id	sid	tid	token	lemma	pos
ap-1863	1	1	acta	acta	PROPN
ap-1863	1	2	polytechnica	polytechnica	PROPN
ap-1863	1	3	doi:10.14311	doi:10.14311	PROPN
ap-1863	1	4	/	/	SYM
ap-1863	1	5	ap.2013.53.0450	ap.2013.53.0450	PROPN
ap-1863	1	6	acta	acta	PROPN
ap-1863	1	7	polytechnica	polytechnica	PROPN
ap-1863	1	8	53(5):450–456	53(5):450–456	PROPN
ap-1863	1	9	,	,	PUNCT
ap-1863	1	10	2013	2013	NUM
ap-1863	1	11	©	©	PROPN
ap-1863	1	12	czech	czech	PROPN
ap-1863	1	13	technical	technical	PROPN
ap-1863	1	14	university	university	PROPN
ap-1863	1	15	in	in	ADP
ap-1863	1	16	prague	prague	PROPN
ap-1863	1	17	,	,	PUNCT
ap-1863	1	18	2013	2013	NUM
ap-1863	1	19	available	available	ADJ
ap-1863	1	20	online	online	ADV
ap-1863	1	21	at	at	ADP
ap-1863	1	22	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-1863	1	23	note	note	NOUN
ap-1863	1	24	on	on	ADP
ap-1863	1	25	verma	verma	PROPN
ap-1863	1	26	bases	basis	NOUN
ap-1863	1	27	for	for	ADP
ap-1863	1	28	representations	representation	NOUN
ap-1863	1	29	of	of	ADP
ap-1863	1	30	simple	simple	ADJ
ap-1863	1	31	lie	lie	NOUN
ap-1863	1	32	algebras	algebras	PROPN
ap-1863	1	33	severin	severin	PROPN
ap-1863	1	34	pošta∗	pošta∗	PROPN
ap-1863	1	35	,	,	PUNCT
ap-1863	1	36	miloslav	miloslav	PROPN
ap-1863	1	37	havlíček	havlíček	PROPN
ap-1863	1	38	department	department	PROPN
ap-1863	1	39	of	of	ADP
ap-1863	1	40	mathematics	mathematic	NOUN
ap-1863	1	41	,	,	PUNCT
ap-1863	1	42	faculty	faculty	NOUN
ap-1863	1	43	of	of	ADP
ap-1863	1	44	nuclear	nuclear	ADJ
ap-1863	1	45	sciences	science	NOUN
ap-1863	1	46	and	and	CCONJ
ap-1863	1	47	physical	physical	ADJ
ap-1863	1	48	engineering	engineering	NOUN
ap-1863	1	49	,	,	PUNCT
ap-1863	1	50	czech	czech	PROPN
ap-1863	1	51	technical	technical	PROPN
ap-1863	1	52	university	university	PROPN
ap-1863	1	53	in	in	ADP
ap-1863	1	54	prague	prague	PROPN
ap-1863	1	55	,	,	PUNCT
ap-1863	1	56	trojanova	trojanova	X
ap-1863	1	57	13	13	NUM
ap-1863	1	58	,	,	PUNCT
ap-1863	1	59	cz-120	cz-120	PROPN
ap-1863	1	60	00	00	NUM
ap-1863	2	1	prague	prague	PROPN
ap-1863	2	2	,	,	PUNCT
ap-1863	2	3	czech	czech	PROPN
ap-1863	2	4	republic	republic	NOUN
ap-1863	2	5	∗	∗	NOUN
ap-1863	2	6	corresponding	correspond	VERB
ap-1863	2	7	author	author	NOUN
ap-1863	2	8	:	:	PUNCT
ap-1863	2	9	severin@km1.fjfi.cvut.cz	severin@km1.fjfi.cvut.cz	PROPN
ap-1863	2	10	abstract	abstract	NOUN
ap-1863	2	11	.	.	PUNCT
ap-1863	3	1	we	we	PRON
ap-1863	3	2	discuss	discuss	VERB
ap-1863	3	3	the	the	DET
ap-1863	3	4	construction	construction	NOUN
ap-1863	3	5	of	of	ADP
ap-1863	3	6	the	the	DET
ap-1863	3	7	verma	verma	PROPN
ap-1863	3	8	basis	basis	NOUN
ap-1863	3	9	of	of	ADP
ap-1863	3	10	the	the	DET
ap-1863	3	11	enveloping	enveloping	NOUN
ap-1863	3	12	algebra	algebra	NOUN
ap-1863	3	13	and	and	CCONJ
ap-1863	3	14	of	of	ADP
ap-1863	3	15	finite	finite	ADJ
ap-1863	3	16	dimensional	dimensional	ADJ
ap-1863	3	17	representations	representation	NOUN
ap-1863	3	18	of	of	ADP
ap-1863	3	19	the	the	DET
ap-1863	3	20	lie	lie	NOUN
ap-1863	3	21	algebra	algebra	NOUN
ap-1863	3	22	an	an	PRON
ap-1863	3	23	.	.	PUNCT
ap-1863	4	1	we	we	PRON
ap-1863	4	2	give	give	VERB
ap-1863	4	3	an	an	DET
ap-1863	4	4	alternate	alternate	ADJ
ap-1863	4	5	proof	proof	NOUN
ap-1863	4	6	of	of	ADP
ap-1863	4	7	so	so	ADV
ap-1863	4	8	-	-	PUNCT
ap-1863	4	9	called	call	VERB
ap-1863	4	10	verma	verma	PROPN
ap-1863	4	11	inequalities	inequality	NOUN
ap-1863	4	12	to	to	ADP
ap-1863	4	13	the	the	DET
ap-1863	4	14	one	one	NOUN
ap-1863	4	15	given	give	VERB
ap-1863	4	16	in	in	ADP
ap-1863	4	17	[	[	X
ap-1863	4	18	1	1	NUM
ap-1863	4	19	]	]	PUNCT
ap-1863	4	20	by	by	ADP
ap-1863	4	21	p.	p.	PROPN
ap-1863	4	22	littelmann	littelmann	PROPN
ap-1863	4	23	.	.	PUNCT
ap-1863	5	1	keywords	keyword	NOUN
ap-1863	5	2	:	:	PUNCT
ap-1863	5	3	verma	verma	PROPN
ap-1863	5	4	basis	basis	NOUN
ap-1863	5	5	,	,	PUNCT
ap-1863	5	6	enveloping	envelop	VERB
ap-1863	5	7	algebra	algebra	NOUN
ap-1863	5	8	,	,	PUNCT
ap-1863	5	9	lie	lie	NOUN
ap-1863	5	10	algebra	algebra	NOUN
ap-1863	5	11	.	.	PUNCT
ap-1863	6	1	submitted	submit	VERB
ap-1863	6	2	:	:	PUNCT
ap-1863	6	3	7	7	NUM
ap-1863	6	4	may	may	PROPN
ap-1863	6	5	2013	2013	NUM
ap-1863	6	6	.	.	PUNCT
ap-1863	7	1	accepted	accept	VERB
ap-1863	7	2	:	:	PUNCT
ap-1863	7	3	2	2	NUM
ap-1863	7	4	july	july	NOUN
ap-1863	7	5	2013	2013	NUM
ap-1863	7	6	.	.	PUNCT
ap-1863	8	1	1	1	X
ap-1863	8	2	.	.	X
ap-1863	8	3	introduction	introduction	NOUN
ap-1863	8	4	the	the	DET
ap-1863	8	5	theory	theory	NOUN
ap-1863	8	6	of	of	ADP
ap-1863	8	7	simple	simple	ADJ
ap-1863	8	8	lie	lie	NOUN
ap-1863	8	9	groups	group	NOUN
ap-1863	8	10	and	and	CCONJ
ap-1863	8	11	their	their	PRON
ap-1863	8	12	representations	representation	NOUN
ap-1863	8	13	(	(	PUNCT
ap-1863	8	14	and	and	CCONJ
ap-1863	8	15	corresponding	correspond	VERB
ap-1863	8	16	representations	representation	NOUN
ap-1863	8	17	of	of	ADP
ap-1863	8	18	simple	simple	ADJ
ap-1863	8	19	lie	lie	NOUN
ap-1863	8	20	algebras	algebra	NOUN
ap-1863	8	21	)	)	PUNCT
ap-1863	8	22	has	have	AUX
ap-1863	8	23	been	be	AUX
ap-1863	8	24	at	at	ADP
ap-1863	8	25	the	the	DET
ap-1863	8	26	center	center	NOUN
ap-1863	8	27	of	of	ADP
ap-1863	8	28	interest	interest	NOUN
ap-1863	8	29	of	of	ADP
ap-1863	8	30	modern	modern	ADJ
ap-1863	8	31	mathematics	mathematic	NOUN
ap-1863	8	32	for	for	ADP
ap-1863	8	33	a	a	DET
ap-1863	8	34	long	long	ADJ
ap-1863	8	35	time	time	NOUN
ap-1863	8	36	,	,	PUNCT
ap-1863	8	37	because	because	SCONJ
ap-1863	8	38	it	it	PRON
ap-1863	8	39	has	have	VERB
ap-1863	8	40	many	many	ADJ
ap-1863	8	41	relationships	relationship	NOUN
ap-1863	8	42	with	with	ADP
ap-1863	8	43	other	other	ADJ
ap-1863	8	44	areas	area	NOUN
ap-1863	8	45	of	of	ADP
ap-1863	8	46	mathematics	mathematic	NOUN
ap-1863	8	47	and	and	CCONJ
ap-1863	8	48	physics	physics	NOUN
ap-1863	8	49	.	.	PUNCT
ap-1863	9	1	the	the	DET
ap-1863	9	2	simple	simple	ADJ
ap-1863	9	3	lie	lie	NOUN
ap-1863	9	4	algebras	algebra	VERB
ap-1863	9	5	over	over	ADP
ap-1863	9	6	the	the	DET
ap-1863	9	7	field	field	NOUN
ap-1863	9	8	of	of	ADP
ap-1863	9	9	complex	complex	ADJ
ap-1863	9	10	numbers	number	NOUN
ap-1863	9	11	were	be	AUX
ap-1863	9	12	classified	classify	VERB
ap-1863	9	13	in	in	ADP
ap-1863	9	14	the	the	DET
ap-1863	9	15	famous	famous	ADJ
ap-1863	9	16	works	work	NOUN
ap-1863	9	17	of	of	ADP
ap-1863	9	18	killing	kill	VERB
ap-1863	9	19	and	and	CCONJ
ap-1863	9	20	cartan	cartan	PROPN
ap-1863	9	21	in	in	ADP
ap-1863	9	22	the	the	DET
ap-1863	9	23	1930s	1930	NOUN
ap-1863	9	24	.	.	PUNCT
ap-1863	10	1	since	since	SCONJ
ap-1863	10	2	then	then	ADV
ap-1863	10	3	we	we	PRON
ap-1863	10	4	have	have	AUX
ap-1863	10	5	known	know	VERB
ap-1863	10	6	that	that	SCONJ
ap-1863	10	7	there	there	PRON
ap-1863	10	8	are	be	VERB
ap-1863	10	9	four	four	NUM
ap-1863	10	10	infinite	infinite	ADJ
ap-1863	10	11	series	series	NOUN
ap-1863	10	12	an	an	PROPN
ap-1863	10	13	,	,	PUNCT
ap-1863	10	14	bn	bn	NOUN
ap-1863	10	15	,	,	PUNCT
ap-1863	10	16	cn	cn	PROPN
ap-1863	10	17	,	,	PUNCT
ap-1863	10	18	dn	dn	PROPN
ap-1863	10	19	,	,	PUNCT
ap-1863	10	20	which	which	PRON
ap-1863	10	21	are	be	AUX
ap-1863	10	22	called	call	VERB
ap-1863	10	23	the	the	DET
ap-1863	10	24	classical	classical	ADJ
ap-1863	10	25	lie	lie	NOUN
ap-1863	10	26	algebras	algebra	NOUN
ap-1863	10	27	,	,	PUNCT
ap-1863	10	28	and	and	CCONJ
ap-1863	10	29	five	five	NUM
ap-1863	10	30	lie	lie	NOUN
ap-1863	10	31	algebras	algebras	PROPN
ap-1863	10	32	e6	e6	PROPN
ap-1863	10	33	,	,	PUNCT
ap-1863	10	34	e7	e7	PROPN
ap-1863	10	35	,	,	PUNCT
ap-1863	10	36	e8	e8	PROPN
ap-1863	10	37	,	,	PUNCT
ap-1863	10	38	f4	f4	PROPN
ap-1863	10	39	and	and	CCONJ
ap-1863	10	40	g2	g2	PROPN
ap-1863	10	41	,	,	PUNCT
ap-1863	10	42	which	which	PRON
ap-1863	10	43	we	we	PRON
ap-1863	10	44	call	call	VERB
ap-1863	10	45	exceptional	exceptional	ADJ
ap-1863	10	46	lie	lie	NOUN
ap-1863	10	47	algebras	algebra	NOUN
ap-1863	10	48	.	.	PUNCT
ap-1863	11	1	the	the	DET
ap-1863	11	2	structure	structure	NOUN
ap-1863	11	3	of	of	ADP
ap-1863	11	4	these	these	DET
ap-1863	11	5	lie	lie	NOUN
ap-1863	11	6	algebras	algebra	NOUN
ap-1863	11	7	is	be	AUX
ap-1863	11	8	described	describe	VERB
ap-1863	11	9	in	in	ADP
ap-1863	11	10	terms	term	NOUN
ap-1863	11	11	of	of	ADP
ap-1863	11	12	special	special	ADJ
ap-1863	11	13	finite	finite	ADJ
ap-1863	11	14	sets	set	NOUN
ap-1863	11	15	of	of	ADP
ap-1863	11	16	elements	element	NOUN
ap-1863	11	17	in	in	ADP
ap-1863	11	18	a	a	DET
ap-1863	11	19	euclidean	euclidean	ADJ
ap-1863	11	20	space	space	NOUN
ap-1863	11	21	,	,	PUNCT
ap-1863	11	22	called	call	VERB
ap-1863	11	23	roots	root	NOUN
ap-1863	11	24	,	,	PUNCT
ap-1863	11	25	which	which	PRON
ap-1863	11	26	generate	generate	VERB
ap-1863	11	27	a	a	DET
ap-1863	11	28	root	root	NOUN
ap-1863	11	29	system	system	NOUN
ap-1863	11	30	.	.	PUNCT
ap-1863	12	1	weyl	weyl	PROPN
ap-1863	12	2	’s	’s	PART
ap-1863	12	3	theorem	theorem	VERB
ap-1863	12	4	assures	assure	NOUN
ap-1863	12	5	that	that	SCONJ
ap-1863	12	6	each	each	DET
ap-1863	12	7	finite	finite	ADJ
ap-1863	12	8	dimensional	dimensional	ADJ
ap-1863	12	9	reducible	reducible	ADJ
ap-1863	12	10	representation	representation	NOUN
ap-1863	12	11	of	of	ADP
ap-1863	12	12	such	such	DET
ap-1863	12	13	a	a	DET
ap-1863	12	14	lie	lie	NOUN
ap-1863	12	15	algebra	algebra	NOUN
ap-1863	12	16	is	be	AUX
ap-1863	12	17	completely	completely	ADV
ap-1863	12	18	reducible	reducible	ADJ
ap-1863	12	19	.	.	PUNCT
ap-1863	13	1	therefore	therefore	ADV
ap-1863	13	2	in	in	ADP
ap-1863	13	3	the	the	DET
ap-1863	13	4	theory	theory	NOUN
ap-1863	13	5	of	of	ADP
ap-1863	13	6	finite	finite	ADJ
ap-1863	13	7	dimensional	dimensional	ADJ
ap-1863	13	8	representations	representation	NOUN
ap-1863	13	9	of	of	ADP
ap-1863	13	10	the	the	DET
ap-1863	13	11	semisimple	semisimple	NOUN
ap-1863	13	12	lie	lie	NOUN
ap-1863	13	13	algebras	algebra	NOUN
ap-1863	13	14	,	,	PUNCT
ap-1863	13	15	which	which	PRON
ap-1863	13	16	are	be	AUX
ap-1863	13	17	direct	direct	ADJ
ap-1863	13	18	sums	sum	NOUN
ap-1863	13	19	of	of	ADP
ap-1863	13	20	simple	simple	ADJ
ap-1863	13	21	ones	one	NOUN
ap-1863	13	22	,	,	PUNCT
ap-1863	13	23	it	it	PRON
ap-1863	13	24	is	be	AUX
ap-1863	13	25	sufficient	sufficient	ADJ
ap-1863	13	26	to	to	PART
ap-1863	13	27	restrict	restrict	VERB
ap-1863	13	28	to	to	ADP
ap-1863	13	29	irreducible	irreducible	ADJ
ap-1863	13	30	finite	finite	ADJ
ap-1863	13	31	dimensional	dimensional	ADJ
ap-1863	13	32	representations	representation	NOUN
ap-1863	13	33	.	.	PUNCT
ap-1863	14	1	the	the	DET
ap-1863	14	2	complete	complete	ADJ
