJ
ap-1872	360	37	-	-	PUNCT
ap-1872	360	38	than	than	ADP
ap-1872	360	39	-	-	PUNCT
ap-1872	360	40	one	one	NUM
ap-1872	360	41	order	order	NOUN
ap-1872	360	42	in	in	ADP
ap-1872	360	43	the	the	DET
ap-1872	360	44	cartan	cartan	ADJ
ap-1872	360	45	generators	generator	NOUN
ap-1872	360	46	.	.	PUNCT
ap-1872	361	1	matrix	matrix	NOUN
ap-1872	361	2	realizations	realization	NOUN
ap-1872	361	3	of	of	ADP
ap-1872	361	4	these	these	DET
ap-1872	361	5	algebras	algebra	NOUN
ap-1872	361	6	surely	surely	ADV
ap-1872	361	7	exist	exist	VERB
ap-1872	361	8	.	.	PUNCT
ap-1872	362	1	thus	thus	ADV
ap-1872	362	2	,	,	PUNCT
ap-1872	362	3	the	the	DET
ap-1872	362	4	above	above	ADV
ap-1872	362	5	mentioned	mention	VERB
ap-1872	362	6	procedure	procedure	NOUN
ap-1872	362	7	for	for	ADP
ap-1872	362	8	building	build	VERB
ap-1872	362	9	the	the	DET
ap-1872	362	10	mixed	mix	VERB
ap-1872	362	11	representations	representation	NOUN
ap-1872	362	12	can	can	AUX
ap-1872	362	13	be	be	AUX
ap-1872	362	14	realized	realize	VERB
ap-1872	362	15	.	.	PUNCT
ap-1872	363	1	it	it	PRON
ap-1872	363	2	may	may	AUX
ap-1872	363	3	lead	lead	VERB
ap-1872	363	4	to	to	ADP
ap-1872	363	5	a	a	DET
ap-1872	363	6	new	new	ADJ
ap-1872	363	7	class	class	NOUN
ap-1872	363	8	of	of	ADP
ap-1872	363	9	matrix	matrix	NOUN
ap-1872	363	10	exactly	exactly	ADV
ap-1872	363	11	-	-	PUNCT
ap-1872	363	12	solvable	solvable	ADJ
ap-1872	363	13	models	model	NOUN
ap-1872	363	14	with	with	ADP
ap-1872	363	15	exceptional	exceptional	ADJ
ap-1872	363	16	weyl	weyl	VERB
ap-1872	363	17	symmetry	symmetry	NOUN
ap-1872	363	18	.	.	PUNCT
ap-1872	364	1	acknowledgements	acknowledgement	NOUN
ap-1872	364	2	it	it	PRON
ap-1872	364	3	was	be	AUX
ap-1872	364	4	planned	plan	VERB
ap-1872	364	5	long	long	ADV
ap-1872	364	6	ago	ago	ADV
ap-1872	364	7	to	to	PART
ap-1872	364	8	dedicate	dedicate	VERB
ap-1872	364	9	this	this	DET
ap-1872	364	10	text	text	NOUN
ap-1872	364	11	to	to	ADP
ap-1872	364	12	miloslav	miloslav	NOUN
ap-1872	364	13	havlicek	havlicek	NOUN
ap-1872	364	14	who	who	PRON
ap-1872	364	15	has	have	AUX
ap-1872	364	16	always	always	ADV
ap-1872	364	17	been	be	AUX
ap-1872	364	18	deeply	deeply	ADV
ap-1872	364	19	respected	respect	VERB
ap-1872	364	20	by	by	ADP
ap-1872	364	21	both	both	DET
ap-1872	364	22	authors	author	NOUN
ap-1872	364	23	as	as	ADP
ap-1872	364	24	a	a	DET
ap-1872	364	25	scientist	scientist	NOUN
ap-1872	364	26	and	and	CCONJ
ap-1872	364	27	also	also	ADV
ap-1872	364	28	as	as	ADP
ap-1872	364	29	a	a	DET
ap-1872	364	30	citizen	citizen	NOUN
ap-1872	364	31	.	.	PUNCT
ap-1872	365	1	the	the	DET
ap-1872	365	2	text	text	NOUN
ap-1872	365	3	is	be	AUX
ap-1872	365	4	based	base	VERB
ap-1872	365	5	mainly	mainly	ADV
ap-1872	365	6	on	on	ADP
ap-1872	365	7	notes	note	NOUN
ap-1872	365	8	jointly	jointly	ADV
ap-1872	365	9	prepared	prepare	VERB
ap-1872	365	10	by	by	ADP
ap-1872	365	11	two	two	NUM
ap-1872	365	12	authors	author	NOUN
ap-1872	365	13	.	.	PUNCT
ap-1872	366	1	it	it	PRON
ap-1872	366	2	does	do	AUX
ap-1872	366	3	not	not	PART
ap-1872	366	4	include	include	VERB
ap-1872	366	5	results	result	NOUN
ap-1872	366	6	of	of	ADP
ap-1872	366	7	the	the	DET
ap-1872	366	8	authors	author	NOUN
ap-1872	366	9	obtained	obtain	VERB
ap-1872	366	10	separately	separately	ADV
ap-1872	366	11	(	(	PUNCT
ap-1872	366	12	except	except	SCONJ
ap-1872	366	13	for	for	ADP
ap-1872	366	14	section	section	NOUN
ap-1872	366	15	4	4	NUM
ap-1872	366	16	)	)	PUNCT
ap-1872	366	17	and	and	CCONJ
ap-1872	366	18	which	which	PRON
ap-1872	366	19	the	the	DET
ap-1872	366	20	authors	author	NOUN
ap-1872	366	21	had	have	VERB
ap-1872	366	22	no	no	DET
ap-1872	366	23	chance	chance	NOUN
ap-1872	366	24	to	to	PART
ap-1872	366	25	discuss	discuss	VERB
ap-1872	366	26	.	.	PUNCT
ap-1872	367	1	thus	thus	ADV
ap-1872	367	2	,	,	PUNCT
ap-1872	367	3	the	the	DET
ap-1872	367	4	text	text	NOUN
ap-1872	367	5	will	will	AUX
ap-1872	367	6	appear	appear	VERB
ap-1872	367	7	somehow	somehow	ADV
ap-1872	367	8	incomplete	incomplete	ADJ
ap-1872	367	9	.	.	PUNCT
ap-1872	368	1	when	when	SCONJ
ap-1872	368	2	the	the	DET
ap-1872	368	3	first	first	ADJ
ap-1872	368	4	author	author	NOUN
ap-1872	368	5	(	(	PUNCT
ap-1872	368	6	yufs	yufs	NOUN
ap-1872	368	7	)	)	PUNCT
ap-1872	368	8	passed	pass	VERB
ap-1872	368	9	away	away	ADV
ap-1872	368	10	,	,	PUNCT
ap-1872	368	11	it	it	PRON
ap-1872	368	12	took	take	VERB
ap-1872	368	13	years	year	NOUN
ap-1872	368	14	for	for	SCONJ
ap-1872	368	15	the	the	DET
ap-1872	368	16	second	second	ADJ
ap-1872	368	17	author	author	NOUN
ap-1872	368	18	(	(	PUNCT
ap-1872	368	19	avt	avt	PROPN
ap-1872	368	20	)	)	PUNCT
ap-1872	368	21	to	to	PART
ap-1872	368	22	return	return	VERB
ap-1872	368	23	to	to	ADP
ap-1872	368	24	the	the	DET
ap-1872	368	25	subject	subject	NOUN
ap-1872	368	26	due	due	ADP
ap-1872	368	27	to	to	ADP
ap-1872	368	28	sad	sad	ADJ
ap-1872	368	29	memories	memory	NOUN
ap-1872	368	30	.	.	PUNCT
ap-1872	369	1	even	even	ADV
ap-1872	369	2	now	now	ADV
ap-1872	369	3	,	,	PUNCT
ap-1872	369	4	almost	almost	ADV
ap-1872	369	5	a	a	PRON
ap-1872	369	6	decade	decade	NOUN
ap-1872	369	7	after	after	ADP
ap-1872	369	8	the	the	DET
ap-1872	369	9	death	death	NOUN
ap-1872	369	10	of	of	ADP
ap-1872	369	11	yura	yura	NOUN
ap-1872	369	12	smirnov	smirnov	PROPN
ap-1872	369	13	,	,	PUNCT
ap-1872	369	14	the	the	DET
ap-1872	369	15	preparation	preparation	NOUN
ap-1872	369	16	of	of	ADP
ap-1872	369	17	this	this	DET
ap-1872	369	18	text	text	NOUN
ap-1872	369	19	was	be	AUX
ap-1872	369	20	quite	quite	ADV
ap-1872	369	21	difficult	difficult	ADJ
ap-1872	369	22	for	for	ADP
ap-1872	369	23	avt	avt	PROPN
ap-1872	369	24	.	.	PUNCT
ap-1872	369	25	avt	avt	PROPN
ap-1872	369	26	thanks	thanks	PROPN
ap-1872	369	27	crm	crm	PROPN
ap-1872	369	28	,	,	PUNCT
ap-1872	369	29	montreal	montreal	PROPN
ap-1872	369	30	for	for	ADP
ap-1872	369	31	their	their	PRON
ap-1872	369	32	kind	kind	ADJ
ap-1872	369	33	hospitality	hospitality	NOUN
ap-1872	369	34	extended	extend	VERB
ap-1872	369	35	to	to	ADP
ap-1872	369	36	him	he	PRON
ap-1872	369	37	.	.	PUNCT
ap-1872	370	1	a	a	DET
ap-1872	370	2	part	part	NOUN
ap-1872	370	3	of	of	ADP
ap-1872	370	4	this	this	DET
ap-1872	370	5	work	work	NOUN
ap-1872	370	6	was	be	AUX
ap-1872	370	7	done	do	VERB
ap-1872	370	8	there	there	ADV
ap-1872	370	9	during	during	ADP
ap-1872	370	10	his	his	PRON
ap-1872	370	11	numerous	numerous	ADJ
ap-1872	370	12	visits	visit	NOUN
ap-1872	370	13	.	.	PUNCT
ap-1872	371	1	avt	avt	PROPN
ap-1872	371	2	is	be	AUX
ap-1872	371	3	grateful	grateful	ADJ
ap-1872	371	4	to	to	ADP
ap-1872	371	5	j	j	PROPN
ap-1872	371	6	c	c	PROPN
ap-1872	371	7	lopez	lopez	PROPN
ap-1872	371	8	vieyra	vieyra	NOUN
ap-1872	371	9	for	for	ADP
ap-1872	371	10	taking	take	VERB
ap-1872	371	11	the	the	DET
ap-1872	371	12	interest	interest	NOUN
ap-1872	371	13	in	in	ADP
ap-1872	371	14	the	the	DET