ap-1863	14	3	classification	classification	NOUN
ap-1863	14	4	of	of	ADP
ap-1863	14	5	these	these	DET
ap-1863	14	6	irreducible	irreducible	ADJ
ap-1863	14	7	finite	finite	ADJ
ap-1863	14	8	dimensional	dimensional	ADJ
ap-1863	14	9	representations	representation	NOUN
ap-1863	14	10	is	be	AUX
ap-1863	14	11	known	know	VERB
ap-1863	14	12	.	.	PUNCT
ap-1863	15	1	their	their	PRON
ap-1863	15	2	sets	set	NOUN
ap-1863	15	3	are	be	AUX
ap-1863	15	4	parametrized	parametrize	VERB
ap-1863	15	5	by	by	ADP
ap-1863	15	6	vectors	vector	NOUN
ap-1863	15	7	of	of	ADP
ap-1863	15	8	nonnegative	nonnegative	ADJ
ap-1863	15	9	integers	integer	NOUN
ap-1863	15	10	called	call	VERB
ap-1863	15	11	highest	high	ADJ
ap-1863	15	12	weights	weight	NOUN
ap-1863	15	13	.	.	PUNCT
ap-1863	16	1	moreover	moreover	ADV
ap-1863	16	2	,	,	PUNCT
ap-1863	16	3	the	the	DET
ap-1863	16	4	characters	character	NOUN
ap-1863	16	5	and	and	CCONJ
ap-1863	16	6	dimensions	dimension	NOUN
ap-1863	16	7	of	of	ADP
ap-1863	16	8	such	such	ADJ
ap-1863	16	9	irreducible	irreducible	ADJ
ap-1863	16	10	finite	finite	ADJ
ap-1863	16	11	dimensional	dimensional	ADJ
ap-1863	16	12	representations	representation	NOUN
ap-1863	16	13	are	be	AUX
ap-1863	16	14	explicitly	explicitly	ADV
ap-1863	16	15	known	know	VERB
ap-1863	16	16	because	because	SCONJ
ap-1863	16	17	of	of	ADP
ap-1863	16	18	the	the	DET
ap-1863	16	19	weyl	weyl	VERB
ap-1863	16	20	formula	formula	NOUN
ap-1863	16	21	[	[	X
ap-1863	16	22	2–5	2–5	X
ap-1863	16	23	]	]	X
ap-1863	16	24	.	.	PUNCT
ap-1863	17	1	practical	practical	ADJ
ap-1863	17	2	use	use	NOUN
ap-1863	17	3	of	of	ADP
ap-1863	17	4	the	the	DET
ap-1863	17	5	simple	simple	ADJ
ap-1863	17	6	lie	lie	NOUN
ap-1863	17	7	groups	group	NOUN
ap-1863	17	8	and	and	CCONJ
ap-1863	17	9	lie	lie	VERB
ap-1863	17	10	algebras	algebra	NOUN
ap-1863	17	11	,	,	PUNCT
ap-1863	17	12	serving	serve	VERB
ap-1863	17	13	as	as	ADP
ap-1863	17	14	a	a	DET
ap-1863	17	15	fundamental	fundamental	ADJ
ap-1863	17	16	tool	tool	NOUN
ap-1863	17	17	for	for	ADP
ap-1863	17	18	studying	study	VERB
ap-1863	17	19	the	the	DET
ap-1863	17	20	symmetries	symmetry	NOUN
ap-1863	17	21	of	of	ADP
ap-1863	17	22	systems	system	NOUN
ap-1863	17	23	examined	examine	VERB
ap-1863	17	24	in	in	ADP
ap-1863	17	25	physics	physics	NOUN
ap-1863	17	26	,	,	PUNCT
ap-1863	17	27	often	often	ADV
ap-1863	17	28	involve	involve	VERB
ap-1863	17	29	constructing	construct	VERB
ap-1863	17	30	the	the	DET
ap-1863	17	31	bases	basis	NOUN
ap-1863	17	32	of	of	ADP
ap-1863	17	33	the	the	DET
ap-1863	17	34	spaces	space	NOUN
ap-1863	17	35	on	on	ADP
ap-1863	17	36	which	which	PRON
ap-1863	17	37	their	their	PRON
ap-1863	17	38	finite	finite	ADJ
ap-1863	17	39	dimensional	dimensional	ADJ
ap-1863	17	40	representations	representation	NOUN
ap-1863	17	41	act	act	NOUN
ap-1863	17	42	.	.	PUNCT
ap-1863	18	1	the	the	DET
ap-1863	18	2	best	well	ADV
ap-1863	18	3	known	know	VERB
ap-1863	18	4	example	example	NOUN
ap-1863	18	5	of	of	ADP
ap-1863	18	6	such	such	ADJ
ap-1863	18	7	constructions	construction	NOUN
ap-1863	18	8	are	be	AUX
ap-1863	18	9	two	two	NUM
ap-1863	18	10	works	work	NOUN
ap-1863	18	11	of	of	ADP
ap-1863	18	12	gelfand	gelfand	NOUN
ap-1863	18	13	and	and	CCONJ
ap-1863	18	14	tsetlin	tsetlin	PROPN
ap-1863	18	15	.	.	PUNCT
ap-1863	19	1	in	in	ADP
ap-1863	19	2	two	two	NUM
ap-1863	19	3	famous	famous	ADJ
ap-1863	19	4	papers	paper	NOUN
ap-1863	19	5	(	(	PUNCT
ap-1863	19	6	see	see	VERB
ap-1863	19	7	[	[	X
ap-1863	19	8	6	6	NUM
ap-1863	19	9	]	]	PUNCT
ap-1863	19	10	and	and	CCONJ
ap-1863	19	11	[	[	X
ap-1863	19	12	7	7	NUM
ap-1863	19	13	]	]	NUM
ap-1863	19	14	)	)	PUNCT
ap-1863	19	15	,	,	PUNCT
ap-1863	19	16	they	they	PRON
ap-1863	19	17	gave	give	VERB
ap-1863	19	18	an	an	DET
ap-1863	19	19	explicit	explicit	ADJ
ap-1863	19	20	construction	construction	NOUN
ap-1863	19	21	of	of	ADP
ap-1863	19	22	bases	basis	NOUN
ap-1863	19	23	for	for	ADP
ap-1863	19	24	a	a	DET
ap-1863	19	25	general	general	ADJ
ap-1863	19	26	linear	linear	ADJ
ap-1863	19	27	lie	lie	NOUN
ap-1863	19	28	algebra	algebra	NOUN
ap-1863	19	29	gl(n	gl(n	NUM
ap-1863	19	30	,	,	PUNCT
ap-1863	19	31	c	c	NOUN
ap-1863	19	32	)	)	PUNCT
ap-1863	19	33	(	(	PUNCT
ap-1863	19	34	resp	resp	NOUN
ap-1863	19	35	.	.	PUNCT
ap-1863	20	1	special	special	ADJ
ap-1863	20	2	linear	linear	ADJ
ap-1863	20	3	lie	lie	NOUN
ap-1863	20	4	algebra	algebra	NOUN
ap-1863	20	5	an	an	PRON
ap-1863	20	6	)	)	PUNCT
ap-1863	20	7	and	and	CCONJ
ap-1863	20	8	for	for	ADP
ap-1863	20	9	orthogonal	orthogonal	ADJ
ap-1863	20	10	lie	lie	NOUN
ap-1863	20	11	algebras	algebras	PROPN
ap-1863	20	12	bn	bn	PROPN
ap-1863	20	13	and	and	CCONJ
ap-1863	20	14	dn	dn	PROPN
ap-1863	20	15	(	(	PUNCT
ap-1863	20	16	for	for	ADP
ap-1863	20	17	detailed	detailed	ADJ
ap-1863	20	18	comments	comment	NOUN
ap-1863	20	19	,	,	PUNCT
ap-1863	20	20	see	see	VERB
ap-1863	20	21	also	also	ADV
ap-1863	20	22	[	[	X
ap-1863	20	23	8	8	NUM
ap-1863	20	24	]	]	NUM
ap-1863	20	25	)	)	PUNCT
ap-1863	20	26	.	.	PUNCT
ap-1863	21	1	these	these	DET
ap-1863	21	2	papers	paper	NOUN
ap-1863	21	3	contain	contain	VERB
ap-1863	21	4	no	no	DET
ap-1863	21	5	comments	comment	NOUN
ap-1863	21	6	and	and	CCONJ
ap-1863	21	7	no	no	DET
ap-1863	21	8	methods	method	NOUN
ap-1863	21	9	for	for	ADP
ap-1863	21	10	deriving	derive	VERB
ap-1863	21	11	the	the	DET
ap-1863	21	12	explicit	explicit	ADJ
ap-1863	21	13	formulas	formula	NOUN
ap-1863	21	14	.	.	PUNCT
ap-1863	22	1	these	these	DET
ap-1863	22	2	papers	paper	NOUN
ap-1863	22	3	also	also	ADV
ap-1863	22	4	do	do	AUX
ap-1863	22	5	not	not	PART
ap-1863	22	6	contain	contain	VERB
ap-1863	22	7	any	any	DET
ap-1863	22	8	references	reference	NOUN
ap-1863	22	9	(	(	PUNCT
ap-1863	22	10	the	the	DET
ap-1863	22	11	hint	hint	NOUN
ap-1863	22	12	that	that	SCONJ
ap-1863	22	13	one	one	PRON
ap-1863	22	14	has	have	AUX
ap-1863	22	15	to	to	PART
ap-1863	22	16	verify	verify	VERB
ap-1863	22	17	the	the	DET
ap-1863	22	18	commutation	commutation	NOUN
ap-1863	22	19	relations	relation	NOUN
ap-1863	22	20	by	by	ADP
ap-1863	22	21	direct	direct	ADJ
ap-1863	22	22	calculation	calculation	NOUN
ap-1863	22	23	is	be	AUX
ap-1863	22	24	not	not	PART
ap-1863	22	25	very	very	ADV
ap-1863	22	26	useful	useful	ADJ
ap-1863	22	27	for	for	ADP
ap-1863	22	28	the	the	DET
ap-1863	22	29	proof	proof	NOUN
ap-1863	22	30	)	)	PUNCT
ap-1863	22	31	.	.	PUNCT
ap-1863	23	1	it	it	PRON
ap-1863	23	2	is	be	AUX
ap-1863	23	3	therefore	therefore	ADV
ap-1863	23	4	no	no	DET
ap-1863	23	5	wonder	wonder	NOUN
ap-1863	23	6	that	that	SCONJ
ap-1863	23	7	their	their	PRON
ap-1863	23	8	formulas	formula	NOUN
ap-1863	23	9	were	be	AUX
ap-1863	23	10	re	re	VERB
ap-1863	23	11	-	-	VERB
ap-1863	23	12	derived	derived	ADJ
ap-1863	23	13	and	and	CCONJ
ap-1863	23	14	verified	verify	VERB
ap-1863	23	15	by	by	ADP
ap-1863	23	16	other	other	ADJ
ap-1863	23	17	authors	author	NOUN
ap-1863	23	18	.	.	PUNCT
ap-1863	24	1	verification	verification	NOUN
ap-1863	24	2	and/or	and/or	CCONJ
ap-1863	24	3	an	an	DET
ap-1863	24	4	independent	independent	ADJ
ap-1863	24	5	derivation	derivation	NOUN
ap-1863	24	6	of	of	ADP
ap-1863	24	7	these	these	DET
ap-1863	24	8	formulas	formula	NOUN
ap-1863	24	9	was	be	AUX
ap-1863	24	10	given	give	VERB
ap-1863	24	11	in	in	ADP
ap-1863	24	12	the	the	DET
ap-1863	24	13	papers	paper	NOUN
ap-1863	24	14	by	by	ADP
ap-1863	24	15	baird	baird	PROPN
ap-1863	24	16	and	and	CCONJ
ap-1863	24	17	biedenharn	biedenharn	PROPN
ap-1863	24	18	(	(	PUNCT
ap-1863	24	19	see	see	VERB
ap-1863	24	20	[	[	X
ap-1863	24	21	9	9	NUM
ap-1863	24	22	,	,	PUNCT
ap-1863	24	23	10	10	NUM
ap-1863	24	24	]	]	NUM
ap-1863	24	25	)	)	PUNCT
ap-1863	24	26	,	,	PUNCT
ap-1863	24	27	and	and	CCONJ
ap-1863	24	28	also	also	ADV
ap-1863	24	29	by	by	ADP
ap-1863	24	30	other	other	ADJ
ap-1863	24	31	authors	author	NOUN
ap-1863	24	32	[	[	X
ap-1863	24	33	11–14	11–14	NUM
ap-1863	24	34	]	]	PUNCT
ap-1863	24	35	.	.	PUNCT
ap-1863	25	1	after	after	ADP
ap-1863	25	2	gelfand	gelfand	PROPN
ap-1863	25	3	and	and	CCONJ
ap-1863	25	4	tsetlin	tsetlin	PROPN
ap-1863	25	5	’s	’s	PART
ap-1863	25	6	construction	construction	NOUN
ap-1863	25	7	of	of	ADP
ap-1863	25	8	representations	representation	NOUN
ap-1863	25	9	,	,	PUNCT
ap-1863	25	10	in	in	ADP
ap-1863	25	11	the	the	DET
ap-1863	25	12	second	second	ADJ
ap-1863	25	13	half	half	NOUN
ap-1863	25	14	of	of	ADP
ap-1863	25	15	the	the	DET
ap-1863	25	16	20th	20th	ADJ
ap-1863	25	17	century	century	NOUN
ap-1863	25	18	and	and	CCONJ
ap-1863	25	19	later	later	ADV
ap-1863	25	20	,	,	PUNCT
ap-1863	25	21	a	a	DET
ap-1863	25	22	range	range	NOUN
ap-1863	25	23	of	of	ADP
ap-1863	25	24	different	different	ADJ
ap-1863	25	25	approaches	approach	NOUN
ap-1863	25	26	were	be	AUX
ap-1863	25	27	developed	develop	VERB
ap-1863	25	28	and	and	CCONJ
ap-1863	25	29	many	many	ADJ
ap-1863	25	30	techniques	technique	NOUN
ap-1863	25	31	were	be	AUX
ap-1863	25	32	adopted	adopt	VERB
ap-1863	25	33	to	to	PART
ap-1863	25	34	construct	construct	VERB
ap-1863	25	35	the	the	DET
ap-1863	25	36	bases	basis	NOUN
ap-1863	25	37	of	of	ADP
ap-1863	25	38	the	the	DET
ap-1863	25	39	representations	representation	NOUN
ap-1863	25	40	of	of	ADP
ap-1863	25	41	classical	classical	ADJ
ap-1863	25	42	series	series	NOUN
ap-1863	25	43	of	of	ADP
ap-1863	25	44	lie	lie	NOUN
ap-1863	25	45	algebras	algebra	NOUN
ap-1863	25	46	.	.	PUNCT
ap-1863	26	1	we	we	PRON
ap-1863	26	2	can	can	AUX
ap-1863	26	3	mention	mention	VERB
ap-1863	26	4	here	here	ADV
ap-1863	26	5	the	the	DET
ap-1863	26	6	gould	gould	PROPN
ap-1863	26	7	paper	paper	NOUN
ap-1863	27	1	[	[	X
ap-1863	27	2	15	15	NUM
ap-1863	27	3	]	]	X
ap-1863	27	4	,	,	PUNCT
ap-1863	27	5	which	which	PRON
ap-1863	27	6	made	make	VERB
ap-1863	27	7	use	use	NOUN
ap-1863	27	8	of	of	ADP
ap-1863	27	9	polynomial	polynomial	ADJ
ap-1863	27	10	identities	identity	NOUN
ap-1863	27	11	satisfied	satisfy	VERB
ap-1863	27	12	by	by	ADP
ap-1863	27	13	the	the	DET
ap-1863	27	14	generators	generator	NOUN
ap-1863	27	15	of	of	ADP
ap-1863	27	16	the	the	DET
ap-1863	27	17	corresponding	corresponding	ADJ
ap-1863	27	18	lie	lie	NOUN
ap-1863	27	19	group	group	NOUN
ap-1863	27	20	,	,	PUNCT
ap-1863	27	21	an	an	DET
ap-1863	27	22	approach	approach	NOUN
ap-1863	27	23	which	which	PRON
ap-1863	27	24	was	be	AUX
ap-1863	27	25	then	then	ADV
ap-1863	27	26	generalized	generalize	VERB
ap-1863	27	27	then	then	ADV
ap-1863	27	28	to	to	ADP
ap-1863	27	29	kac	kac	PROPN
ap-1863	27	30	-	-	PUNCT
ap-1863	27	31	moody	moody	PROPN
ap-1863	27	32	algebras	algebra	NOUN
ap-1863	28	1	[	[	X
ap-1863	28	2	16	16	NUM
ap-1863	28	3	]	]	PUNCT
ap-1863	28	4	,	,	PUNCT
ap-1863	28	5	and	and	CCONJ
ap-1863	28	6	the	the	DET
ap-1863	28	7	approach	approach	NOUN
ap-1863	28	8	of	of	ADP
ap-1863	28	9	asherova	asherova	NOUN
ap-1863	28	10	,	,	PUNCT
ap-1863	28	11	smirnov	smirnov	PROPN
ap-1863	28	12	and	and	CCONJ
ap-1863	28	13	tolstoy	tolstoy	NOUN
ap-1863	28	14	involving	involve	VERB
ap-1863	28	15	projection	projection	NOUN
ap-1863	28	16	operators	operator	NOUN
ap-1863	28	17	[	[	X
ap-1863	28	18	17	17	NUM
ap-1863	28	19	,	,	PUNCT
ap-1863	28	20	18	18	NUM
ap-1863	28	21	]	]	PUNCT
ap-1863	28	22	,	,	PUNCT
ap-1863	28	23	which	which	PRON
ap-1863	28	24	prove	prove	VERB
ap-1863	28	25	their	their	PRON
ap-1863	28	26	usefulness	usefulness	NOUN
ap-1863	28	27	also	also	ADV
ap-1863	28	28	in	in	ADP
ap-1863	28	29	the	the	DET
ap-1863	28	30	field	field	NOUN
ap-1863	28	31	of	of	ADP
ap-1863	28	32	lie	lie	NOUN
ap-1863	28	33	superalgebras	superalgebra	NOUN
ap-1863	28	34	and	and	CCONJ
ap-1863	28	35	quantum	quantum	NOUN
ap-1863	28	36	algebras	algebra	NOUN
ap-1863	29	1	[	[	X
ap-1863	29	2	19	19	NUM
ap-1863	29	3	]	]	PUNCT
ap-1863	29	4	.	.	PUNCT
ap-1863	30	1	the	the	DET
ap-1863	30	2	results	result	NOUN
ap-1863	30	3	of	of	ADP
ap-1863	30	4	tarasov	tarasov	NOUN
ap-1863	30	5	and	and	CCONJ
ap-1863	30	6	nazarov	nazarov	ADJ
ap-1863	30	7	[	[	X
ap-1863	30	8	20	20	NUM
ap-1863	30	9	]	]	PUNCT
ap-1863	30	10	also	also	ADV
ap-1863	30	11	belong	belong	VERB
ap-1863	30	12	to	to	ADP
ap-1863	30	13	this	this	DET
ap-1863	30	14	group	group	NOUN
ap-1863	30	15	.	.	PUNCT
ap-1863	31	1	another	another	DET
ap-1863	31	2	approach	approach	NOUN
ap-1863	31	3	,	,	PUNCT
ap-1863	31	4	based	base	VERB
ap-1863	31	5	on	on	ADP
ap-1863	31	6	using	use	VERB
ap-1863	31	7	weyl	weyl	VERB
ap-1863	31	8	realization	realization	NOUN
ap-1863	31	9	[	[	X
ap-1863	31	10	21	21	NUM
ap-1863	31	11	]	]	PUNCT
ap-1863	31	12	of	of	ADP
ap-1863	31	13	the	the	DET
ap-1863	31	14	representations	representation	NOUN
ap-1863	31	15	of	of	ADP
ap-1863	31	16	corresponding	correspond	VERB
ap-1863	31	17	groups	group	NOUN
ap-1863	31	18	in	in	ADP
ap-1863	31	19	tensor	tensor	NOUN
ap-1863	31	20	spaces	space	NOUN
ap-1863	31	21	,	,	PUNCT
ap-1863	31	22	was	be	AUX
ap-1863	31	23	developed	develop	VERB
ap-1863	31	24	in	in	ADP
ap-1863	31	25	many	many	ADJ
ap-1863	31	26	papers	paper	NOUN
ap-1863	31	27	[	[	X
ap-1863	31	28	22–26	22–26	NOUN
ap-1863	31	29	]	]	PUNCT
ap-1863	31	30	.	.	PUNCT
ap-1863	32	1	so	so	ADV
ap-1863	32	2	-	-	PUNCT
ap-1863	32	3	called	call	VERB
ap-1863	32	4	special	special	ADJ
ap-1863	32	5	bases	basis	NOUN
ap-1863	32	6	were	be	AUX
ap-1863	32	7	constructed	construct	VERB
ap-1863	32	8	by	by	ADP
ap-1863	32	9	de	de	X
ap-1863	32	10	concini	concini	PROPN
ap-1863	32	11	and	and	CCONJ
ap-1863	32	12	kazhdan	kazhdan	VERB
ap-1863	33	1	[	[	X
ap-1863	33	2	27	27	NUM
ap-1863	33	3	]	]	PUNCT
ap-1863	33	4	,	,	PUNCT
ap-1863	33	5	and	and	CCONJ
ap-1863	33	6	their	their	PRON
ap-1863	33	7	q	q	NOUN
ap-1863	33	8	-	-	PUNCT
ap-1863	33	9	analogs	analog	NOUN
ap-1863	33	10	by	by	ADP
ap-1863	33	11	xi	xi	PROPN
ap-1863	34	1	[	[	X
ap-1863	34	2	28	28	NUM
ap-1863	34	3	]	]	PUNCT
ap-1863	34	4	.	.	PUNCT
ap-1863	35	1	proper	proper	ADJ
ap-1863	35	2	bases	basis	NOUN
ap-1863	35	3	were	be	AUX
ap-1863	35	4	constructed	construct	VERB
ap-1863	35	5	by	by	ADP
ap-1863	35	6	gelfand	gelfand	NOUN
ap-1863	35	7	and	and	CCONJ
ap-1863	35	8	zelevinsky	zelevinsky	PROPN
ap-1863	35	9	[	[	X
ap-1863	35	10	29	29	NUM
ap-1863	35	11	]	]	PUNCT
ap-1863	35	12	,	,	PUNCT
ap-1863	35	13	retakh	retakh	NOUN
ap-1863	35	14	and	and	CCONJ
ap-1863	35	15	zelevinsky	zelevinsky	PROPN
ap-1863	36	1	[	[	X
ap-1863	36	2	30	30	NUM
ap-1863	36	3	]	]	PUNCT
ap-1863	36	4	,	,	PUNCT
ap-1863	36	5	and	and	CCONJ
ap-1863	36	6	similar	similar	ADJ
ap-1863	36	7	good	good	ADJ
ap-1863	36	8	bases	basis	NOUN
ap-1863	36	9	were	be	AUX
ap-1863	36	10	constructed	construct	VERB
ap-1863	36	11	by	by	ADP
ap-1863	36	12	mathieu	mathieu	PROPN
ap-1863	37	1	[	[	X
ap-1863	37	2	31	31	NUM
ap-1863	37	3	]	]	PUNCT
ap-1863	37	4	.	.	PUNCT
ap-1863	38	1	another	another	DET
ap-1863	38	2	well	well	ADV
ap-1863	38	3	known	know	VERB
ap-1863	38	4	group	group	NOUN
ap-1863	38	5	of	of	ADP
ap-1863	38	6	bases	basis	NOUN
ap-1863	38	7	are	be	AUX
ap-1863	38	8	crystal	crystal	NOUN
ap-1863	38	9	bases	basis	NOUN
ap-1863	38	10	.	.	PUNCT
ap-1863	39	1	they	they	PRON
ap-1863	39	2	were	be	AUX
ap-1863	39	3	constructed	construct	VERB
ap-1863	39	4	by	by	ADP
ap-1863	39	5	lusztig	lusztig	ADJ
ap-1863	39	6	[	[	X
ap-1863	39	7	32	32	NUM
ap-1863	39	8	,	,	PUNCT
ap-1863	39	9	33	33	NUM
ap-1863	39	10	]	]	PUNCT
ap-1863	39	11	,	,	PUNCT
ap-1863	39	12	kashiwara	kashiwara	PROPN
ap-1863	40	1	[	[	X
ap-1863	40	2	34	34	NUM
ap-1863	40	3	]	]	PUNCT
ap-1863	40	4	,	,	PUNCT
ap-1863	40	5	du	du	PROPN
ap-1863	41	1	[	[	X
ap-1863	41	2	35	35	NUM
ap-1863	41	3	,	,	PUNCT
ap-1863	41	4	36	36	NUM
ap-1863	41	5	]	]	PUNCT
ap-1863	41	6	,	,	PUNCT
ap-1863	41	7	kang	kang	PROPN
ap-1863	42	1	[	[	X
ap-1863	42	2	37	37	NUM
ap-1863	42	3	]	]	PUNCT
ap-1863	42	4	,	,	PUNCT
ap-1863	42	5	and	and	CCONJ
ap-1863	42	6	others	other	NOUN
ap-1863	43	1	[	[	X
ap-1863	43	2	38–41	38–41	NUM
ap-1863	43	3	]	]	PUNCT
ap-1863	43	4	.	.	PUNCT
ap-1863	44	1	450	450	NUM
ap-1863	44	2	http://dx.doi.org/10.14311/ap.2013.53.0450	http://dx.doi.org/10.14311/ap.2013.53.0450	NOUN
ap-1863	44	3	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-1863	44	4	vol	vol	NOUN
ap-1863	44	5	.	.	PUNCT
ap-1863	45	1	53	53	NUM
ap-1863	45	2	no	no	NOUN
ap-1863	45	3	.	.	PUNCT
ap-1863	46	1	5/2013	5/2013	NUM
ap-1863	46	2	note	note	NOUN
ap-1863	46	3	on	on	ADP
ap-1863	46	4	verma	verma	PROPN
ap-1863	46	5	bases	basis	NOUN
ap-1863	46	6	for	for	ADP
ap-1863	46	7	representations	representation	NOUN
ap-1863	46	8	of	of	ADP
ap-1863	46	9	simple	simple	ADJ
ap-1863	46	10	lie	lie	NOUN
ap-1863	46	11	algebras	algebras	PROPN
ap-1863	46	12	2	2	PROPN
ap-1863	46	13	.	.	PUNCT
ap-1863	46	14	verma	verma	PROPN
ap-1863	46	15	bases	basis	NOUN
ap-1863	46	16	besides	besides	SCONJ
ap-1863	46	17	these	these	DET
ap-1863	46	18	approaches	approach	NOUN
ap-1863	46	19	,	,	PUNCT
ap-1863	46	20	an	an	DET
ap-1863	46	21	important	important	ADJ
ap-1863	46	22	role	role	NOUN
ap-1863	46	23	is	be	AUX
ap-1863	46	24	played	play	VERB
ap-1863	46	25	by	by	ADP
ap-1863	46	26	bases	basis	NOUN
ap-1863	46	27	which	which	PRON
ap-1863	46	28	have	have	VERB
ap-1863	46	29	special	special	ADJ
ap-1863	46	30	properties	property	NOUN
ap-1863	46	31	as	as	ADP
ap-1863	46	32	bases	basis	NOUN
ap-1863	46	33	in	in	ADP
ap-1863	46	34	the	the	DET
ap-1863	46	35	universal	universal	ADJ
ap-1863	46	36	enveloping	enveloping	NOUN
ap-1863	46	37	algebra	algebra	NOUN
ap-1863	46	38	of	of	ADP
ap-1863	46	39	a	a	DET
ap-1863	46	40	given	give	VERB
ap-1863	46	41	simple	simple	ADJ
ap-1863	46	42	lie	lie	NOUN
ap-1863	46	43	algebra	algebra	NOUN
ap-1863	46	44	,	,	PUNCT
ap-1863	46	45	and	and	CCONJ
ap-1863	46	46	which	which	PRON
ap-1863	46	47	can	can	AUX
ap-1863	46	48	then	then	ADV
ap-1863	46	49	be	be	AUX
ap-1863	46	50	restricted	restrict	VERB
ap-1863	46	51	by	by	ADP
ap-1863	46	52	taking	take	VERB
ap-1863	46	53	a	a	DET
ap-1863	46	54	suitable	suitable	ADJ
ap-1863	46	55	subset	subset	NOUN
ap-1863	46	56	to	to	ADP
ap-1863	46	57	the	the	DET
ap-1863	46	58	basis	basis	NOUN
ap-1863	46	59	of	of	ADP
ap-1863	46	60	a	a	DET
ap-1863	46	61	given	give	VERB
ap-1863	46	62	representation	representation	NOUN
ap-1863	46	63	of	of	ADP
ap-1863	46	64	that	that	DET
ap-1863	46	65	lie	lie	NOUN
ap-1863	46	66	algebra	algebra	NOUN
ap-1863	46	67	.	.	PUNCT
ap-1863	47	1	such	such	ADJ
ap-1863	47	2	bases	basis	NOUN
ap-1863	47	3	are	be	AUX
ap-1863	47	4	called	call	VERB
ap-1863	47	5	monomial	monomial	ADJ
ap-1863	47	6	bases	basis	NOUN
ap-1863	47	7	,	,	PUNCT
ap-1863	47	8	and	and	CCONJ
ap-1863	47	9	were	be	AUX
ap-1863	47	10	constructed	construct	VERB
ap-1863	47	11	in	in	ADP
ap-1863	47	12	the	the	DET
ap-1863	47	13	standard	standard	ADJ
ap-1863	47	14	monomial	monomial	ADJ
ap-1863	47	15	theories	theory	NOUN
ap-1863	47	16	developed	develop	VERB
ap-1863	47	17	by	by	ADP
ap-1863	47	18	lakshmibai	lakshmibai	PROPN
ap-1863	47	19	,	,	PUNCT
ap-1863	47	20	musili	musili	NOUN
ap-1863	47	21	and	and	CCONJ
ap-1863	47	22	seshadri	seshadri	ADJ
ap-1863	47	23	[	[	X
ap-1863	47	24	42	42	NUM
ap-1863	47	25	]	]	PUNCT
ap-1863	47	26	,	,	PUNCT
ap-1863	47	27	by	by	ADP
ap-1863	47	28	littelmann	littelmann	NOUN
ap-1863	48	1	[	[	X
ap-1863	48	2	1	1	NUM
ap-1863	48	3	,	,	PUNCT
ap-1863	48	4	43	43	NUM
ap-1863	48	5	]	]	PUNCT
ap-1863	48	6	,	,	PUNCT
ap-1863	48	7	its	its	PRON
ap-1863	48	8	q	q	NOUN
ap-1863	48	9	-	-	PUNCT
ap-1863	48	10	analogs	analog	NOUN
ap-1863	48	11	by	by	ADP
ap-1863	48	12	chari	chari	PROPN
ap-1863	48	13	and	and	CCONJ
ap-1863	48	14	xi	xi	X
ap-1863	49	1	[	[	X
ap-1863	49	2	44	44	NUM
ap-1863	49	3	]	]	PUNCT
ap-1863	49	4	and	and	CCONJ
ap-1863	49	5	others	other	NOUN
ap-1863	49	6	.	.	PUNCT
ap-1863	50	1	one	one	NUM
ap-1863	50	2	of	of	ADP
ap-1863	50	3	the	the	DET
ap-1863	50	4	advantages	advantage	NOUN
ap-1863	50	5	of	of	ADP
ap-1863	50	6	these	these	DET
ap-1863	50	7	bases	basis	NOUN
ap-1863	50	8	is	be	AUX
ap-1863	50	9	that	that	SCONJ
ap-1863	50	10	the	the	DET
ap-1863	50	11	basis	basis	NOUN
ap-1863	50	12	vectors	vector	NOUN
ap-1863	50	13	are	be	AUX
ap-1863	50	14	eigenvectors	eigenvector	NOUN
ap-1863	50	15	of	of	ADP
ap-1863	50	16	cartan	cartan	ADJ
ap-1863	50	17	subalgebra	subalgebra	NOUN
ap-1863	50	18	,	,	PUNCT
ap-1863	50	19	and	and	CCONJ
ap-1863	50	20	therefore	therefore	ADV
ap-1863	50	21	such	such	DET
ap-1863	50	22	a	a	DET
ap-1863	50	23	basis	basis	NOUN
ap-1863	50	24	is	be	AUX
ap-1863	50	25	suitable	suitable	ADJ
ap-1863	50	26	for	for	ADP
ap-1863	50	27	various	various	ADJ
ap-1863	50	28	modifications	modification	NOUN
ap-1863	50	29	.	.	PUNCT
ap-1863	51	1	on	on	ADP
ap-1863	51	2	the	the	DET
ap-1863	51	3	other	other	ADJ
ap-1863	51	4	hand	hand	NOUN
ap-1863	51	5	,	,	PUNCT
ap-1863	51	6	there	there	PRON
ap-1863	51	7	is	be	VERB
ap-1863	51	8	no	no	DET
ap-1863	51	9	explicit	explicit	ADJ
ap-1863	51	10	form	form	NOUN
ap-1863	51	11	of	of	ADP
ap-1863	51	12	matrix	matrix	NOUN
ap-1863	51	13	elements	element	NOUN
ap-1863	51	14	of	of	ADP
ap-1863	51	15	operators	operator	NOUN
ap-1863	51	16	expressed	express	VERB
ap-1863	51	17	in	in	ADP
ap-1863	51	18	these	these	DET
ap-1863	51	19	bases	basis	NOUN
ap-1863	51	20	.	.	PUNCT