ap-1872	371	15	work	work	NOUN
ap-1872	371	16	and	and	CCONJ
ap-1872	371	17	for	for	ADP
ap-1872	371	18	technical	technical	ADJ
ap-1872	371	19	assistance	assistance	NOUN
ap-1872	371	20	.	.	PUNCT
ap-1872	372	1	this	this	DET
ap-1872	372	2	work	work	NOUN
ap-1872	372	3	was	be	AUX
ap-1872	372	4	supported	support	VERB
ap-1872	372	5	in	in	ADP
ap-1872	372	6	part	part	NOUN
ap-1872	372	7	by	by	ADP
ap-1872	372	8	the	the	DET
ap-1872	372	9	university	university	NOUN
ap-1872	372	10	program	program	NOUN
ap-1872	372	11	fenomec	fenomec	NOUN
ap-1872	372	12	,	,	PUNCT
ap-1872	372	13	by	by	ADP
ap-1872	372	14	papiit	papiit	NOUN
ap-1872	372	15	grant	grant	NOUN
ap-1872	372	16	in109512	in109512	PROPN
ap-1872	372	17	,	,	PUNCT
ap-1872	372	18	and	and	CCONJ
ap-1872	372	19	by	by	ADP
ap-1872	372	20	conacyt	conacyt	ADJ
ap-1872	372	21	grant	grant	NOUN
ap-1872	372	22	166189	166189	NUM
ap-1872	372	23	(	(	PUNCT
ap-1872	372	24	mexico	mexico	PROPN
ap-1872	372	25	)	)	PUNCT
ap-1872	372	26	.	.	PUNCT
ap-1872	373	1	references	reference	NOUN
ap-1872	373	2	[	[	X
ap-1872	373	3	1	1	X
ap-1872	373	4	]	]	X
ap-1872	373	5	a.v	a.v	PROPN
ap-1872	373	6	.	.	PROPN
ap-1872	373	7	turbiner	turbiner	NOUN
ap-1872	373	8	.	.	PUNCT
ap-1872	374	1	quasi	quasi	ADJ
ap-1872	374	2	-	-	ADJ
ap-1872	374	3	exactly	exactly	ADV
ap-1872	374	4	-	-	PUNCT
ap-1872	374	5	solvable	solvable	ADJ
ap-1872	374	6	problems	problem	NOUN
ap-1872	374	7	and	and	CCONJ
ap-1872	374	8	the	the	DET
ap-1872	374	9	sl(2	sl(2	PROPN
ap-1872	374	10	,	,	PUNCT
ap-1872	374	11	r	r	NOUN
ap-1872	374	12	)	)	PUNCT
ap-1872	374	13	group	group	NOUN
ap-1872	374	14	,	,	PUNCT
ap-1872	374	15	comm.math.phys	comm.math.phy	NOUN
ap-1872	374	16	.	.	PUNCT
ap-1872	375	1	118	118	NUM
ap-1872	375	2	:	:	PUNCT
ap-1872	375	3	467	467	NUM
ap-1872	375	4	-	-	SYM
ap-1872	375	5	474	474	NUM
ap-1872	375	6	,	,	PUNCT
ap-1872	375	7	1988	1988	NUM
ap-1872	375	8	.	.	PUNCT
ap-1872	376	1	[	[	X
ap-1872	376	2	2	2	NUM
ap-1872	376	3	]	]	PUNCT
ap-1872	376	4	c.	c.	PROPN
ap-1872	376	5	burdik	burdik	PROPN
ap-1872	376	6	.	.	PUNCT
ap-1872	377	1	realisations	realisation	NOUN
ap-1872	377	2	of	of	ADP
ap-1872	377	3	the	the	DET
ap-1872	377	4	real	real	ADJ
ap-1872	377	5	semisimple	semisimple	NOUN
ap-1872	377	6	lie	lie	NOUN
ap-1872	377	7	algebras	algebra	VERB
ap-1872	377	8	:	:	PUNCT
ap-1872	377	9	a	a	DET
ap-1872	377	10	method	method	NOUN
ap-1872	377	11	of	of	ADP
ap-1872	377	12	construction	construction	NOUN
ap-1872	377	13	,	,	PUNCT
ap-1872	377	14	j.	j.	PROPN
ap-1872	377	15	phys	phys	PROPN
ap-1872	377	16	.	.	PUNCT
ap-1872	378	1	a18	a18	PROPN
ap-1872	378	2	:	:	PUNCT
ap-1872	378	3	3101	3101	NUM
ap-1872	378	4	-	-	SYM
ap-1872	378	5	3111	3111	NUM
ap-1872	378	6	,	,	PUNCT
ap-1872	378	7	1985	1985	NUM
ap-1872	378	8	.	.	PUNCT
ap-1872	379	1	[	[	X
ap-1872	379	2	3	3	X
ap-1872	379	3	]	]	X
ap-1872	379	4	c.	c.	PROPN
ap-1872	379	5	burdik	burdik	PROPN
ap-1872	379	6	,	,	PUNCT
ap-1872	379	7	m.	m.	NOUN
ap-1872	379	8	havlicek	havlicek	PROPN
ap-1872	379	9	.	.	PUNCT
ap-1872	380	1	boson	boson	NOUN
ap-1872	380	2	realization	realization	NOUN
ap-1872	380	3	of	of	ADP
ap-1872	380	4	the	the	DET
ap-1872	380	5	semi	semi	ADJ
ap-1872	380	6	-	-	ADJ
ap-1872	380	7	simple	simple	ADJ
ap-1872	380	8	lie	lie	NOUN
ap-1872	380	9	algebras	algebra	NOUN
ap-1872	380	10	,	,	PUNCT
ap-1872	380	11	in	in	ADP
ap-1872	380	12	symmetry	symmetry	NOUN
ap-1872	380	13	in	in	ADP
ap-1872	380	14	physics	physics	NOUN
ap-1872	380	15	:	:	PUNCT
ap-1872	380	16	in	in	ADP
ap-1872	380	17	memory	memory	NOUN
ap-1872	380	18	of	of	ADP
ap-1872	380	19	robert	robert	PROPN
ap-1872	380	20	t.	t.	PROPN
ap-1872	380	21	sharp	sharp	PROPN
ap-1872	380	22	,	,	PUNCT
ap-1872	380	23	crm	crm	PROPN
ap-1872	380	24	proceeding	proceeding	NOUN
ap-1872	380	25	2004	2004	NUM
ap-1872	380	26	,	,	PUNCT
ap-1872	380	27	vol.34	vol.34	PROPN
ap-1872	380	28	,	,	PUNCT
ap-1872	380	29	p.87	p.87	PROPN
ap-1872	380	30	-	-	X
ap-1872	380	31	98	98	NUM
ap-1872	380	32	,	,	PUNCT
ap-1872	380	33	edited	edit	VERB
ap-1872	380	34	by	by	ADP
ap-1872	380	35	r.t	r.t	PROPN
ap-1872	380	36	.	.	PROPN
ap-1872	380	37	sharp	sharp	PROPN
ap-1872	380	38	,	,	PUNCT
ap-1872	380	39	p.	p.	PROPN
ap-1872	380	40	winternitz	winternitz	PROPN
ap-1872	380	41	.	.	PUNCT
ap-1872	381	1	[	[	X
ap-1872	381	2	4	4	NUM
ap-1872	381	3	]	]	X
ap-1872	381	4	i.m	i.m	PROPN
ap-1872	381	5	.	.	PROPN
ap-1872	381	6	gelfand	gelfand	PROPN
ap-1872	381	7	and	and	CCONJ
ap-1872	381	8	m.l	m.l	PROPN
ap-1872	381	9	.	.	PROPN
ap-1872	381	10	tsetlin	tsetlin	PROPN
ap-1872	381	11	.	.	PUNCT
ap-1872	382	1	finite	finite	ADJ
ap-1872	382	2	-	-	ADJ
ap-1872	382	3	dimensional	dimensional	ADJ
ap-1872	382	4	representations	representation	NOUN
ap-1872	382	5	of	of	ADP
ap-1872	382	6	groups	group	NOUN
ap-1872	382	7	of	of	ADP
ap-1872	382	8	orthogonal	orthogonal	ADJ
ap-1872	382	9	matrices	matrix	NOUN
ap-1872	382	10	,	,	PUNCT
ap-1872	382	11	dokl	dokl	NOUN
ap-1872	382	12	.	.	PUNCT
ap-1872	383	1	akad	akad	PROPN
ap-1872	383	2	.	.	PUNCT
ap-1872	384	1	nauk	nauk	NOUN
ap-1872	384	2	sssr	sssr	NOUN
ap-1872	384	3	71	71	NUM
ap-1872	384	4	:	:	PUNCT
ap-1872	384	5	1017–1020	1017–1020	NUM
ap-1872	384	6	,	,	PUNCT
ap-1872	384	7	1950	1950	NUM
ap-1872	384	8	(	(	PUNCT
ap-1872	384	9	in	in	ADP
ap-1872	384	10	russian	russian	ADJ
ap-1872	384	11	)	)	PUNCT
ap-1872	384	12	english	english	PROPN
ap-1872	384	13	transl	transl	PROPN
ap-1872	384	14	.	.	PUNCT
ap-1872	385	1	in	in	ADP
ap-1872	385	2	:	:	PUNCT
ap-1872	385	3	i.m	i.m	PROPN
ap-1872	385	4	.	.	PROPN
ap-1872	385	5	gelfand	gelfand	PROPN
ap-1872	385	6	,	,	PUNCT
ap-1872	385	7	collected	collect	VERB
ap-1872	385	8	papers	paper	NOUN
ap-1872	385	9	.	.	PUNCT
ap-1872	386	1	vol	vol	NOUN
ap-1872	386	2	ii	ii	PROPN
ap-1872	386	3	,	,	PUNCT
ap-1872	386	4	berlin	berlin	PROPN
ap-1872	386	5	:	:	PUNCT
ap-1872	386	6	springer	springer	NOUN
ap-1872	386	7	-	-	PUNCT
ap-1872	386	8	verlag	verlag	PROPN
ap-1872	386	9	1988	1988	NUM
ap-1872	386	10	,	,	PUNCT
ap-1872	386	11	pp	pp	ADV
ap-1872	386	12	.	.	PUNCT
ap-1872	387	1	657–661	657–661	NUM
ap-1872	387	2	.	.	PUNCT
ap-1872	388	1	[	[	X
ap-1872	388	2	5	5	X
ap-1872	388	3	]	]	PUNCT
ap-1872	388	4	w.	w.	NOUN
ap-1872	388	5	rühl	rühl	PROPN
ap-1872	388	6	and	and	CCONJ
ap-1872	388	7	a.	a.	NOUN
ap-1872	388	8	v.	v.	PROPN
ap-1872	388	9	turbiner	turbiner	NOUN
ap-1872	388	10	.	.	PUNCT
ap-1872	389	1	exact	exact	ADJ
ap-1872	389	2	solvability	solvability	NOUN
ap-1872	389	3	of	of	ADP
ap-1872	389	4	the	the	DET
ap-1872	389	5	calogero	calogero	PROPN
ap-1872	389	6	and	and	CCONJ
ap-1872	389	7	sutherland	sutherland	PROPN
ap-1872	389	8	models	model	NOUN
ap-1872	389	9	,	,	PUNCT
ap-1872	389	10	mod	mod	PROPN
ap-1872	389	11	.	.	PUNCT
ap-1872	390	1	phys	phys	PROPN
ap-1872	390	2	.	.	PUNCT
ap-1872	391	1	lett	lett	PROPN
ap-1872	391	2	.	.	PUNCT
ap-1872	392	1	a10	a10	NOUN
ap-1872	392	2	:	:	PUNCT