ap-1863	52	1	verma	verma	PROPN
ap-1863	52	2	bases	basis	NOUN
ap-1863	52	3	as	as	SCONJ
ap-1863	52	4	introduced	introduce	VERB
ap-1863	52	5	in	in	ADP
ap-1863	52	6	[	[	X
ap-1863	52	7	45	45	NUM
ap-1863	52	8	]	]	PUNCT
ap-1863	52	9	are	be	AUX
ap-1863	52	10	of	of	ADP
ap-1863	52	11	this	this	DET
ap-1863	52	12	type	type	NOUN
ap-1863	52	13	.	.	PUNCT
ap-1863	53	1	these	these	DET
ap-1863	53	2	bases	basis	NOUN
ap-1863	53	3	were	be	AUX
ap-1863	53	4	constructed	construct	VERB
ap-1863	53	5	for	for	ADP
ap-1863	53	6	the	the	DET
ap-1863	53	7	lie	lie	NOUN
ap-1863	53	8	algebras	algebra	VERB
ap-1863	53	9	an	an	PRON
ap-1863	53	10	in	in	ADP
ap-1863	53	11	[	[	X
ap-1863	53	12	46	46	NUM
ap-1863	53	13	]	]	PUNCT
ap-1863	53	14	and	and	CCONJ
ap-1863	53	15	for	for	ADP
ap-1863	53	16	some	some	DET
ap-1863	53	17	concrete	concrete	ADJ
ap-1863	53	18	examples	example	NOUN
ap-1863	53	19	of	of	ADP
ap-1863	53	20	other	other	ADJ
ap-1863	53	21	lie	lie	NOUN
ap-1863	53	22	algebras	algebra	NOUN
ap-1863	53	23	of	of	ADP
ap-1863	53	24	low	low	ADJ
ap-1863	53	25	rank	rank	NOUN
ap-1863	53	26	(	(	PUNCT
ap-1863	53	27	see	see	VERB
ap-1863	53	28	also	also	ADV
ap-1863	53	29	[	[	X
ap-1863	53	30	47	47	NUM
ap-1863	53	31	]	]	PUNCT
ap-1863	53	32	)	)	PUNCT
ap-1863	53	33	.	.	PUNCT
ap-1863	54	1	in	in	ADP
ap-1863	54	2	[	[	X
ap-1863	54	3	48	48	NUM
ap-1863	54	4	,	,	PUNCT
ap-1863	54	5	49	49	NUM
ap-1863	54	6	]	]	PUNCT
ap-1863	54	7	proof	proof	NOUN
ap-1863	54	8	of	of	ADP
ap-1863	54	9	the	the	DET
ap-1863	54	10	so	so	ADV
ap-1863	54	11	-	-	PUNCT
ap-1863	54	12	called	call	VERB
ap-1863	54	13	verma	verma	PROPN
ap-1863	54	14	conjecture	conjecture	NOUN
ap-1863	54	15	for	for	ADP
ap-1863	54	16	the	the	DET
ap-1863	54	17	lie	lie	NOUN
ap-1863	54	18	algebra	algebra	NOUN
ap-1863	54	19	an	an	PRON
ap-1863	54	20	was	be	AUX
ap-1863	54	21	given	give	VERB
ap-1863	54	22	by	by	ADP
ap-1863	54	23	raghavan	raghavan	PROPN
ap-1863	54	24	and	and	CCONJ
ap-1863	54	25	sankaran	sankaran	ADJ
ap-1863	54	26	.	.	PUNCT
ap-1863	55	1	note	note	VERB
ap-1863	55	2	that	that	SCONJ
ap-1863	55	3	the	the	DET
ap-1863	55	4	basis	basis	NOUN
ap-1863	55	5	in	in	ADP
ap-1863	55	6	enveloping	envelop	VERB
ap-1863	55	7	algebra	algebra	NOUN
ap-1863	55	8	from	from	ADP
ap-1863	55	9	which	which	PRON
ap-1863	55	10	we	we	PRON
ap-1863	55	11	can	can	AUX
ap-1863	55	12	obtain	obtain	VERB
ap-1863	55	13	the	the	DET
ap-1863	55	14	corresponding	corresponding	ADJ
ap-1863	55	15	verma	verma	PROPN
ap-1863	55	16	basis	basis	NOUN
ap-1863	55	17	by	by	ADP
ap-1863	55	18	restriction	restriction	NOUN
ap-1863	55	19	was	be	AUX
ap-1863	55	20	given	give	VERB
ap-1863	55	21	in	in	ADP
ap-1863	55	22	[	[	X
ap-1863	55	23	1	1	NUM
ap-1863	55	24	]	]	PUNCT
ap-1863	55	25	.	.	PUNCT
ap-1863	56	1	the	the	DET
ap-1863	56	2	basis	basis	NOUN
ap-1863	56	3	vectors	vector	NOUN
ap-1863	56	4	of	of	ADP
ap-1863	56	5	the	the	DET
ap-1863	56	6	verma	verma	PROPN
ap-1863	56	7	basis	basis	NOUN
ap-1863	56	8	are	be	AUX
ap-1863	56	9	constructed	construct	VERB
ap-1863	56	10	from	from	ADP
ap-1863	56	11	the	the	DET
ap-1863	56	12	highest	high	ADJ
ap-1863	56	13	weight	weight	NOUN
ap-1863	56	14	vector	vector	NOUN
ap-1863	56	15	(	(	PUNCT
ap-1863	56	16	vacuum	vacuum	NOUN
ap-1863	56	17	state	state	NOUN
ap-1863	56	18	)	)	PUNCT
ap-1863	56	19	in	in	ADP
ap-1863	56	20	a	a	DET
ap-1863	56	21	way	way	NOUN
ap-1863	56	22	consisting	consist	VERB
ap-1863	56	23	of	of	ADP
ap-1863	56	24	the	the	DET
ap-1863	56	25	action	action	NOUN
ap-1863	56	26	of	of	ADP
ap-1863	56	27	some	some	DET
ap-1863	56	28	specified	specify	VERB
ap-1863	56	29	sequence	sequence	NOUN
ap-1863	56	30	of	of	ADP
ap-1863	56	31	the	the	DET
ap-1863	56	32	elements	element	NOUN
ap-1863	56	33	corresponding	correspond	VERB
ap-1863	56	34	to	to	ADP
ap-1863	56	35	simple	simple	ADJ
ap-1863	56	36	roots	root	NOUN
ap-1863	56	37	.	.	PUNCT
ap-1863	57	1	each	each	DET
ap-1863	57	2	set	set	NOUN
ap-1863	57	3	of	of	ADP
ap-1863	57	4	basis	basis	NOUN
ap-1863	57	5	vectors	vector	NOUN
ap-1863	57	6	is	be	AUX
ap-1863	57	7	constructed	construct	VERB
ap-1863	57	8	using	use	VERB
ap-1863	57	9	sequences	sequence	NOUN
ap-1863	57	10	given	give	VERB
ap-1863	57	11	by	by	ADP
ap-1863	57	12	a	a	DET
ap-1863	57	13	certain	certain	ADJ
ap-1863	57	14	set	set	NOUN
ap-1863	57	15	of	of	ADP
ap-1863	57	16	inequalities	inequality	NOUN
ap-1863	57	17	(	(	PUNCT
ap-1863	57	18	called	call	VERB
ap-1863	57	19	verma	verma	PROPN
ap-1863	57	20	inequalities	inequality	NOUN
ap-1863	57	21	)	)	PUNCT
ap-1863	57	22	.	.	PUNCT
ap-1863	58	1	let	let	VERB
ap-1863	58	2	us	we	PRON
ap-1863	58	3	briefly	briefly	ADV
ap-1863	58	4	describe	describe	VERB
ap-1863	58	5	the	the	DET
ap-1863	58	6	main	main	ADJ
ap-1863	58	7	result	result	NOUN
ap-1863	58	8	for	for	SCONJ
ap-1863	58	9	the	the	DET
ap-1863	58	10	lie	lie	NOUN
ap-1863	58	11	algebra	algebra	NOUN
ap-1863	58	12	an	an	PRON
ap-1863	58	13	.	.	PUNCT
ap-1863	59	1	let	let	VERB
ap-1863	59	2	an	an	DET
ap-1863	59	3	=	=	PUNCT
ap-1863	59	4	sl(n+	sl(n+	NOUN
ap-1863	59	5	1,c	1,c	NOUN
ap-1863	59	6	)	)	PUNCT
ap-1863	60	1	=	=	SYM
ap-1863	60	2	n+⊕h⊕n−	n+⊕h⊕n−	ADJ
ap-1863	60	3	be	be	AUX
ap-1863	60	4	the	the	DET
ap-1863	60	5	decomposition	decomposition	NOUN
ap-1863	60	6	of	of	ADP
ap-1863	60	7	the	the	DET
ap-1863	60	8	lie	lie	NOUN
ap-1863	60	9	algebra	algebra	VERB
ap-1863	60	10	sl(n+	sl(n+	PROPN
ap-1863	60	11	1,c	1,c	NOUN
ap-1863	60	12	)	)	PUNCT
ap-1863	60	13	into	into	ADP
ap-1863	60	14	strictly	strictly	ADV
ap-1863	60	15	upper	upper	ADJ
ap-1863	60	16	triangular	triangular	NOUN
ap-1863	60	17	,	,	PUNCT
ap-1863	60	18	diagonal	diagonal	ADJ
ap-1863	60	19	and	and	CCONJ
ap-1863	60	20	strictly	strictly	ADV
ap-1863	60	21	lower	low	ADJ
ap-1863	60	22	triangular	triangular	NOUN
ap-1863	60	23	matrices	matrix	NOUN
ap-1863	60	24	.	.	PUNCT
ap-1863	61	1	denote	denote	VERB
ap-1863	61	2	u(an	u(an	PROPN
ap-1863	61	3	)	)	PUNCT
ap-1863	61	4	,	,	PUNCT
ap-1863	61	5	u(a+	u(a+	NOUN
ap-1863	61	6	n	n	X
ap-1863	61	7	)	)	PUNCT
ap-1863	61	8	and	and	CCONJ
ap-1863	61	9	u(a−n	u(a−n	PROPN
ap-1863	61	10	)	)	PUNCT
ap-1863	61	11	corresponding	correspond	VERB
ap-1863	61	12	enveloping	enveloping	NOUN
ap-1863	61	13	algebras	algebra	NOUN
ap-1863	61	14	of	of	ADP
ap-1863	61	15	an	an	DET
ap-1863	61	16	,	,	PUNCT
ap-1863	61	17	n+	n+	PUNCT
ap-1863	61	18	and	and	CCONJ
ap-1863	61	19	n−.	n−.	VERB
ap-1863	61	20	let	let	VERB
ap-1863	61	21	φ	φ	PROPN
ap-1863	61	22	be	be	AUX
ap-1863	61	23	the	the	DET
ap-1863	61	24	root	root	NOUN
ap-1863	61	25	system	system	NOUN
ap-1863	61	26	of	of	ADP
ap-1863	61	27	an	an	DET
ap-1863	61	28	and	and	CCONJ
ap-1863	61	29	fixed	fixed	ADJ
ap-1863	61	30	h	h	NOUN
ap-1863	61	31	such	such	ADJ
ap-1863	61	32	that	that	SCONJ
ap-1863	61	33	φ	φ	PROPN
ap-1863	61	34	=	=	SYM
ap-1863	61	35	φ+	φ+	X
ap-1863	61	36	∪	∪	ADP
ap-1863	61	37	φ−	φ−	PROPN
ap-1863	61	38	,	,	PUNCT
ap-1863	61	39	where	where	SCONJ
ap-1863	61	40	n+	n+	AUX
ap-1863	61	41	=	=	PROPN
ap-1863	61	42	⊕	⊕	PROPN
ap-1863	61	43	β∈φ+	β∈φ+	PUNCT
ap-1863	61	44	gβ	gβ	VERB
ap-1863	61	45	.	.	PUNCT
ap-1863	62	1	for	for	ADP
ap-1863	62	2	the	the	DET
ap-1863	62	3	positive	positive	ADJ
ap-1863	62	4	root	root	NOUN
ap-1863	62	5	β	β	X
ap-1863	62	6	∈	∈	PROPN
ap-1863	62	7	φ+	φ+	NOUN
ap-1863	62	8	denote	denote	VERB
ap-1863	62	9	by	by	ADP
ap-1863	62	10	fβ	fβ	ADJ
ap-1863	62	11	∈	∈	PROPN
ap-1863	62	12	gβ	gβ	NOUN
ap-1863	62	13	and	and	CCONJ
ap-1863	62	14	eβ	eβ	NOUN
ap-1863	62	15	∈	∈	PROPN
ap-1863	62	16	g−β	g−β	PROPN
ap-1863	62	17	fixed	fix	VERB
ap-1863	62	18	elements	element	NOUN
ap-1863	62	19	of	of	ADP
ap-1863	62	20	the	the	DET
ap-1863	62	21	chevalley	chevalley	ADJ
ap-1863	62	22	basis	basis	NOUN
ap-1863	62	23	of	of	ADP
ap-1863	62	24	an	an	PRON
ap-1863	62	25	.	.	NOUN
ap-1863	62	26	for	for	ADP
ap-1863	62	27	a	a	DET
ap-1863	62	28	fixed	fix	VERB
ap-1863	62	29	ordering	ordering	NOUN
ap-1863	62	30	of	of	ADP
ap-1863	62	31	simple	simple	ADJ
ap-1863	62	32	roots	root	NOUN
ap-1863	62	33	{	{	PUNCT
ap-1863	62	34	β1	β1	NOUN
ap-1863	62	35	,	,	PUNCT
ap-1863	62	36	.	.	PUNCT
ap-1863	62	37	.	.	PUNCT
ap-1863	63	1	.	.	PUNCT
ap-1863	64	1	,	,	PUNCT
ap-1863	64	2	βn	βn	ADJ
ap-1863	64	3	}	}	PUNCT
ap-1863	64	4	denote	denote	NOUN
ap-1863	64	5	fβj	fβj	NOUN
ap-1863	64	6	by	by	ADP
ap-1863	64	7	fj	fj	PROPN
ap-1863	64	8	and	and	CCONJ
ap-1863	64	9	the	the	DET
ap-1863	64	10	corresponding	correspond	VERB
ap-1863	64	11	eβj	eβj	NOUN
ap-1863	64	12	by	by	ADP
ap-1863	64	13	ej	ej	PROPN
ap-1863	64	14	.	.	PUNCT
ap-1863	65	1	put	put	VERB
ap-1863	65	2	hj	hj	NOUN
ap-1863	66	1	=	=	PUNCT
ap-1863	67	1	[	[	X
ap-1863	67	2	ej	ej	X
ap-1863	67	3	,	,	PUNCT
ap-1863	67	4	fj	fj	PROPN
ap-1863	67	5	]	]	PUNCT
ap-1863	67	6	.	.	PUNCT
ap-1863	68	1	then	then	ADV
ap-1863	68	2	the	the	DET
ap-1863	68	3	set	set	NOUN
ap-1863	68	4	of	of	ADP
ap-1863	68	5	the	the	DET
ap-1863	68	6	following	follow	VERB
ap-1863	68	7	monomials	monomial	NOUN
ap-1863	68	8	(	(	PUNCT
ap-1863	68	9	so	so	ADV
ap-1863	68	10	-	-	PUNCT
ap-1863	68	11	called	call	VERB
ap-1863	68	12	verma	verma	PROPN
ap-1863	68	13	monomials	monomial	NOUN
ap-1863	68	14	)	)	PUNCT
ap-1863	68	15	,	,	PUNCT
ap-1863	68	16	f	f	PROPN
ap-1863	68	17	a1	a1	PROPN
ap-1863	68	18	1	1	NUM
ap-1863	68	19	1	1	NUM
ap-1863	68	20	(	(	PUNCT
ap-1863	68	21	f	f	PROPN
ap-1863	68	22	a2	a2	PROPN
ap-1863	68	23	2	2	NUM
ap-1863	68	24	2	2	NUM
ap-1863	68	25	f	f	PROPN
ap-1863	68	26	a2	a2	PROPN
ap-1863	68	27	1	1	NUM
ap-1863	68	28	1	1	NUM
ap-1863	68	29	)	)	PUNCT
ap-1863	68	30	(	(	PUNCT
ap-1863	68	31	f	f	PROPN
ap-1863	68	32	a3	a3	VERB
ap-1863	68	33	3	3	NUM
ap-1863	68	34	3	3	NUM
ap-1863	68	35	f	f	PROPN
ap-1863	68	36	a3	a3	NOUN
ap-1863	68	37	2	2	NUM
ap-1863	68	38	2	2	NUM
ap-1863	68	39	f	f	NOUN
ap-1863	68	40	a3	a3	NOUN
ap-1863	68	41	1	1	NUM
ap-1863	68	42	1	1	NUM
ap-1863	68	43	)	)	PUNCT
ap-1863	68	44	·	·	PUNCT
ap-1863	68	45	·	·	PUNCT
ap-1863	68	46	·	·	PUNCT
ap-1863	69	1	(	(	PUNCT
ap-1863	69	2	f	f	X
ap-1863	69	3	an	an	DET
ap-1863	69	4	n	n	CCONJ
ap-1863	69	5	n	n	NOUN
ap-1863	69	6	f	f	NOUN
ap-1863	69	7	an	an	DET
ap-1863	69	8	n−1	n−1	PROPN
ap-1863	69	9	n−1	n−1	PROPN
ap-1863	69	10	·	·	PUNCT
ap-1863	69	11	·	·	PUNCT
ap-1863	69	12	·	·	PUNCT
ap-1863	70	1	f	f	X
ap-1863	70	2	an	an	DET
ap-1863	70	3	2	2	NUM
ap-1863	70	4	2	2	NUM
ap-1863	70	5	f	f	NOUN
ap-1863	70	6	an	an	DET
ap-1863	70	7	1	1	NUM
ap-1863	70	8	1	1	NUM
ap-1863	70	9	)	)	PUNCT
ap-1863	70	10	,	,	PUNCT
ap-1863	70	11	where	where	SCONJ
ap-1863	70	12	ack	ack	VERB
ap-1863	70	13	≤	≤	ADJ
ap-1863	70	14	ack+1	ack+1	X