ap-1872	392	3	2213–2222	2213–2222	NUM
ap-1872	392	4	,	,	PUNCT
ap-1872	392	5	1995	1995	NUM
ap-1872	392	6	arxiv	arxiv	NOUN
ap-1872	392	7	:	:	PUNCT
ap-1872	392	8	hep	hep	NOUN
ap-1872	392	9	-	-	PROPN
ap-1872	392	10	th/9506105	th/9506105	NOUN
ap-1872	392	11	.	.	PUNCT
ap-1872	393	1	[	[	X
ap-1872	393	2	6	6	NUM
ap-1872	393	3	]	]	X
ap-1872	393	4	a.v	a.v	PROPN
ap-1872	393	5	.	.	PROPN
ap-1872	393	6	turbiner	turbiner	PROPN
ap-1872	393	7	.	.	PUNCT
ap-1872	394	1	hidden	hide	VERB
ap-1872	394	2	algebra	algebra	NOUN
ap-1872	394	3	of	of	ADP
ap-1872	394	4	three	three	NUM
ap-1872	394	5	-	-	PUNCT
ap-1872	394	6	body	body	NOUN
ap-1872	394	7	integrable	integrable	ADJ
ap-1872	394	8	systems	system	NOUN
ap-1872	394	9	,	,	PUNCT
ap-1872	394	10	mod.phys.lett	mod.phys.lett	NUM
ap-1872	394	11	.	.	PUNCT
ap-1872	395	1	a13	a13	PROPN
ap-1872	395	2	:	:	PUNCT
ap-1872	395	3	1473	1473	NUM
ap-1872	395	4	-	-	SYM
ap-1872	395	5	1483	1483	NUM
ap-1872	395	6	,	,	PUNCT
ap-1872	395	7	1998	1998	NUM
ap-1872	395	8	[	[	X
ap-1872	395	9	7	7	X
ap-1872	395	10	]	]	X
ap-1872	395	11	a.v	a.v	PROPN
ap-1872	395	12	.	.	PROPN
ap-1872	395	13	turbiner	turbiner	PROPN
ap-1872	395	14	.	.	PUNCT
ap-1872	396	1	bc2	bc2	VERB
ap-1872	396	2	lame	lame	ADJ
ap-1872	396	3	polynomials	polynomial	NOUN
ap-1872	396	4	,	,	PUNCT
ap-1872	396	5	talks	talk	NOUN
ap-1872	396	6	presented	present	VERB
ap-1872	396	7	at	at	ADP
ap-1872	396	8	1085	1085	NUM
ap-1872	396	9	special	special	ADJ
ap-1872	396	10	session	session	NOUN
ap-1872	396	11	of	of	ADP
ap-1872	396	12	the	the	DET
ap-1872	396	13	american	american	PROPN
ap-1872	396	14	mathematical	mathematical	PROPN
ap-1872	396	15	society	society	NOUN
ap-1872	396	16	,	,	PUNCT
ap-1872	396	17	tucson	tucson	PROPN
ap-1872	396	18	az	az	PROPN
ap-1872	396	19	,	,	PUNCT
ap-1872	396	20	usa	usa	PROPN
ap-1872	396	21	(	(	PUNCT
ap-1872	396	22	october	october	PROPN
ap-1872	396	23	2012	2012	NUM
ap-1872	396	24	)	)	PUNCT
ap-1872	396	25	and	and	CCONJ
ap-1872	396	26	at	at	ADP
ap-1872	396	27	the	the	DET
ap-1872	396	28	annual	annual	ADJ
ap-1872	396	29	meeting	meeting	NOUN
ap-1872	396	30	of	of	ADP
ap-1872	396	31	the	the	DET
ap-1872	396	32	canadian	canadian	PROPN
ap-1872	396	33	mathematical	mathematical	ADJ
ap-1872	396	34	society	society	NOUN
ap-1872	396	35	,	,	PUNCT
ap-1872	396	36	montreal	montreal	PROPN
ap-1872	396	37	,	,	PUNCT
ap-1872	396	38	canada	canada	PROPN
ap-1872	396	39	(	(	PUNCT
ap-1872	396	40	december	december	PROPN
ap-1872	396	41	2012	2012	NUM
ap-1872	396	42	)	)	PUNCT
ap-1872	397	1	[	[	X
ap-1872	397	2	8	8	NUM
ap-1872	397	3	]	]	X
ap-1872	397	4	a.	a.	NOUN
ap-1872	397	5	v.	v.	PROPN
ap-1872	397	6	turbiner	turbiner	PROPN
ap-1872	397	7	,	,	PUNCT
ap-1872	397	8	lie	lie	NOUN
ap-1872	397	9	algebras	algebra	NOUN
ap-1872	397	10	and	and	CCONJ
ap-1872	397	11	linear	linear	PROPN
ap-1872	397	12	operators	operator	NOUN
ap-1872	397	13	with	with	ADP
ap-1872	397	14	invariant	invariant	ADJ
ap-1872	397	15	subspace	subspace	NOUN
ap-1872	397	16	,	,	PUNCT
ap-1872	397	17	in	in	ADP
ap-1872	397	18	lie	lie	NOUN
ap-1872	397	19	algebras	algebra	NOUN
ap-1872	397	20	,	,	PUNCT
ap-1872	397	21	cohomologies	cohomologie	NOUN
ap-1872	397	22	and	and	CCONJ
ap-1872	397	23	new	new	ADJ
ap-1872	397	24	findings	finding	NOUN
ap-1872	397	25	in	in	ADP
ap-1872	397	26	quantum	quantum	ADJ
ap-1872	397	27	mechanics	mechanic	NOUN
ap-1872	397	28	(	(	PUNCT
ap-1872	397	29	n.	n.	PROPN