ap-1863	70	15	(	(	PUNCT
ap-1863	70	16	1	1	NUM
ap-1863	70	17	)	)	PUNCT
ap-1863	70	18	is	be	AUX
ap-1863	70	19	a	a	DET
ap-1863	70	20	linear	linear	ADJ
ap-1863	70	21	basis	basis	NOUN
ap-1863	70	22	of	of	ADP
ap-1863	70	23	u(a−n	u(a−n	PROPN
ap-1863	70	24	)	)	PUNCT
ap-1863	70	25	.	.	PUNCT
ap-1863	71	1	a	a	DET
ap-1863	71	2	similar	similar	ADJ
ap-1863	71	3	basis	basis	NOUN
ap-1863	71	4	consisting	consist	VERB
ap-1863	71	5	of	of	ADP
ap-1863	71	6	vectors	vector	NOUN
ap-1863	71	7	generated	generate	VERB
ap-1863	71	8	by	by	ADP
ap-1863	71	9	appropriate	appropriate	ADJ
ap-1863	71	10	sequences	sequence	NOUN
ap-1863	71	11	of	of	ADP
ap-1863	71	12	ej	ej	PROPN
ap-1863	71	13	’s	’s	PART
ap-1863	71	14	spans	span	NOUN
ap-1863	71	15	u(a+	u(a+	PROPN
ap-1863	71	16	n	n	CCONJ
ap-1863	71	17	)	)	PUNCT
ap-1863	71	18	.	.	PUNCT
ap-1863	72	1	together	together	ADV
ap-1863	72	2	with	with	ADP
ap-1863	72	3	the	the	DET
ap-1863	72	4	enveloping	enveloping	NOUN
ap-1863	72	5	algebra	algebra	NOUN
ap-1863	72	6	of	of	ADP
ap-1863	72	7	h	h	NOUN
ap-1863	72	8	one	one	NOUN
ap-1863	72	9	can	can	AUX
ap-1863	72	10	obtain	obtain	VERB
ap-1863	72	11	a	a	DET
ap-1863	72	12	basis	basis	NOUN
ap-1863	72	13	of	of	ADP
ap-1863	72	14	the	the	DET
ap-1863	72	15	whole	whole	ADJ
ap-1863	72	16	u(an	u(an	PROPN
ap-1863	72	17	)	)	PUNCT
ap-1863	72	18	.	.	PUNCT
ap-1863	73	1	if	if	SCONJ
ap-1863	73	2	we	we	PRON
ap-1863	73	3	now	now	ADV
ap-1863	73	4	restrict	restrict	VERB
ap-1863	73	5	to	to	ADP
ap-1863	73	6	the	the	DET
ap-1863	73	7	elements	element	NOUN
ap-1863	73	8	generated	generate	VERB
ap-1863	73	9	by	by	ADP
ap-1863	73	10	sequences	sequence	NOUN
ap-1863	73	11	fulfilling	fulfil	VERB
ap-1863	73	12	verma	verma	PROPN
ap-1863	73	13	inequalities	inequality	NOUN
ap-1863	73	14	0	0	NUM
ap-1863	73	15	≤	≤	NUM
ap-1863	73	16	ack	ack	VERB
ap-1863	73	17	≤	≤	PROPN
ap-1863	73	18	min{ack−1	min{ack−1	VERB
ap-1863	73	19	+	+	CCONJ
ap-1863	73	20	λn−c+k	λn−c+k	NOUN
ap-1863	73	21	,	,	PUNCT
ap-1863	73	22	a	a	DET
ap-1863	73	23	c+1	c+1	NUM
ap-1863	73	24	k+1	k+1	NOUN
ap-1863	73	25	}	}	PUNCT
ap-1863	73	26	,	,	PUNCT
ap-1863	73	27	where	where	SCONJ
ap-1863	73	28	an+1	an+1	X
ap-1863	73	29	k	k	NOUN
ap-1863	73	30	=	=	PUNCT
ap-1863	74	1	+	+	NOUN
ap-1863	74	2	∞	∞	NUM
ap-1863	74	3	and	and	CCONJ
ap-1863	74	4	ak0	ak0	NOUN
ap-1863	74	5	=	=	SYM
ap-1863	74	6	0	0	NUM
ap-1863	74	7	for	for	ADP
ap-1863	74	8	all	all	DET
ap-1863	74	9	k	k	NOUN
ap-1863	74	10	,	,	PUNCT
ap-1863	74	11	acting	act	VERB
ap-1863	74	12	on	on	ADP
ap-1863	74	13	the	the	DET
ap-1863	74	14	highest	high	ADJ
ap-1863	74	15	weight	weight	NOUN
ap-1863	74	16	vector	vector	NOUN
ap-1863	74	17	|0	|0	NUM
ap-1863	74	18	〉	〉	PROPN
ap-1863	74	19	(	(	PUNCT
ap-1863	74	20	vacuum	vacuum	NOUN
ap-1863	74	21	state	state	NOUN
ap-1863	74	22	)	)	PUNCT
ap-1863	74	23	with	with	ADP
ap-1863	74	24	the	the	DET
ap-1863	74	25	highest	high	ADJ
ap-1863	74	26	weight	weight	NOUN
ap-1863	74	27	(	(	PUNCT
ap-1863	74	28	λ1	λ1	ADJ
ap-1863	74	29	,	,	PUNCT
ap-1863	74	30	.	.	PUNCT
ap-1863	74	31	.	.	PUNCT
ap-1863	75	1	.	.	PUNCT
ap-1863	76	1	,	,	PUNCT
ap-1863	76	2	λn	λn	NOUN
ap-1863	76	3	)	)	PUNCT
ap-1863	76	4	,	,	PUNCT
ap-1863	76	5	where	where	SCONJ
ap-1863	76	6	λj	λj	PROPN
ap-1863	76	7	are	be	AUX
ap-1863	76	8	nonnegative	nonnegative	ADJ
ap-1863	76	9	integers	integer	NOUN
ap-1863	76	10	,	,	PUNCT
ap-1863	76	11	we	we	PRON
ap-1863	76	12	obtain	obtain	VERB
ap-1863	76	13	a	a	DET
ap-1863	76	14	basis	basis	NOUN
ap-1863	76	15	of	of	ADP
ap-1863	76	16	the	the	DET
ap-1863	76	17	representation	representation	NOUN
ap-1863	76	18	space	space	NOUN
ap-1863	76	19	of	of	ADP
ap-1863	76	20	the	the	DET
ap-1863	76	21	corresponding	corresponding	ADJ
ap-1863	76	22	finite	finite	ADJ
ap-1863	76	23	dimensional	dimensional	ADJ
ap-1863	76	24	representation	representation	NOUN
ap-1863	76	25	.	.	PUNCT
ap-1863	77	1	3	3	X
ap-1863	77	2	.	.	X
ap-1863	77	3	verma	verma	PROPN
ap-1863	77	4	monomials	monomial	VERB
ap-1863	77	5	inequalities	inequality	NOUN
ap-1863	77	6	as	as	ADP
ap-1863	77	7	a	a	DET
ap-1863	77	8	contribution	contribution	NOUN
ap-1863	77	9	to	to	ADP
ap-1863	77	10	the	the	DET
ap-1863	77	11	above	above	ADJ
ap-1863	77	12	discussion	discussion	NOUN
ap-1863	77	13	,	,	PUNCT
ap-1863	77	14	we	we	PRON
ap-1863	77	15	give	give	VERB
ap-1863	77	16	an	an	DET
ap-1863	77	17	alternate	alternate	ADJ
ap-1863	77	18	proof	proof	NOUN
ap-1863	77	19	of	of	ADP
ap-1863	77	20	(	(	PUNCT
ap-1863	77	21	1	1	NUM
ap-1863	77	22	)	)	PUNCT
ap-1863	77	23	to	to	ADP
ap-1863	77	24	the	the	DET
ap-1863	77	25	proof	proof	NOUN
ap-1863	77	26	given	give	VERB
ap-1863	77	27	in	in	ADP
ap-1863	77	28	[	[	X
ap-1863	77	29	1	1	NUM
ap-1863	77	30	]	]	PUNCT
ap-1863	77	31	.	.	PUNCT
ap-1863	78	1	lemma	lemma	PROPN
ap-1863	78	2	3.1	3.1	NUM
ap-1863	78	3	.	.	PUNCT
ap-1863	79	1	for	for	ADP
ap-1863	79	2	any	any	DET
ap-1863	79	3	n	n	CCONJ
ap-1863	79	4	,	,	PUNCT
ap-1863	79	5	m	m	VERB
ap-1863	79	6	≥	≥	NOUN
ap-1863	79	7	1	1	NUM
ap-1863	79	8	and	and	CCONJ
ap-1863	79	9	k	k	PROPN
ap-1863	79	10	≥	≥	X
ap-1863	79	11	0	0	NUM
ap-1863	79	12	we	we	PRON
ap-1863	79	13	have	have	VERB
ap-1863	79	14	fni	fni	PROPN
ap-1863	80	1	f	f	PROPN
ap-1863	80	2	k	k	PROPN
ap-1863	80	3	i−1f	i−1f	PROPN
ap-1863	80	4	m	m	VERB
ap-1863	80	5	i	i	NOUN
ap-1863	80	6	∈	∈	PROPN
ap-1863	80	7	span{fki−1f	span{fki−1f	X
ap-1863	81	1	n+m	n+m	PROPN
ap-1863	81	2	i	i	PRON
ap-1863	81	3	,	,	PUNCT
ap-1863	81	4	fk−1	fk−1	PROPN
ap-1863	81	5	i−1	i−1	PROPN
ap-1863	81	6	f	f	PROPN
ap-1863	81	7	n+m	n+m	PROPN
ap-1863	81	8	i	i	PRON
ap-1863	81	9	fi−1	fi−1	PROPN
ap-1863	81	10	,	,	PUNCT
ap-1863	81	11	.	.	PUNCT
ap-1863	81	12	.	.	PUNCT
ap-1863	82	1	.	.	PUNCT
ap-1863	83	1	,	,	PUNCT
ap-1863	83	2	f	f	PROPN
ap-1863	83	3	n+m	n+m	NUM
ap-1863	83	4	i	i	PRON
ap-1863	83	5	fki−1	fki−1	PROPN
ap-1863	83	6	}	}	PUNCT
ap-1863	83	7	,	,	PUNCT
ap-1863	83	8	(	(	PUNCT
ap-1863	83	9	2	2	X
ap-1863	83	10	)	)	PUNCT
ap-1863	83	11	fn+m	fn+m	PROPN
ap-1863	83	12	i−1	i−1	PROPN
ap-1863	83	13	fni	fni	PROPN
ap-1863	83	14	∈	∈	PROPN
ap-1863	83	15	span{fni−1f	span{fni−1f	PROPN
ap-1863	83	16	n	n	CCONJ
ap-1863	83	17	i	i	PRON
ap-1863	83	18	f	f	PROPN
ap-1863	83	19	m	m	VERB
ap-1863	83	20	i−1	i−1	PROPN
ap-1863	83	21	,	,	PUNCT
ap-1863	83	22	fn−1	fn−1	ADJ
ap-1863	83	23	i−1	i−1	PROPN
ap-1863	83	24	f	f	PROPN
ap-1863	84	1	n	n	INTJ
ap-1863	85	1	i	i	NOUN
ap-1863	85	2	f	f	NOUN
ap-1863	85	3	m+1	m+1	PROPN
ap-1863	85	4	i−1	i−1	PROPN
ap-1863	85	5	,	,	PUNCT
ap-1863	85	6	.	.	PUNCT
ap-1863	85	7	.	.	PUNCT
ap-1863	85	8	.	.	PUNCT
ap-1863	86	1	,	,	PUNCT
ap-1863	87	1	fni	fni	PROPN
ap-1863	87	2	f	f	PROPN
ap-1863	87	3	m+n	m+n	PROPN
ap-1863	87	4	i−1	i−1	PROPN
ap-1863	87	5	}	}	PUNCT
ap-1863	87	6	,	,	PUNCT
ap-1863	87	7	(	(	PUNCT
ap-1863	87	8	3	3	X
ap-1863	87	9	)	)	PUNCT
ap-1863	87	10	and	and	CCONJ
ap-1863	87	11	(	(	PUNCT
ap-1863	87	12	2	2	NUM
ap-1863	87	13	)	)	PUNCT
ap-1863	87	14	,	,	PUNCT
ap-1863	87	15	(	(	PUNCT
ap-1863	87	16	3	3	X
ap-1863	87	17	)	)	PUNCT
ap-1863	87	18	in	in	ADP
ap-1863	87	19	which	which	DET
ap-1863	87	20	fi	fi	NOUN
ap-1863	87	21	and	and	CCONJ
ap-1863	87	22	fi−1	fi−1	PROPN
ap-1863	87	23	are	be	AUX
ap-1863	87	24	interchanged	interchange	VERB
ap-1863	87	25	.	.	PUNCT
ap-1863	88	1	proof	proof	NOUN
ap-1863	88	2	.	.	PUNCT
ap-1863	89	1	to	to	PART
ap-1863	89	2	show	show	VERB
ap-1863	89	3	(	(	PUNCT
ap-1863	89	4	2	2	X
ap-1863	89	5	)	)	PUNCT
ap-1863	89	6	we	we	PRON
ap-1863	89	7	first	first	ADV
ap-1863	89	8	prove	prove	VERB
ap-1863	89	9	the	the	DET
ap-1863	89	10	following	follow	VERB
ap-1863	89	11	identity	identity	NOUN
ap-1863	89	12	:	:	PUNCT
ap-1863	89	13	for	for	ADP
ap-1863	89	14	any	any	DET
ap-1863	89	15	m	m	PROPN
ap-1863	89	16	≥	≥	NOUN
ap-1863	89	17	1	1	NUM
ap-1863	89	18	and	and	CCONJ
ap-1863	89	19	i	i	PRON
ap-1863	89	20	=	=	NOUN
ap-1863	89	21	2	2	NUM
ap-1863	89	22	,	,	PUNCT
ap-1863	89	23	3	3	NUM
ap-1863	89	24	,	,	PUNCT
ap-1863	89	25	.	.	PUNCT
ap-1863	89	26	.	.	PUNCT
ap-1863	90	1	.	.	PUNCT
ap-1863	91	1	,	,	PUNCT
ap-1863	91	2	n	n	CCONJ
ap-1863	91	3	we	we	PRON
ap-1863	91	4	have	have	VERB
ap-1863	91	5	fifi−1f	fifi−1f	NUM
ap-1863	91	6	m	m	VERB
ap-1863	92	1	i	i	NOUN
ap-1863	92	2	=	=	NOUN
ap-1863	92	3	1	1	NUM
ap-1863	92	4	m+	m+	NUM
ap-1863	92	5	1	1	NUM
ap-1863	92	6	(	(	PUNCT
ap-1863	92	7	fm+1	fm+1	NUM
ap-1863	92	8	i	i	PRON
ap-1863	92	9	fi−1	fi−1	PROPN
ap-1863	92	10	+	+	PROPN
ap-1863	92	11	mfi−1f	mfi−1f	NOUN
ap-1863	92	12	m+1	m+1	NUM
ap-1863	92	13	i	i	NOUN
ap-1863	92	14	)	)	PUNCT
ap-1863	92	15	.	.	PUNCT
ap-1863	93	1	(	(	PUNCT
ap-1863	93	2	4	4	X
ap-1863	93	3	)	)	PUNCT
ap-1863	93	4	for	for	ADP
ap-1863	93	5	m	m	PROPN
ap-1863	93	6	=	=	SYM
ap-1863	93	7	1	1	NUM
ap-1863	93	8	,	,	PUNCT
ap-1863	93	9	(	(	PUNCT
ap-1863	93	10	4	4	X
ap-1863	93	11	)	)	PUNCT
ap-1863	93	12	follows	follow	VERB
ap-1863	93	13	from	from	ADP
ap-1863	93	14	the	the	DET
ap-1863	93	15	fact	fact	NOUN
ap-1863	93	16	that	that	SCONJ
ap-1863	93	17	[	[	PUNCT
ap-1863	93	18	fi	fi	NOUN
ap-1863	93	19	,	,	PUNCT
ap-1863	93	20	[	[	X
ap-1863	93	21	fi	fi	NOUN
ap-1863	93	22	,	,	PUNCT
ap-1863	93	23	fi−1	fi−1	PROPN
ap-1863	93	24	]	]	X
ap-1863	93	25	]	]	PUNCT
ap-1863	94	1	=	=	PUNCT
ap-1863	94	2	0	0	X
ap-1863	94	3	.	.	PUNCT
ap-1863	95	1	now	now	ADV
ap-1863	95	2	let	let	VERB
ap-1863	95	3	us	we	PRON
ap-1863	95	4	assume	assume	VERB
ap-1863	95	5	validity	validity	NOUN
ap-1863	95	6	for	for	ADP
ap-1863	95	7	m	m	PRON
ap-1863	95	8	and	and	CCONJ
ap-1863	95	9	calculate	calculate	VERB
ap-1863	95	10	the	the	DET
ap-1863	95	11	equation	equation	NOUN
ap-1863	95	12	fifi−1f	fifi−1f	NOUN
ap-1863	95	13	m+1	m+1	NUM
ap-1863	96	1	i	i	NOUN
ap-1863	96	2	=	=	NOUN
ap-1863	96	3	1	1	NUM
ap-1863	96	4	2(f2	2(f2	NUM
ap-1863	96	5	i	i	PRON
ap-1863	96	6	fi−1	fi−1	PROPN
ap-1863	96	7	+	+	CCONJ
ap-1863	96	8	fi−1f	fi−1f	PROPN
ap-1863	96	9	2	2	NUM
ap-1863	96	10	i	i	NOUN
ap-1863	96	11	)	)	PUNCT
ap-1863	96	12	fmi	fmi	PROPN
ap-1863	96	13	=	=	SYM
ap-1863	96	14	1	1	NUM
ap-1863	96	15	2(m+	2(m+	NUM
ap-1863	96	16	1)fi(f	1)fi(f	NUM
ap-1863	96	17	m+1	m+1	NUM
ap-1863	96	18	i	i	PROPN
ap-1863	96	19	fi−1	fi−1	PROPN
ap-1863	96	20	+	+	PROPN
ap-1863	96	21	mfi−1f	mfi−1f	NOUN
ap-1863	96	22	m+1	m+1	NUM
ap-1863	96	23	i	i	NOUN
ap-1863	96	24	)	)	PUNCT
ap-1863	97	1	+	+	CCONJ
ap-1863	97	2	1	1	NUM
ap-1863	97	3	2fi−1f	2fi−1f	NUM
ap-1863	97	4	m+2	m+2	PUNCT
ap-1863	97	5	i	i	NOUN
ap-1863	97	6	=	=	NOUN
ap-1863	98	1	1	1	NUM
ap-1863	98	2	2(m+	2(m+	NUM
ap-1863	98	3	1)f	1)f	NUM
ap-1863	99	1	m+2	m+2	NOUN
ap-1863	99	2	i	i	PRON