ap-1872	397	30	kamran	kamran	PROPN
ap-1872	397	31	and	and	CCONJ
ap-1872	397	32	p.	p.	PROPN
ap-1872	397	33	j.	j.	PROPN
ap-1872	397	34	olver	olver	PROPN
ap-1872	397	35	,	,	PUNCT
ap-1872	397	36	eds	eds	PROPN
ap-1872	397	37	.	.	PUNCT
ap-1872	397	38	)	)	PUNCT
ap-1872	397	39	,	,	PUNCT
ap-1872	397	40	ams	am	NOUN
ap-1872	397	41	contemporary	contemporary	PROPN
ap-1872	397	42	mathematics	mathematics	PROPN
ap-1872	397	43	,	,	PUNCT
ap-1872	397	44	vol	vol	NOUN
ap-1872	397	45	.	.	PROPN
ap-1872	397	46	160	160	NUM
ap-1872	397	47	,	,	PUNCT
ap-1872	397	48	pp	pp	ADJ
ap-1872	397	49	.	.	PUNCT
ap-1872	398	1	263–310	263–310	NUM
ap-1872	398	2	,	,	PUNCT
ap-1872	398	3	1994	1994	NUM
ap-1872	398	4	;	;	PUNCT
ap-1872	398	5	arxiv	arxiv	NOUN
ap-1872	398	6	:	:	PUNCT
ap-1872	398	7	funct	funct	NOUN
ap-1872	398	8	-	-	PUNCT
ap-1872	398	9	an/9301001	an/9301001	NOUN
ap-1872	398	10	[	[	X
ap-1872	398	11	9	9	NUM
ap-1872	398	12	]	]	PUNCT
ap-1872	398	13	s.	s.	PROPN
ap-1872	398	14	lie	lie	PROPN
ap-1872	398	15	.	.	PUNCT
ap-1872	399	1	gruppenregister	gruppenregister	PROPN
ap-1872	399	2	,	,	PUNCT
ap-1872	399	3	vol	vol	NOUN
ap-1872	399	4	.	.	PROPN
ap-1872	399	5	5	5	NUM
ap-1872	399	6	,	,	PUNCT
ap-1872	399	7	b.g	b.g	PROPN
ap-1872	399	8	.	.	PROPN
ap-1872	399	9	teubner	teubner	NOUN
ap-1872	399	10	,	,	PUNCT
ap-1872	399	11	leipzig	leipzig	NOUN
ap-1872	399	12	,	,	PUNCT
ap-1872	399	13	1924	1924	NUM
ap-1872	399	14	,	,	PUNCT
ap-1872	399	15	767	767	NUM
ap-1872	399	16	-	-	SYM
ap-1872	399	17	773	773	NUM
ap-1872	400	1	[	[	X
ap-1872	400	2	10	10	NUM
ap-1872	400	3	]	]	PUNCT
ap-1872	400	4	a.	a.	PROPN
ap-1872	400	5	gonzález	gonzález	PROPN
ap-1872	400	6	-	-	PUNCT
ap-1872	400	7	lopéz	lopéz	PROPN
ap-1872	400	8	,	,	PUNCT
ap-1872	400	9	n.	n.	PROPN
ap-1872	400	10	kamran	kamran	PROPN
ap-1872	400	11	and	and	CCONJ
ap-1872	400	12	p.j	p.j	PROPN
ap-1872	400	13	.	.	PROPN
ap-1872	400	14	olver	olver	PROPN
ap-1872	400	15	.	.	PUNCT
ap-1872	401	1	quasi	quasi	ADJ
ap-1872	401	2	-	-	ADJ
ap-1872	401	3	exactly	exactly	ADV
ap-1872	401	4	-	-	PUNCT
ap-1872	401	5	solvable	solvable	ADJ
ap-1872	401	6	lie	lie	NOUN
ap-1872	401	7	algebras	algebra	NOUN
ap-1872	401	8	of	of	ADP
ap-1872	401	9	the	the	DET
ap-1872	401	10	first	first	ADJ
ap-1872	401	11	order	order	NOUN
ap-1872	401	12	differential	differential	NOUN
ap-1872	401	13	operators	operator	NOUN
ap-1872	401	14	in	in	ADP
ap-1872	401	15	two	two	NUM
ap-1872	401	16	complex	complex	ADJ
ap-1872	401	17	variables	variable	NOUN
ap-1872	401	18	,	,	PUNCT
ap-1872	401	19	j.phys	j.phy	NOUN
ap-1872	401	20	.	.	PUNCT
ap-1872	402	1	a24	a24	PROPN
ap-1872	402	2	:	:	PUNCT
ap-1872	402	3	3995–4008	3995–4008	NUM
ap-1872	402	4	,	,	PUNCT
ap-1872	402	5	1991	1991	NUM
ap-1872	402	6	;	;	PUNCT
ap-1872	402	7	lie	lie	NOUN
ap-1872	402	8	algebras	algebra	NOUN
ap-1872	402	9	of	of	ADP
ap-1872	402	10	differential	differential	ADJ
ap-1872	402	11	operators	operator	NOUN
ap-1872	402	12	in	in	ADP
ap-1872	402	13	two	two	NUM
ap-1872	402	14	complex	complex	ADJ
ap-1872	402	15	variables	variable	NOUN
ap-1872	402	16	,	,	PUNCT
ap-1872	402	17	american	american	PROPN
ap-1872	402	18	j.	j.	PROPN
ap-1872	402	19	math	math	PROPN
ap-1872	402	20	.	.	PUNCT
ap-1872	403	1	114	114	NUM
ap-1872	403	2	:	:	SYM
ap-1872	403	3	1163–1185	1163–1185	NUM
ap-1872	403	4	,	,	PUNCT
ap-1872	403	5	1992	1992	NUM
ap-1872	403	6	;	;	PUNCT
ap-1872	403	7	[	[	X
ap-1872	403	8	11	11	NUM
ap-1872	403	9	]	]	X
ap-1872	403	10	f.	f.	PROPN
ap-1872	403	11	tremblay	tremblay	PROPN
ap-1872	403	12	,	,	PUNCT
ap-1872	403	13	a.v	a.v	PROPN
ap-1872	403	14	.	.	PROPN
ap-1872	403	15	turbiner	turbiner	NOUN
ap-1872	403	16	and	and	CCONJ
ap-1872	403	17	p.	p.	PROPN
ap-1872	403	18	winternitz	winternitz	PROPN
ap-1872	403	19	.	.	PUNCT
ap-1872	404	1	an	an	DET
ap-1872	404	2	infinite	infinite	ADJ
ap-1872	404	3	family	family	NOUN
ap-1872	404	4	of	of	ADP
ap-1872	404	5	solvable	solvable	ADJ
ap-1872	404	6	and	and	CCONJ
ap-1872	404	7	integrable	integrable	ADJ
ap-1872	404	8	quantum	quantum	NOUN
ap-1872	404	9	systems	system	NOUN
ap-1872	404	10	on	on	ADP
ap-1872	404	11	a	a	DET
ap-1872	404	12	plane	plane	NOUN
ap-1872	404	13	,	,	PUNCT
ap-1872	404	14	journal	journal	NOUN
ap-1872	404	15	of	of	ADP
ap-1872	404	16	phys	phys	PROPN
ap-1872	404	17	.	.	PUNCT
ap-1872	405	1	a42	a42	PROPN
ap-1872	405	2	,	,	PUNCT
ap-1872	405	3	242001	242001	NUM
ap-1872	405	4	,	,	PUNCT
ap-1872	405	5	2009	2009	NUM
ap-1872	405	6	;	;	PUNCT
ap-1872	405	7	10	10	NUM
ap-1872	405	8	pp	pp	NOUN
ap-1872	405	9	arxiv:0904.0738	arxiv:0904.0738	NOUN
ap-1872	405	10	[	[	X
ap-1872	405	11	12	12	NUM
ap-1872	405	12	]	]	X
ap-1872	405	13	f.	f.	PROPN
ap-1872	405	14	calogero	calogero	PROPN
ap-1872	405	15	.	.	PUNCT
ap-1872	406	1	solution	solution	NOUN
ap-1872	406	2	of	of	ADP
ap-1872	406	3	a	a	DET
ap-1872	406	4	three	three	NUM
ap-1872	406	5	-	-	PUNCT
ap-1872	406	6	body	body	NOUN
ap-1872	406	7	problem	problem	NOUN
ap-1872	406	8	in	in	ADP
ap-1872	406	9	one	one	NUM
ap-1872	406	10	dimension	dimension	NOUN
ap-1872	406	11	,	,	PUNCT
ap-1872	406	12	j.	j.	PROPN
ap-1872	406	13	math	math	PROPN
ap-1872	406	14	.	.	PUNCT
ap-1872	407	1	phys	phy	NOUN
ap-1872	407	2	.	.	PUNCT
ap-1872	408	1	10	10	NUM
ap-1872	408	2	:	:	SYM
ap-1872	408	3	2191–2196	2191–2196	NUM
ap-1872	408	4	,	,	PUNCT
ap-1872	408	5	1969	1969	NUM
ap-1872	408	6	[	[	X
ap-1872	408	7	13	13	NUM
ap-1872	408	8	]	]	X
ap-1872	408	9	b.	b.	PROPN
ap-1872	408	10	sutherland	sutherland	PROPN
ap-1872	408	11	.	.	PUNCT
ap-1872	409	1	exact	exact	ADJ
ap-1872	409	2	results	result	NOUN
ap-1872	409	3	for	for	ADP
ap-1872	409	4	a	a	DET
ap-1872	409	5	quantum	quantum	ADJ
ap-1872	409	6	many	many	ADJ
ap-1872	409	7	-	-	PUNCT
ap-1872	409	8	body	body	NOUN
ap-1872	409	9	problem	problem	NOUN
ap-1872	409	10	in	in	ADP
ap-1872	409	11	one	one	NUM
ap-1872	409	12	dimension	dimension	NOUN
ap-1872	409	13	i	i	PRON
ap-1872	409	14	,	,	PUNCT
ap-1872	409	15	phys	phy	NOUN
ap-1872	409	16	.	.	PUNCT
ap-1872	410	1	rev	rev	PROPN
ap-1872	410	2	.	.	PROPN
ap-1872	410	3	a4	a4	PROPN
ap-1872	410	4	:	:	PUNCT
ap-1872	410	5	2019	2019	NUM
ap-1872	410	6	-	-	SYM
ap-1872	410	7	2021	2021	NUM
ap-1872	410	8	,	,	PUNCT
ap-1872	410	9	1971	1971	NUM
ap-1872	410	10	[	[	X
ap-1872	410	11	14	14	NUM
ap-1872	410	12	]	]	X
ap-1872	410	13	a.v	a.v	PROPN
ap-1872	410	14	.	.	PROPN
ap-1872	410	15	turbiner	turbiner	NOUN
ap-1872	410	16	.	.	PUNCT
ap-1872	411	1	from	from	ADP
ap-1872	411	2	quantum	quantum	PROPN
ap-1872	411	3	an	an	DET
ap-1872	411	4	(	(	PUNCT
ap-1872	411	5	calogero	calogero	PROPN
ap-1872	411	6	)	)	PUNCT
ap-1872	411	7	to	to	ADP
ap-1872	411	8	h4	h4	PROPN
ap-1872	411	9	(	(	PUNCT
ap-1872	411	10	rational	rational	ADJ
ap-1872	411	11	)	)	PUNCT
ap-1872	411	12	model	model	NOUN
ap-1872	411	13	,	,	PUNCT
ap-1872	411	14	sigma	sigma	NOUN
ap-1872	411	15	7	7	NUM
ap-1872	411	16	:	:	SYM
ap-1872	411	17	071	071	NUM