ap-1863	99	3	fi−1	fi−1	PROPN
ap-1863	99	4	+	+	PROPN
ap-1863	99	5	m	m	PROPN
ap-1863	99	6	2(m+	2(m+	NOUN
ap-1863	99	7	1)fifi−1f	1)fifi−1f	NUM
ap-1863	100	1	m+1	m+1	NUM
ap-1863	100	2	i	i	PRON
ap-1863	100	3	+	+	NOUN
ap-1863	100	4	1	1	NUM
ap-1863	100	5	2fi−1f	2fi−1f	NUM
ap-1863	100	6	m+2	m+2	X
ap-1863	100	7	i	i	PRON
ap-1863	100	8	,	,	PUNCT
ap-1863	100	9	from	from	ADP
ap-1863	100	10	which	which	PRON
ap-1863	100	11	,	,	PUNCT
ap-1863	100	12	isolating	isolate	VERB
ap-1863	100	13	the	the	DET
ap-1863	100	14	term	term	NOUN
ap-1863	100	15	fifi−1f	fifi−1f	NOUN
ap-1863	100	16	m+1	m+1	NUM
ap-1863	100	17	i	i	PRON
ap-1863	100	18	we	we	PRON
ap-1863	100	19	get	get	VERB
ap-1863	100	20	the	the	DET
ap-1863	100	21	desired	desire	VERB
ap-1863	100	22	result	result	NOUN
ap-1863	100	23	.	.	PUNCT
ap-1863	101	1	we	we	PRON
ap-1863	101	2	now	now	ADV
ap-1863	101	3	generalize	generalize	VERB
ap-1863	101	4	formula	formula	NOUN
ap-1863	101	5	(	(	PUNCT
ap-1863	101	6	4	4	NUM
ap-1863	101	7	)	)	PUNCT
ap-1863	101	8	to	to	ADP
ap-1863	101	9	the	the	DET
ap-1863	101	10	form	form	NOUN
ap-1863	102	1	fif	fif	PROPN
ap-1863	102	2	k	k	PROPN
ap-1863	102	3	i−1f	i−1f	PROPN
ap-1863	102	4	m	m	VERB
ap-1863	102	5	i	i	NOUN
ap-1863	102	6	=	=	NOUN
ap-1863	102	7	1	1	NUM
ap-1863	102	8	m+	m+	NUM
ap-1863	102	9	1	1	NUM
ap-1863	102	10	(	(	PUNCT
ap-1863	102	11	kfk−1	kfk−1	PROPN
ap-1863	102	12	i−1	i−1	PROPN
ap-1863	102	13	f	f	PROPN
ap-1863	103	1	m+1	m+1	PROPN
ap-1863	103	2	i	i	PROPN
ap-1863	103	3	fi−1	fi−1	PROPN
ap-1863	103	4	+	+	CCONJ
ap-1863	103	5	(	(	PUNCT
ap-1863	103	6	m−	m−	PROPN
ap-1863	103	7	k	k	PROPN
ap-1863	103	8	+	+	CCONJ
ap-1863	103	9	1)fki−1f	1)fki−1f	NUM
ap-1863	104	1	m+1	m+1	NUM
ap-1863	104	2	i	i	PROPN
ap-1863	104	3	)	)	PUNCT
ap-1863	104	4	.	.	PUNCT
ap-1863	105	1	(	(	PUNCT
ap-1863	105	2	5	5	X
ap-1863	105	3	)	)	PUNCT
ap-1863	105	4	this	this	DET
ap-1863	105	5	formula	formula	NOUN
ap-1863	105	6	is	be	AUX
ap-1863	105	7	proved	prove	VERB
ap-1863	105	8	similarly	similarly	ADV
ap-1863	105	9	by	by	ADP
ap-1863	105	10	induction	induction	NOUN
ap-1863	105	11	on	on	ADP
ap-1863	105	12	k.	k.	PROPN
ap-1863	105	13	multiplying	multiply	VERB
ap-1863	105	14	both	both	DET
ap-1863	105	15	sides	side	NOUN
ap-1863	105	16	of	of	ADP
ap-1863	105	17	(	(	PUNCT
ap-1863	105	18	5	5	NUM
ap-1863	105	19	)	)	PUNCT
ap-1863	105	20	by	by	ADP
ap-1863	105	21	fi−1	fi−1	PROPN
ap-1863	105	22	,	,	PUNCT
ap-1863	105	23	we	we	PRON
ap-1863	105	24	obtain	obtain	VERB
ap-1863	105	25	fi−1fif	fi−1fif	PROPN
ap-1863	106	1	k	k	PROPN
ap-1863	107	1	i−1f	i−1f	PROPN
ap-1863	108	1	m	m	VERB
ap-1863	108	2	i	i	NOUN
ap-1863	108	3	=	=	NOUN
ap-1863	108	4	1	1	NUM
ap-1863	108	5	m+	m+	NUM
ap-1863	108	6	1	1	NUM
ap-1863	108	7	(	(	PUNCT
ap-1863	108	8	kfki−1f	kfki−1f	NOUN
ap-1863	108	9	m+1	m+1	NUM
ap-1863	108	10	i	i	PROPN
ap-1863	108	11	fi−1	fi−1	PROPN
ap-1863	108	12	+	+	CCONJ
ap-1863	108	13	(	(	PUNCT
ap-1863	108	14	m−	m−	PROPN
ap-1863	108	15	k	k	PROPN
ap-1863	109	1	+	+	CCONJ
ap-1863	109	2	1)fk+1	1)fk+1	NUM
ap-1863	110	1	i−1	i−1	PROPN
ap-1863	110	2	f	f	PROPN
ap-1863	110	3	m+1	m+1	NUM
ap-1863	110	4	i	i	PROPN
ap-1863	110	5	)	)	PUNCT
ap-1863	110	6	,	,	PUNCT
ap-1863	110	7	fi−1fif	fi−1fif	PROPN
ap-1863	110	8	k	k	PROPN
ap-1863	111	1	i−1f	i−1f	PROPN
ap-1863	111	2	m	m	VERB
ap-1863	111	3	i	i	NOUN
ap-1863	111	4	=	=	NOUN
ap-1863	111	5	1	1	NUM
ap-1863	111	6	2	2	NUM
ap-1863	111	7	(	(	PUNCT
ap-1863	111	8	f2	f2	PROPN
ap-1863	111	9	i−1fifif	i−1fifif	NOUN
ap-1863	111	10	2	2	NUM
ap-1863	111	11	i−1	i−1	PROPN
ap-1863	111	12	)	)	PUNCT
ap-1863	112	1	fk−1	fk−1	NOUN
ap-1863	112	2	i−1	i−1	PROPN
ap-1863	113	1	f	f	PROPN
ap-1863	113	2	m	m	VERB
ap-1863	113	3	i	i	NOUN
ap-1863	113	4	=	=	NOUN
ap-1863	113	5	1	1	NUM
ap-1863	113	6	2f	2f	NUM
ap-1863	113	7	2	2	NUM
ap-1863	113	8	i−1	i−1	PROPN
ap-1863	113	9	1	1	NUM
ap-1863	113	10	m+	m+	NUM
ap-1863	113	11	1	1	NUM
ap-1863	113	12	(	(	PUNCT
ap-1863	113	13	(	(	PUNCT
ap-1863	113	14	k	k	X
ap-1863	113	15	−	−	PROPN
ap-1863	113	16	1)fk−2	1)fk−2	NUM
ap-1863	114	1	i−1	i−1	PROPN
ap-1863	114	2	f	f	PROPN
ap-1863	115	1	m+1	m+1	PROPN
ap-1863	115	2	i	i	PROPN
ap-1863	115	3	fi−1	fi−1	PROPN
ap-1863	115	4	+	+	CCONJ
ap-1863	115	5	(	(	PUNCT
ap-1863	115	6	m−	m−	PROPN
ap-1863	115	7	k	k	PROPN
ap-1863	116	1	+	+	CCONJ
ap-1863	116	2	2)fk−1	2)fk−1	NUM
ap-1863	116	3	i−1	i−1	PROPN
ap-1863	116	4	f	f	PROPN
ap-1863	117	1	m+1	m+1	NUM
ap-1863	117	2	i	i	PROPN
ap-1863	117	3	)	)	PUNCT
ap-1863	118	1	+	+	CCONJ
ap-1863	118	2	1	1	NUM
ap-1863	118	3	2fif	2fif	NUM
ap-1863	118	4	k+1	k+1	NOUN
ap-1863	118	5	i−1	i−1	PROPN
ap-1863	118	6	f	f	PROPN
ap-1863	118	7	m	m	VERB
ap-1863	118	8	i	i	INTJ
ap-1863	118	9	.	.	PUNCT
ap-1863	119	1	451	451	NUM
ap-1863	119	2	s.	s.	PROPN
ap-1863	119	3	pošta	pošta	PROPN
ap-1863	119	4	,	,	PUNCT
ap-1863	119	5	m.	m.	NOUN
ap-1863	119	6	havlíček	havlíček	PROPN
ap-1863	119	7	acta	acta	PROPN
ap-1863	119	8	polytechnica	polytechnica	PROPN
ap-1863	119	9	extracting	extract	VERB
ap-1863	119	10	terms	term	NOUN
ap-1863	119	11	fifk+1	fifk+1	VERB
ap-1863	119	12	i−1	i−1	PROPN
ap-1863	119	13	f	f	PROPN
ap-1863	119	14	m	m	VERB
ap-1863	119	15	i	i	PRON
ap-1863	119	16	we	we	PRON
ap-1863	119	17	obtain	obtain	VERB
ap-1863	119	18	(	(	PUNCT
ap-1863	119	19	5	5	NUM
ap-1863	119	20	)	)	PUNCT
ap-1863	119	21	for	for	ADP
ap-1863	119	22	k	k	PROPN
ap-1863	119	23	+	+	PROPN
ap-1863	119	24	1	1	X
ap-1863	119	25	.	.	PUNCT
ap-1863	120	1	the	the	DET
ap-1863	120	2	last	last	ADJ
ap-1863	120	3	step	step	NOUN
ap-1863	120	4	is	be	AUX
ap-1863	120	5	to	to	PART
ap-1863	120	6	prove	prove	VERB
ap-1863	120	7	the	the	DET
ap-1863	120	8	following	follow	VERB
ap-1863	120	9	identity	identity	NOUN
ap-1863	120	10	:	:	PUNCT
ap-1863	120	11	for	for	ADP
ap-1863	120	12	any	any	DET
ap-1863	120	13	n	n	CCONJ
ap-1863	120	14	,	,	PUNCT
ap-1863	120	15	k	k	PROPN
ap-1863	120	16	,	,	PUNCT
ap-1863	120	17	m	m	VERB
ap-1863	120	18	≥	≥	NOUN
ap-1863	120	19	0	0	NUM
ap-1863	120	20	we	we	PRON
ap-1863	120	21	have	have	VERB
ap-1863	120	22	fni	fni	PROPN
ap-1863	121	1	f	f	PROPN
ap-1863	121	2	k	k	PROPN
ap-1863	121	3	i−1f	i−1f	PROPN
ap-1863	121	4	m	m	VERB
ap-1863	121	5	i	i	NOUN
ap-1863	121	6	=	=	NOUN
ap-1863	121	7	1	1	NUM
ap-1863	121	8	(	(	PUNCT
ap-1863	121	9	m+n	m+n	NOUN
ap-1863	121	10	n	n	NOUN
ap-1863	121	11	)	)	PUNCT
ap-1863	121	12	n∑	n∑	NOUN
ap-1863	122	1	l=0	l=0	PROPN
ap-1863	122	2	(	(	PUNCT
ap-1863	122	3	k	k	NOUN
ap-1863	122	4	l	l	NOUN
ap-1863	122	5	)	)	PUNCT
ap-1863	122	6	(	(	PUNCT
ap-1863	122	7	m−	m−	PROPN
ap-1863	122	8	k	k	PROPN
ap-1863	122	9	+	+	CCONJ
ap-1863	122	10	n	n	CCONJ
ap-1863	122	11	n−	n−	PROPN
ap-1863	122	12	l	l	NOUN
ap-1863	122	13	)	)	PUNCT
ap-1863	123	1	×	×	NOUN
ap-1863	123	2	fk−li−1	fk−li−1	PROPN
ap-1863	124	1	f	f	X
ap-1863	124	2	m+n	m+n	PROPN
ap-1863	125	1	i	i	PRON
ap-1863	125	2	f	f	PROPN
ap-1863	125	3	li−1	li−1	PROPN
ap-1863	125	4	.	.	PUNCT
ap-1863	126	1	(	(	PUNCT
ap-1863	126	2	6	6	NUM
ap-1863	126	3	)	)	PUNCT
ap-1863	126	4	this	this	PRON
ap-1863	126	5	can	can	AUX
ap-1863	126	6	be	be	AUX
ap-1863	126	7	shown	show	VERB
ap-1863	126	8	by	by	ADP
ap-1863	126	9	induction	induction	NOUN
ap-1863	126	10	on	on	ADP
ap-1863	126	11	n.	n.	NOUN
ap-1863	126	12	to	to	PART
ap-1863	126	13	show	show	VERB
ap-1863	126	14	(	(	PUNCT
ap-1863	126	15	3	3	X
ap-1863	126	16	)	)	PUNCT
ap-1863	126	17	we	we	PRON
ap-1863	126	18	apply	apply	VERB
ap-1863	126	19	dixmier	dixmier	NOUN
ap-1863	126	20	’s	’s	PART
ap-1863	126	21	antiisomorphism	antiisomorphism	NOUN
ap-1863	126	22	(	(	PUNCT
ap-1863	126	23	see	see	VERB
ap-1863	126	24	[	[	X
ap-1863	126	25	3	3	NUM
ap-1863	126	26	]	]	PUNCT
ap-1863	126	27	,	,	PUNCT
ap-1863	126	28	2.2.18	2.2.18	NUM
ap-1863	126	29	.	.	PUNCT
ap-1863	126	30	,	,	PUNCT
ap-1863	127	1	p.	p.	NOUN
ap-1863	127	2	73	73	NUM
ap-1863	127	3	)	)	PUNCT
ap-1863	127	4	to	to	ADP
ap-1863	127	5	(	(	PUNCT
ap-1863	127	6	6	6	NUM
ap-1863	127	7	)	)	PUNCT
ap-1863	127	8	to	to	PART
ap-1863	127	9	obtain	obtain	VERB
ap-1863	127	10	the	the	DET
ap-1863	127	11	relation	relation	NOUN
ap-1863	127	12	fmi	fmi	PROPN
ap-1863	127	13	f	f	PROPN
ap-1863	127	14	k	k	PROPN
ap-1863	127	15	i−1fi	i−1fi	PROPN
ap-1863	127	16	=	=	PUNCT
ap-1863	128	1	1	1	NUM
ap-1863	128	2	m+	m+	NUM
ap-1863	128	3	1	1	NUM
ap-1863	128	4	(	(	PUNCT
ap-1863	128	5	kfi−1f	kfi−1f	PROPN
ap-1863	128	6	m+1	m+1	X
ap-1863	128	7	i	i	PRON
ap-1863	128	8	fk−1	fk−1	VERB
ap-1863	128	9	i−1	i−1	PROPN
ap-1863	128	10	+	+	CCONJ
ap-1863	128	11	(	(	PUNCT
ap-1863	128	12	m−	m−	PROPN
ap-1863	128	13	k	k	PROPN
ap-1863	129	1	+	+	PROPN
ap-1863	129	2	1)fm+1	1)fm+1	NUM
ap-1863	129	3	i	i	NOUN
ap-1863	129	4	fki−1	fki−1	PROPN
ap-1863	129	5	)	)	PUNCT
ap-1863	129	6	,	,	PUNCT
ap-1863	129	7	which	which	PRON
ap-1863	129	8	allows	allow	VERB
ap-1863	129	9	inductively	inductively	ADV
ap-1863	129	10	to	to	PART
ap-1863	129	11	prove	prove	VERB
ap-1863	129	12	fn+1	fn+1	ADJ
ap-1863	129	13	i−1	i−1	PROPN
ap-1863	129	14	f	f	PROPN
ap-1863	130	1	n	n	ADV
ap-1863	131	1	i	i	PRON
ap-1863	131	2	=	=	PROPN
ap-1863	131	3	n+1∑	n+1∑	PROPN
ap-1863	131	4	l=1	l=1	PROPN
ap-1863	131	5	(	(	PUNCT
ap-1863	131	6	−1)l+1	−1)l+1	PROPN
ap-1863	131	7	(	(	PUNCT
ap-1863	131	8	n+	n+	NOUN
ap-1863	131	9	1	1	NUM
ap-1863	131	10	l	l	NOUN
ap-1863	131	11	)	)	PUNCT
ap-1863	131	12	fn+1−l	fn+1−l	VERB
ap-1863	131	13	i−1	i−1	PROPN
ap-1863	131	14	fni	fni	PROPN
ap-1863	131	15	f	f	PROPN
ap-1863	131	16	l	l	PROPN
ap-1863	131	17	i−1	i−1	PROPN
ap-1863	131	18	.	.	PUNCT
ap-1863	132	1	(	(	PUNCT
ap-1863	132	2	7	7	X
ap-1863	132	3	)	)	PUNCT
ap-1863	132	4	multiplying	multiplying	NOUN
ap-1863	132	5	(	(	PUNCT
ap-1863	132	6	7	7	NUM
ap-1863	132	7	)	)	PUNCT
ap-1863	132	8	by	by	ADP
ap-1863	132	9	fi−1	fi−1	PROPN
ap-1863	132	10	and	and	CCONJ
ap-1863	132	11	repeatedly	repeatedly	ADV
ap-1863	132	12	applying	apply	VERB
ap-1863	132	13	(	(	PUNCT
ap-1863	132	14	7	7	NUM
ap-1863	132	15	)	)	PUNCT
ap-1863	132	16	to	to	ADP
ap-1863	132	17	the	the	DET
ap-1863	132	18	right	right	ADJ
ap-1863	132	19	-	-	PUNCT
ap-1863	132	20	hand	hand	NOUN
ap-1863	132	21	side	side	NOUN
ap-1863	132	22	we	we	PRON
ap-1863	132	23	finally	finally	ADV
ap-1863	132	24	obtain	obtain	VERB
ap-1863	132	25	(	(	PUNCT
ap-1863	132	26	3	3	NUM
ap-1863	132	27	)	)	PUNCT
ap-1863	132	28	.	.	PUNCT
ap-1863	133	1	replacing	replace	VERB
ap-1863	133	2	fi	fi	NOUN
ap-1863	133	3	and	and	CCONJ
ap-1863	133	4	fi−1	fi−1	PROPN
ap-1863	133	5	and	and	CCONJ
ap-1863	133	6	using	use	VERB
ap-1863	133	7	a	a	DET
ap-1863	133	8	similar	similar	ADJ
ap-1863	133	9	approach	approach	NOUN