ap-1872	411	18	,	,	PUNCT
ap-1872	411	19	2011	2011	NUM
ap-1872	411	20	;	;	PUNCT
ap-1872	411	21	20	20	NUM
ap-1872	411	22	pp	pp	ADV
ap-1872	411	23	from	from	ADP
ap-1872	411	24	quantum	quantum	PROPN
ap-1872	411	25	an	an	DET
ap-1872	411	26	(	(	PUNCT
ap-1872	411	27	sutherland	sutherland	NOUN
ap-1872	411	28	)	)	PUNCT
ap-1872	411	29	to	to	PART
ap-1872	411	30	e8	e8	PROPN
ap-1872	411	31	trigonometric	trigonometric	PROPN
ap-1872	411	32	model	model	NOUN
ap-1872	411	33	:	:	PUNCT
ap-1872	411	34	space	space	NOUN
ap-1872	411	35	-	-	PUNCT
ap-1872	411	36	of	of	ADP
ap-1872	411	37	-	-	PUNCT
ap-1872	411	38	orbits	orbit	NOUN
ap-1872	411	39	view	view	NOUN
ap-1872	411	40	,	,	PUNCT
ap-1872	411	41	sigma	sigma	PROPN
ap-1872	411	42	9	9	NUM
ap-1872	411	43	:	:	SYM
ap-1872	411	44	003	003	NUM
ap-1872	411	45	,	,	PUNCT
ap-1872	411	46	2013	2013	NUM
ap-1872	411	47	;	;	PUNCT
ap-1872	411	48	25	25	NUM
ap-1872	411	49	pp	pp	ADP
ap-1872	411	50	469	469	NUM
ap-1872	411	51	http://arxiv.org/abs/hep-th/9506105	http://arxiv.org/abs/hep-th/9506105	PROPN
ap-1872	411	52	http://arxiv.org/abs/funct-an/9301001	http://arxiv.org/abs/funct-an/9301001	PROPN
ap-1872	411	53	http://arxiv.org/abs/0904.0738	http://arxiv.org/abs/0904.0738	NOUN
ap-1872	411	54	acta	acta	PROPN
ap-1872	411	55	polytechnica	polytechnica	PROPN
ap-1872	411	56	53(5):462–469	53(5):462–469	PROPN
ap-1872	411	57	,	,	PUNCT
ap-1872	411	58	2013	2013	NUM
ap-1872	411	59	1	1	NUM
ap-1872	411	60	introduction	introduction	NOUN
ap-1872	411	61	2	2	NUM
ap-1872	411	62	the	the	DET
ap-1872	411	63	algebra	algebra	NOUN
ap-1872	411	64	gl_n	gl_n	PROPN
ap-1872	411	65	in	in	ADP
ap-1872	411	66	mixed	mixed	ADJ
ap-1872	411	67	representation	representation	NOUN
ap-1872	411	68	3	3	NUM
ap-1872	411	69	example	example	NOUN
ap-1872	411	70	:	:	PUNCT
ap-1872	411	71	the	the	DET
ap-1872	411	72	algebra	algebra	NOUN
ap-1872	411	73	gl_3	gl_3	NOUN
ap-1872	411	74	in	in	ADP
ap-1872	411	75	mixed	mixed	ADJ
ap-1872	411	76	representation	representation	NOUN
ap-1872	411	77	3.1	3.1	NUM
ap-1872	411	78	reps	rep	NOUN
ap-1872	411	79	in	in	ADP
ap-1872	411	80	1x1	1x1	NUM
ap-1872	411	81	matrices	matrix	NOUN
ap-1872	411	82	3.2	3.2	NUM
ap-1872	411	83	reps	rep	NOUN
ap-1872	411	84	in	in	ADP
ap-1872	411	85	2x2	2x2	NUM
ap-1872	411	86	matrices	matrix	NOUN
ap-1872	411	87	3.3	3.3	NUM
ap-1872	411	88	reps	rep	NOUN
ap-1872	411	89	in	in	ADP
ap-1872	411	90	3x3	3x3	NUM
ap-1872	411	91	matrices	matrix	NOUN
ap-1872	411	92	4	4	NUM
ap-1872	411	93	algebra	algebra	NOUN
ap-1872	411	94	g^(m	g^(m	NOUN
ap-1872	411	95	)	)	PUNCT
ap-1872	411	96	in	in	ADP
ap-1872	411	97	mixed	mixed	ADJ
ap-1872	411	98	representation	representation	NOUN
ap-1872	411	99	5	5	NUM
ap-1872	411	100	extension	extension	NOUN
ap-1872	411	101	of	of	ADP
ap-1872	411	102	the	the	DET
ap-1872	411	103	3	3	NUM
ap-1872	411	104	-	-	PUNCT
ap-1872	411	105	body	body	NOUN
ap-1872	411	106	calogero	calogero	NOUN
ap-1872	411	107	model	model	NOUN
ap-1872	411	108	6	6	NUM
ap-1872	411	109	extension	extension	NOUN
ap-1872	411	110	of	of	ADP
ap-1872	411	111	the	the	DET
ap-1872	411	112	3	3	NUM
ap-1872	411	113	-	-	PUNCT
ap-1872	411	114	body	body	NOUN
ap-1872	411	115	sutherland	sutherland	NOUN
ap-1872	411	116	model	model	NOUN
ap-1872	411	117	7	7	NUM
ap-1872	411	118	conclusions	conclusion	NOUN
ap-1872	411	119	acknowledgements	acknowledgement	NOUN
ap-1872	411	120	references	reference	NOUN