ap-1863	133	10	,	,	PUNCT
ap-1863	133	11	we	we	PRON
ap-1863	133	12	subsequently	subsequently	ADV
ap-1863	133	13	obtain	obtain	VERB
ap-1863	133	14	the	the	DET
ap-1863	133	15	following	follow	VERB
ap-1863	133	16	formulas	formula	NOUN
ap-1863	133	17	:	:	PUNCT
ap-1863	133	18	fi−1fif	fi−1fif	PROPN
ap-1863	133	19	m	m	NOUN
ap-1863	133	20	i−1	i−1	NOUN
ap-1863	134	1	=	=	PUNCT
ap-1863	135	1	1	1	NUM
ap-1863	136	1	m+	m+	NUM
ap-1863	137	1	1	1	NUM
ap-1863	138	1	(	(	PUNCT
ap-1863	138	2	fm+1	fm+1	VERB
ap-1863	138	3	i−1	i−1	PROPN
ap-1863	138	4	fi	fi	NOUN
ap-1863	139	1	+	+	NOUN
ap-1863	139	2	mfif	mfif	NOUN
ap-1863	139	3	m+1	m+1	ADJ
ap-1863	139	4	i−1	i−1	PROPN
ap-1863	139	5	)	)	PUNCT
ap-1863	139	6	,	,	PUNCT
ap-1863	140	1	fi−1f	fi−1f	PROPN
ap-1863	140	2	k	k	PROPN
ap-1863	141	1	i	i	PRON
ap-1863	141	2	f	f	VERB
ap-1863	141	3	m	m	VERB
ap-1863	141	4	i−1	i−1	NOUN
ap-1863	141	5	=	=	PUNCT
ap-1863	141	6	1	1	NUM
ap-1863	141	7	m+	m+	NUM
ap-1863	141	8	1	1	NUM
ap-1863	142	1	(	(	PUNCT
ap-1863	143	1	kfk−1	kfk−1	PROPN
ap-1863	144	1	i	i	PRON
ap-1863	144	2	fm+1	fm+1	VERB
ap-1863	144	3	i−1	i−1	PROPN
ap-1863	144	4	fi	fi	NOUN
ap-1863	145	1	+	+	CCONJ
ap-1863	145	2	(	(	PUNCT
ap-1863	145	3	m−	m−	PROPN
ap-1863	145	4	k	k	PROPN
ap-1863	146	1	+	+	NUM
ap-1863	146	2	1)fki	1)fki	NUM
ap-1863	146	3	fm+1	fm+1	PROPN
ap-1863	146	4	i−1	i−1	PROPN
ap-1863	146	5	)	)	PUNCT
ap-1863	146	6	,	,	PUNCT
ap-1863	146	7	fni−1f	fni−1f	X
ap-1863	147	1	k	k	PROPN
ap-1863	148	1	i	i	PRON
ap-1863	148	2	f	f	NOUN
ap-1863	148	3	m	m	VERB
ap-1863	148	4	i−1	i−1	NOUN
ap-1863	148	5	=	=	SYM
ap-1863	148	6	1	1	NUM
ap-1863	148	7	(	(	PUNCT
ap-1863	148	8	m+n	m+n	NOUN
ap-1863	148	9	n	n	NOUN
ap-1863	148	10	)	)	PUNCT
ap-1863	148	11	n∑	n∑	NOUN
ap-1863	149	1	l=0	l=0	PROPN
ap-1863	149	2	(	(	PUNCT
ap-1863	149	3	k	k	NOUN
ap-1863	149	4	l	l	NOUN
ap-1863	149	5	)	)	PUNCT
ap-1863	149	6	(	(	PUNCT
ap-1863	149	7	m−	m−	PROPN
ap-1863	149	8	k	k	PROPN
ap-1863	149	9	+	+	CCONJ
ap-1863	149	10	n	n	CCONJ
ap-1863	149	11	n−	n−	PROPN
ap-1863	149	12	l	l	NOUN
ap-1863	149	13	)	)	PUNCT
ap-1863	149	14	×	×	NOUN
ap-1863	149	15	fk−li	fk−li	VERB
ap-1863	149	16	fm+n	fm+n	PROPN
ap-1863	149	17	i−1	i−1	PROPN
ap-1863	149	18	f	f	PROPN
ap-1863	149	19	li	li	PROPN
ap-1863	149	20	,	,	PUNCT
ap-1863	149	21	fn+1	fn+1	VERB
ap-1863	149	22	i	i	PRON
ap-1863	149	23	fni−1	fni−1	PROPN
ap-1863	149	24	=	=	PUNCT
ap-1863	149	25	n+1∑	n+1∑	PROPN
ap-1863	149	26	l=1	l=1	PROPN
ap-1863	149	27	(	(	PUNCT
ap-1863	149	28	−1)l+1	−1)l+1	PROPN
ap-1863	149	29	(	(	PUNCT
ap-1863	149	30	n+	n+	NOUN
ap-1863	149	31	1	1	NUM
ap-1863	149	32	l	l	NOUN
ap-1863	149	33	)	)	PUNCT
ap-1863	149	34	fn+1−l	fn+1−l	VERB
ap-1863	150	1	i	i	PRON
ap-1863	150	2	fni−1f	fni−1f	X
ap-1863	151	1	l	l	NOUN
ap-1863	151	2	i	i	INTJ
ap-1863	151	3	.	.	PUNCT
ap-1863	152	1	due	due	ADP
ap-1863	152	2	to	to	ADP
ap-1863	152	3	the	the	DET
ap-1863	152	4	poincaré	poincaré	PROPN
ap-1863	152	5	-	-	PUNCT
ap-1863	152	6	birkhoff	birkhoff	NOUN
ap-1863	152	7	-	-	PUNCT
ap-1863	152	8	witt	witt	NOUN
ap-1863	152	9	theorem	theorem	NOUN
ap-1863	152	10	,	,	PUNCT
ap-1863	152	11	ordered	order	VERB
ap-1863	152	12	monomials	monomials	AUX
ap-1863	152	13	es12	es12	PROPN
ap-1863	152	14	12	12	NUM
ap-1863	152	15	e	e	NOUN
ap-1863	152	16	s13	s13	NOUN
ap-1863	152	17	13	13	NUM
ap-1863	152	18	·	·	PUNCT
ap-1863	152	19	·	·	PUNCT
ap-1863	152	20	·	·	PUNCT
ap-1863	152	21	e	e	X
ap-1863	152	22	s1,n+1	s1,n+1	PROPN
ap-1863	152	23	1,n+1	1,n+1	NUM
ap-1863	152	24	e	e	NOUN
ap-1863	152	25	s23	s23	NOUN
ap-1863	152	26	23	23	NUM
ap-1863	152	27	e	e	NOUN
ap-1863	152	28	s24	s24	NOUN
ap-1863	152	29	24	24	NUM
ap-1863	152	30	·	·	PUNCT
ap-1863	152	31	·	·	PUNCT
ap-1863	152	32	·	·	PUNCT
ap-1863	152	33	e	e	X
ap-1863	152	34	s2,n+1	s2,n+1	VERB
ap-1863	152	35	2,n+1	2,n+1	NUM
ap-1863	152	36	·	·	PUNCT
ap-1863	152	37	·	·	PUNCT
ap-1863	152	38	·	·	PUNCT
ap-1863	152	39	esn−1,n+1	esn−1,n+1	PROPN
ap-1863	152	40	n−1,n+1e	n−1,n+1e	PROPN
ap-1863	152	41	sn	sn	PROPN
ap-1863	152	42	,	,	PUNCT
ap-1863	152	43	n+1	n+1	PROPN
ap-1863	152	44	n	n	CCONJ
ap-1863	152	45	,	,	PUNCT
ap-1863	152	46	n+1	n+1	PROPN
ap-1863	152	47	,	,	PUNCT
ap-1863	152	48	sij	sij	PROPN
ap-1863	152	49	≥	≥	PROPN
ap-1863	152	50	0	0	NUM
ap-1863	152	51	,	,	PUNCT
ap-1863	152	52	(	(	PUNCT
ap-1863	152	53	8)	8)	NUM
ap-1863	152	54	where	where	SCONJ
ap-1863	152	55	ei	ei	NOUN
ap-1863	152	56	,	,	PUNCT
ap-1863	152	57	i+1	i+1	NOUN
ap-1863	152	58	=	=	NOUN
ap-1863	152	59	fi	fi	NOUN
ap-1863	152	60	and	and	CCONJ
ap-1863	152	61	eik	eik	NOUN
ap-1863	152	62	=	=	PUNCT
ap-1863	153	1	[	[	X
ap-1863	153	2	ei	ei	X
ap-1863	153	3	,	,	PUNCT
ap-1863	153	4	k−1	k−1	PROPN
ap-1863	153	5	,	,	PUNCT
ap-1863	153	6	ek−1,k	ek−1,k	PROPN
ap-1863	153	7	]	]	PUNCT
ap-1863	153	8	,	,	PUNCT
ap-1863	153	9	i+	i+	X
ap-1863	153	10	1	1	NUM
ap-1863	153	11	<	<	X
ap-1863	153	12	k	k	X
ap-1863	153	13	,	,	PUNCT
ap-1863	153	14	(	(	PUNCT
ap-1863	153	15	9	9	X
ap-1863	153	16	)	)	PUNCT
ap-1863	153	17	form	form	NOUN
ap-1863	153	18	a	a	DET
ap-1863	153	19	basis	basis	NOUN
ap-1863	153	20	of	of	ADP
ap-1863	153	21	u(a−n	u(a−n	PROPN
ap-1863	153	22	)	)	PUNCT
ap-1863	153	23	.	.	PUNCT
ap-1863	154	1	let	let	VERB
ap-1863	154	2	us	we	PRON
ap-1863	154	3	consider	consider	VERB
ap-1863	154	4	any	any	DET
ap-1863	154	5	such	such	ADJ
ap-1863	154	6	monomial	monomial	NOUN
ap-1863	154	7	and	and	CCONJ
ap-1863	154	8	denote	denote	VERB
ap-1863	154	9	it	it	PRON
ap-1863	154	10	by	by	ADP
ap-1863	154	11	v.	v.	ADP
ap-1863	154	12	the	the	DET
ap-1863	154	13	relations	relation	NOUN
ap-1863	154	14	(	(	PUNCT
ap-1863	154	15	9	9	X
ap-1863	154	16	)	)	PUNCT
ap-1863	154	17	express	express	VERB
ap-1863	154	18	any	any	DET
ap-1863	154	19	generator	generator	NOUN
ap-1863	154	20	eik	eik	PROPN
ap-1863	154	21	,	,	PUNCT
ap-1863	154	22	i	i	PRON
ap-1863	154	23	<	<	X
ap-1863	154	24	k	k	PROPN
ap-1863	154	25	as	as	ADP
ap-1863	154	26	a	a	DET
ap-1863	154	27	commutator	commutator	NOUN
ap-1863	154	28	of	of	ADP
ap-1863	154	29	simple	simple	ADJ
ap-1863	154	30	ones	one	NOUN
ap-1863	154	31	f1	f1	NOUN
ap-1863	154	32	,	,	PUNCT
ap-1863	154	33	.	.	PUNCT
ap-1863	154	34	.	.	PUNCT
ap-1863	155	1	.	.	PUNCT
ap-1863	156	1	,	,	PUNCT
ap-1863	156	2	fn	fn	X
ap-1863	156	3	.	.	PUNCT
ap-1863	157	1	therefore	therefore	ADV
ap-1863	157	2	v	v	NOUN
ap-1863	157	3	is	be	AUX
ap-1863	157	4	a	a	DET
ap-1863	157	5	linear	linear	ADJ
ap-1863	157	6	combination	combination	NOUN
ap-1863	157	7	of	of	ADP
ap-1863	157	8	(	(	PUNCT
ap-1863	157	9	unordered	unordered	ADJ
ap-1863	157	10	)	)	PUNCT
ap-1863	157	11	monomials	monomial	NOUN
ap-1863	157	12	from	from	ADP
ap-1863	157	13	these	these	DET
ap-1863	157	14	simple	simple	ADJ
ap-1863	157	15	generators	generator	NOUN
ap-1863	157	16	and	and	CCONJ
ap-1863	157	17	such	such	ADJ
ap-1863	157	18	monomials	monomial	NOUN
ap-1863	157	19	can	can	AUX
ap-1863	157	20	be	be	AUX
ap-1863	157	21	written	write	VERB
ap-1863	157	22	in	in	ADP
ap-1863	157	23	the	the	DET
ap-1863	157	24	form	form	NOUN
ap-1863	157	25	v′	v′	NOUN
ap-1863	157	26	=	=	SYM
ap-1863	157	27	v1f	v1f	PROPN
ap-1863	157	28	r1	r1	PROPN
ap-1863	157	29	n	n	CCONJ
ap-1863	157	30	v2f	v2f	X
ap-1863	157	31	r2	r2	PROPN
ap-1863	157	32	n	n	X
ap-1863	157	33	·	·	PUNCT
ap-1863	157	34	·	·	PUNCT
ap-1863	157	35	·	·	PUNCT
ap-1863	158	1	vmfrm	vmfrm	PROPN
ap-1863	158	2	n	n	PRON
ap-1863	158	3	vm+1	vm+1	NOUN
ap-1863	158	4	,	,	PUNCT
ap-1863	158	5	(	(	PUNCT
ap-1863	158	6	10	10	NUM
ap-1863	158	7	)	)	PUNCT
ap-1863	158	8	where	where	SCONJ
ap-1863	158	9	vi	vi	PROPN
ap-1863	158	10	∈	∈	PROPN
ap-1863	158	11	u(a−n−1	u(a−n−1	X
ap-1863	158	12	)	)	PUNCT
ap-1863	158	13	⊂	⊂	PROPN
ap-1863	158	14	u(a−n	u(a−n	PROPN
ap-1863	158	15	)	)	PUNCT
ap-1863	158	16	and	and	CCONJ
ap-1863	158	17	the	the	DET
ap-1863	158	18	monomials	monomial	NOUN
ap-1863	158	19	v2	v2	PROPN
ap-1863	158	20	,	,	PUNCT
ap-1863	158	21	v3	v3	PROPN
ap-1863	158	22	,	,	PUNCT
ap-1863	158	23	.	.	PUNCT
ap-1863	158	24	.	.	PUNCT
ap-1863	158	25	.	.	PUNCT
ap-1863	159	1	,	,	PUNCT
ap-1863	159	2	vm	vm	PROPN
ap-1863	159	3	6∈	6∈	PROPN
ap-1863	159	4	u(a−n−2	u(a−n−2	PROPN
ap-1863	159	5	)	)	PUNCT
ap-1863	159	6	(	(	PUNCT
ap-1863	159	7	i.	i.	PROPN
ap-1863	159	8	e.	e.	PROPN
ap-1863	160	1	they	they	PRON
ap-1863	160	2	contain	contain	VERB
ap-1863	160	3	generator	generator	NOUN
ap-1863	160	4	fn−1	fn−1	ADJ
ap-1863	160	5	,	,	PUNCT
ap-1863	160	6	otherwise	otherwise	ADV
ap-1863	160	7	we	we	PRON
ap-1863	160	8	use	use	VERB
ap-1863	160	9	the	the	DET
ap-1863	160	10	relation	relation	NOUN
ap-1863	160	11	frnvjf	frnvjf	PROPN
ap-1863	160	12	s	s	PART
ap-1863	160	13	n	n	NOUN
ap-1863	160	14	=	=	PUNCT
ap-1863	160	15	fr+sn	fr+sn	PROPN
ap-1863	160	16	vj	vj	NOUN
ap-1863	161	1	and	and	CCONJ
ap-1863	161	2	the	the	DET
ap-1863	161	3	product	product	NOUN
ap-1863	161	4	can	can	AUX
ap-1863	161	5	be	be	AUX
ap-1863	161	6	truncated	truncate	VERB
ap-1863	161	7	)	)	PUNCT
ap-1863	161	8	.	.	PUNCT
ap-1863	162	1	theorem	theorem	ADJ
ap-1863	162	2	3.2	3.2	NUM
ap-1863	162	3	.	.	PUNCT
ap-1863	163	1	let	let	VERB
ap-1863	163	2	us	we	PRON
ap-1863	163	3	denote	denote	VERB
ap-1863	163	4	vr	vr	PROPN
ap-1863	163	5	,	,	PUNCT
ap-1863	163	6	m	m	NOUN
ap-1863	163	7	=	=	VERB
ap-1863	163	8	span	span	NOUN
ap-1863	163	9	{	{	PUNCT
ap-1863	163	10	v1f	v1f	X
ap-1863	163	11	r1	r1	PROPN
ap-1863	163	12	n	n	CCONJ
ap-1863	163	13	v2f	v2f	X
ap-1863	163	14	r2	r2	PROPN
ap-1863	163	15	n	n	X
ap-1863	163	16	·	·	PUNCT
ap-1863	163	17	·	·	PUNCT
ap-1863	163	18	·	·	PUNCT
ap-1863	164	1	vmfrm	vmfrm	PROPN
ap-1863	164	2	n	n	CCONJ
ap-1863	164	3	vm+1	vm+1	NUM
ap-1863	164	4	∣∣	∣∣	NUM
ap-1863	164	5	vi	vi	PROPN
ap-1863	164	6	∈	∈	PROPN
ap-1863	164	7	u(a−n−1	u(a−n−1	NUM
ap-1863	164	8	)	)	PUNCT
ap-1863	164	9	,	,	PUNCT
ap-1863	164	10	r1	r1	PROPN
ap-1863	164	11	+	+	CCONJ
ap-1863	164	12	r2	r2	PROPN
ap-1863	164	13	+	+	CCONJ
ap-1863	164	14	·	·	PUNCT
ap-1863	164	15	·	·	PUNCT
ap-1863	164	16	·	·	PUNCT
ap-1863	164	17	+	+	NUM
ap-1863	164	18	rm	rm	NOUN
ap-1863	164	19	=	=	SYM
ap-1863	164	20	r	r	NOUN
ap-1863	164	21	}	}	PUNCT
ap-1863	164	22	.	.	PUNCT
ap-1863	165	1	(	(	PUNCT
ap-1863	165	2	11	11	NUM
ap-1863	165	3	)	)	PUNCT
ap-1863	165	4	then	then	ADV
ap-1863	165	5	we	we	PRON
ap-1863	165	6	have	have	VERB
ap-1863	165	7	v′	v′	NOUN
ap-1863	165	8	∈	∈	PROPN
ap-1863	165	9	vr,1	vr,1	NOUN
ap-1863	165	10	.	.	PUNCT
ap-1863	166	1	proof	proof	NOUN
ap-1863	166	2	.	.	PUNCT
ap-1863	167	1	by	by	ADP
ap-1863	167	2	induction	induction	NOUN
ap-1863	167	3	on	on	ADP
ap-1863	167	4	n.	n.	PROPN
ap-1863	167	5	if	if	SCONJ
ap-1863	167	6	n	n	NOUN
ap-1863	167	7	=	=	SYM
ap-1863	167	8	2	2	NUM
ap-1863	167	9	,	,	PUNCT
ap-1863	167	10	we	we	PRON
ap-1863	167	11	have	have	VERB
ap-1863	167	12	v′	v′	NOUN
ap-1863	168	1	=	=	SYM
ap-1863	168	2	fs1	fs1	NOUN
ap-1863	168	3	1	1	NUM
ap-1863	168	4	fr1	fr1	PROPN
ap-1863	168	5	2	2	NUM
ap-1863	168	6	fs2	fs2	PROPN
ap-1863	168	7	1	1	NUM
ap-1863	168	8	fr2	fr2	PROPN
ap-1863	168	9	2	2	NUM
ap-1863	168	10	·	·	PUNCT
ap-1863	168	11	·	·	PUNCT
ap-1863	168	12	·	·	PUNCT
ap-1863	169	1	f	f	X
ap-1863	169	2	sm	sm	PROPN
ap-1863	169	3	1	1	NUM
ap-1863	169	4	frm	frm	PROPN
ap-1863	169	5	2	2	NUM
ap-1863	169	6	f	f	NOUN
ap-1863	169	7	sm+1	sm+1	PROPN
ap-1863	169	8	1	1	NUM
ap-1863	169	9	.	.	PUNCT
ap-1863	170	1	(	(	PUNCT
ap-1863	170	2	12	12	NUM
ap-1863	170	3	)	)	PUNCT
ap-1863	170	4	if	if	SCONJ
ap-1863	170	5	m	m	PROPN
ap-1863	170	6	≥	≥	NOUN
ap-1863	170	7	2	2	NUM
ap-1863	170	8	,	,	PUNCT
ap-1863	170	9	we	we	PRON
ap-1863	170	10	use	use	VERB
ap-1863	170	11	formula	formula	NOUN
ap-1863	170	12	(	(	PUNCT
ap-1863	170	13	2	2	NUM
ap-1863	170	14	)	)	PUNCT
ap-1863	170	15	from	from	ADP
ap-1863	170	16	lemma	lemma	PROPN
ap-1863	170	17	3.1	3.1	NUM
ap-1863	170	18	applied	apply	VERB
ap-1863	170	19	to	to	ADP
ap-1863	170	20	the	the	DET
ap-1863	170	21	product	product	NOUN
ap-1863	170	22	fr1	fr1	PROPN
ap-1863	170	23	2	2	NUM
ap-1863	170	24	fs2	fs2	PROPN
ap-1863	170	25	1	1	NUM
ap-1863	170	26	fr2	fr2	PROPN
ap-1863	170	27	2	2	NUM
ap-1863	170	28	and	and	CCONJ
ap-1863	170	29	we	we	PRON
ap-1863	170	30	obtain	obtain	VERB
ap-1863	170	31	v′	v′	NOUN
ap-1863	170	32	∈	∈	PROPN
ap-1863	170	33	vr	vr	NOUN
ap-1863	170	34	,	,	PUNCT
ap-1863	170	35	m−1	m−1	PROPN
ap-1863	170	36	.	.	PUNCT
ap-1863	171	1	in	in	ADP
ap-1863	171	2	the	the	DET
ap-1863	171	3	general	general	ADJ
ap-1863	171	4	case	case	NOUN
ap-1863	171	5	we	we	PRON
ap-1863	171	6	write	write	VERB
ap-1863	171	7	vi	vi	PROPN
ap-1863	171	8	=	=	SYM
ap-1863	171	9	wif	wif	PROPN
ap-1863	171	10	si	si	PROPN
ap-1863	172	1	n	n	PROPN
ap-1863	172	2	w	w	PROPN
ap-1863	172	3	′	′	NUM
ap-1863	173	1	i	i	PROPN
ap-1863	173	2	,	,	PUNCT
ap-1863	173	3	w	w	PROPN
ap-1863	173	4	,	,	PUNCT
ap-1863	173	5	w′	w′	PROPN
ap-1863	173	6	∈	∈	PROPN
ap-1863	173	7	u(a−n−1	u(a−n−1	ADJ
ap-1863	173	8	)	)	PUNCT
ap-1863	173	9	,	,	PUNCT
ap-1863	173	10	and	and	CCONJ
ap-1863	173	11	,	,	PUNCT
ap-1863	173	12	therefore	therefore	ADV
ap-1863	173	13	,	,	PUNCT
ap-1863	173	14	[	[	X
ap-1863	173	15	w	w	X
ap-1863	173	16	,	,	PUNCT
ap-1863	173	17	fn+1	fn+1	X
ap-1863	173	18	]	]	PUNCT
ap-1863	173	19	=	=	PUNCT
ap-1863	174	1	[	[	X
ap-1863	174	2	w′	w′	NOUN
ap-1863	174	3	,	,	PUNCT
ap-1863	174	4	fn+1	fn+1	X
ap-1863	174	5	]	]	PUNCT
ap-1863	174	6	=	=	SYM
ap-1863	174	7	0	0	X
ap-1863	174	8	.	.	PUNCT
ap-1863	175	1	for	for	ADP
ap-1863	175	2	monomial	monomial	ADJ
ap-1863	175	3	v′	v′	NOUN
ap-1863	175	4	we	we	PRON
ap-1863	175	5	can	can	AUX
ap-1863	175	6	write	write	VERB
ap-1863	175	7	v′	v′	NOUN
ap-1863	175	8	=	=	SYM
ap-1863	175	9	v1f	v1f	PROPN
ap-1863	175	10	r1	r1	VERB
ap-1863	175	11	n+1w2f	n+1w2f	ADJ
ap-1863	175	12	s2	s2	PROPN
ap-1863	175	13	n	n	CCONJ
ap-1863	175	14	w	w	NOUN
ap-1863	175	15	′	′	NUM
ap-1863	175	16	2f	2f	NUM
ap-1863	175	17	r2	r2	NOUN
ap-1863	175	18	n+1	n+1	X
ap-1863	175	19	·	·	PUNCT
ap-1863	175	20	·	·	PUNCT
ap-1863	175	21	·	·	PUNCT
ap-1863	176	1	=	=	SYM
ap-1863	176	2	v1w2f	v1w2f	VERB
ap-1863	176	3	r1	r1	NOUN
ap-1863	176	4	n+1f	n+1f	PROPN
ap-1863	176	5	s2	s2	PROPN
ap-1863	176	6	n	n	CCONJ
ap-1863	176	7	f	f	PROPN
ap-1863	176	8	r2	r2	PROPN
ap-1863	177	1	n+1w	n+1w	PROPN
ap-1863	177	2	′	′	NUM
ap-1863	177	3	2	2	NUM
ap-1863	177	4	·	·	PUNCT
ap-1863	177	5	·	·	PUNCT
ap-1863	177	6	·	·	PUNCT
ap-1863	177	7	and	and	CCONJ
ap-1863	177	8	we	we	PRON
ap-1863	177	9	use	use	VERB
ap-1863	177	10	the	the	DET
ap-1863	177	11	same	same	ADJ
ap-1863	177	12	argument	argument	NOUN
ap-1863	177	13	as	as	ADP
ap-1863	177	14	in	in	ADP
ap-1863	177	15	the	the	DET
ap-1863	177	16	case	case	NOUN
ap-1863	177	17	n	n	NOUN
ap-1863	177	18	=	=	SYM
ap-1863	177	19	2	2	X
ap-1863	177	20	.	.	PUNCT
ap-1863	178	1	it	it	PRON
ap-1863	178	2	follows	follow	VERB
ap-1863	178	3	from	from	ADP
ap-1863	178	4	the	the	DET
ap-1863	178	5	above	above	ADJ
ap-1863	178	6	theorem	theorem	NOUN
ap-1863	178	7	that	that	SCONJ
ap-1863	178	8	the	the	DET
ap-1863	178	9	set	set	NOUN
ap-1863	178	10	u(a−n	u(a−n	PROPN
ap-1863	178	11	)	)	PUNCT
ap-1863	178	12	is	be	AUX
ap-1863	178	13	spanned	span	VERB
ap-1863	178	14	by	by	ADP
ap-1863	178	15	monomials	monomial	NOUN
ap-1863	178	16	of	of	ADP
ap-1863	178	17	a	a	DET
ap-1863	178	18	special	special	ADJ
ap-1863	178	19	type	type	NOUN
ap-1863	178	20	.	.	PUNCT
ap-1863	179	1	when	when	SCONJ
ap-1863	179	2	n	n	X
ap-1863	179	3	=	=	SYM
ap-1863	179	4	2	2	NUM
ap-1863	179	5	these	these	DET
ap-1863	179	6	monomials	monomial	NOUN
ap-1863	179	7	are	be	AUX
ap-1863	179	8	of	of	ADP
ap-1863	179	9	the	the	DET
ap-1863	179	10	form	form	NOUN
ap-1863	179	11	{	{	PUNCT
ap-1863	179	12	fs1	fs1	PROPN
ap-1863	179	13	1	1	NUM
ap-1863	179	14	fr1	fr1	PROPN
ap-1863	179	15	2	2	NUM
ap-1863	179	16	fs2	fs2	PROPN
ap-1863	179	17	1	1	NUM
ap-1863	179	18	|s1	|s1	NOUN
ap-1863	179	19	,	,	PUNCT
ap-1863	179	20	s2	s2	PROPN
ap-1863	179	21	,	,	PUNCT
ap-1863	179	22	r1	r1	NOUN
ap-1863	179	23	≥	≥	NUM
ap-1863	179	24	0	0	NUM
ap-1863	179	25	}	}	PUNCT
ap-1863	179	26	.	.	PUNCT
ap-1863	180	1	due	due	ADP
ap-1863	180	2	to	to	ADP
ap-1863	180	3	formula	formula	NOUN
ap-1863	180	4	(	(	PUNCT
ap-1863	180	5	3	3	NUM
ap-1863	180	6	)	)	PUNCT
ap-1863	180	7	from	from	ADP
ap-1863	180	8	lemma	lemma	PROPN
ap-1863	180	9	3.1	3.1	NUM
ap-1863	180	10	the	the	DET
ap-1863	180	11	monomials	monomial	NOUN
ap-1863	180	12	fs1	fs1	PROPN
ap-1863	180	13	1	1	NUM
ap-1863	180	14	fr1	fr1	PROPN
ap-1863	180	15	2	2	NUM
ap-1863	180	16	fs2	fs2	PROPN
ap-1863	180	17	1	1	NUM
ap-1863	180	18	,	,	PUNCT
ap-1863	180	19	where	where	SCONJ
ap-1863	180	20	s1	s1	PROPN
ap-1863	180	21	>	>	X
ap-1863	180	22	r1	r1	PROPN
ap-1863	180	23	are	be	AUX
ap-1863	180	24	linearly	linearly	ADV
ap-1863	180	25	dependent	dependent	ADJ
ap-1863	180	26	on	on	ADP
ap-1863	180	27	those	those	PRON
ap-1863	180	28	having	have	VERB
ap-1863	180	29	s1	s1	PROPN
ap-1863	180	30	≤	≤	NUM
ap-1863	180	31	r1	r1	NOUN
ap-1863	180	32	,	,	PUNCT
ap-1863	180	33	therefore	therefore	ADV
ap-1863	180	34	we	we	PRON
ap-1863	180	35	can	can	AUX
ap-1863	180	36	restrict	restrict	VERB
ap-1863	180	37	to	to	ADP
ap-1863	180	38	the	the	DET
ap-1863	180	39	set	set	NOUN
ap-1863	180	40	{	{	PUNCT
ap-1863	180	41	fs1	fs1	PROPN
ap-1863	180	42	1	1	NUM
ap-1863	180	43	fr1	fr1	PROPN
ap-1863	180	44	2	2	NUM
ap-1863	180	45	fs2	fs2	PROPN
ap-1863	180	46	1	1	NUM
ap-1863	180	47	|s1	|s1	NOUN
ap-1863	180	48	,	,	PUNCT
ap-1863	180	49	s2	s2	PROPN
ap-1863	180	50	,	,	PUNCT
ap-1863	180	51	r1	r1	PROPN
ap-1863	180	52	≥	≥	NUM
ap-1863	180	53	0	0	NUM
ap-1863	180	54	,	,	PUNCT
ap-1863	180	55	s1	s1	PROPN
ap-1863	180	56	≤	≤	PROPN
ap-1863	180	57	r1	r1	PROPN
ap-1863	180	58	}	}	PUNCT
ap-1863	180	59	.	.	PUNCT
ap-1863	181	1	(	(	PUNCT
ap-1863	181	2	13	13	NUM
ap-1863	181	3	)	)	PUNCT
ap-1863	181	4	we	we	PRON
ap-1863	181	5	can	can	AUX
ap-1863	181	6	generalize	generalize	VERB
ap-1863	181	7	this	this	DET
ap-1863	181	8	assertion	assertion	NOUN
ap-1863	181	9	for	for	ADP
ap-1863	181	10	n	n	X
ap-1863	181	11	>	>	X
ap-1863	181	12	2	2	NUM
ap-1863	181	13	as	as	SCONJ
ap-1863	181	14	follows	follow	VERB
ap-1863	181	15	.	.	PUNCT
ap-1863	182	1	theorem	theorem	VERB
ap-1863	182	2	3.3	3.3	NUM
ap-1863	182	3	.	.	PUNCT
ap-1863	183	1	u(a−n	u(a−n	PROPN
ap-1863	183	2	)	)	PUNCT
ap-1863	183	3	=	=	PRON
ap-1863	183	4	span	span	NOUN
ap-1863	183	5	{	{	PUNCT
ap-1863	183	6	fk1n	fk1n	PROPN
ap-1863	183	7	1	1	NUM
ap-1863	183	8	fk2n	fk2n	PROPN
ap-1863	183	9	2	2	NUM
ap-1863	183	10	·	·	PUNCT
ap-1863	183	11	·	·	PUNCT
ap-1863	183	12	·	·	PUNCT
ap-1863	183	13	fknn	fknn	PROPN
ap-1863	183	14	n	n	CCONJ
ap-1863	183	15	f	f	PROPN
ap-1863	183	16	k1,n−1	k1,n−1	ADJ
ap-1863	183	17	1	1	NUM
ap-1863	183	18	f	f	NOUN
ap-1863	183	19	k2,n−1	k2,n−1	PROPN
ap-1863	183	20	2	2	NUM
ap-1863	183	21	·	·	PUNCT
ap-1863	183	22	·	·	PUNCT
ap-1863	183	23	·	·	PUNCT
ap-1863	184	1	f	f	X
ap-1863	184	2	kn−1,n−1	kn−1,n−1	PROPN
ap-1863	184	3	n−1	n−1	PROPN
ap-1863	184	4	.	.	PUNCT
ap-1863	184	5	.	.	PUNCT
ap-1863	184	6	.	.	PUNCT
ap-1863	185	1	fk12	fk12	PROPN
ap-1863	185	2	1	1	NUM
ap-1863	185	3	fk22	fk22	PROPN
ap-1863	185	4	2	2	NUM
ap-1863	185	5	fk11	fk11	PROPN
ap-1863	185	6	1	1	NUM
ap-1863	185	7	∣∣kij	∣∣kij	PROPN
ap-1863	185	8	≤	≤	NUM
ap-1863	185	9	ki+1,j	ki+1,j	NOUN
ap-1863	185	10	,	,	PUNCT
ap-1863	185	11	i	i	PRON
ap-1863	185	12	=	=	NOUN
ap-1863	185	13	1	1	NUM
ap-1863	185	14	,	,	PUNCT
ap-1863	185	15	.	.	PUNCT
ap-1863	185	16	.	.	PUNCT
ap-1863	186	1	.	.	PUNCT
ap-1863	187	1	,	,	PUNCT
ap-1863	187	2	n−	n−	NOUN
ap-1863	187	3	1	1	NUM
ap-1863	187	4	,	,	PUNCT
ap-1863	187	5	j	j	PROPN
ap-1863	187	6	=	=	SYM
ap-1863	187	7	1	1	NUM
ap-1863	187	8	,	,	PUNCT
ap-1863	187	9	.	.	PUNCT
ap-1863	187	10	.	.	PUNCT
ap-1863	188	1	.	.	PUNCT
ap-1863	189	1	,	,	PUNCT
ap-1863	189	2	n	n	CCONJ
ap-1863	189	3	}	}	PUNCT
ap-1863	189	4	.	.	PUNCT
ap-1863	190	1	(	(	PUNCT
ap-1863	190	2	14	14	NUM
ap-1863	190	3	)	)	PUNCT
ap-1863	190	4	(	(	PUNCT
ap-1863	190	5	we	we	PRON
ap-1863	190	6	call	call	VERB
ap-1863	190	7	verma	verma	PROPN
ap-1863	190	8	monomials	monomial	VERB
ap-1863	190	9	those	those	DET
ap-1863	190	10	monomials	monomial	NOUN
ap-1863	190	11	appearing	appear	VERB
ap-1863	190	12	on	on	ADP
ap-1863	190	13	the	the	DET
ap-1863	190	14	right	right	ADJ
ap-1863	190	15	hand	hand	NOUN
ap-1863	190	16	side	side	NOUN
ap-1863	190	17	of	of	ADP
ap-1863	190	18	this	this	DET
ap-1863	190	19	equality	equality	NOUN
ap-1863	190	20	.	.	PUNCT
ap-1863	190	21	)	)	PUNCT
ap-1863	191	1	proof	proof	NOUN
ap-1863	191	2	.	.	PUNCT
ap-1863	192	1	we	we	PRON
ap-1863	192	2	proceed	proceed	VERB
ap-1863	192	3	by	by	ADP
ap-1863	192	4	induction	induction	NOUN
ap-1863	192	5	on	on	ADP
ap-1863	192	6	n.	n.	NOUN
ap-1863	192	7	for	for	ADP
ap-1863	192	8	n	n	NOUN
ap-1863	192	9	=	=	SYM
ap-1863	192	10	2	2	NUM
ap-1863	192	11	the	the	DET
ap-1863	192	12	assertion	assertion	NOUN
ap-1863	192	13	is	be	AUX
ap-1863	192	14	true	true	ADJ
ap-1863	192	15	,	,	PUNCT
ap-1863	192	16	now	now	ADV
ap-1863	192	17	assume	assume	VERB
ap-1863	192	18	validity	validity	NOUN
ap-1863	192	19	for	for	ADP
ap-1863	192	20	n	n	PRON
ap-1863	192	21	and	and	CCONJ
ap-1863	192	22	we	we	PRON
ap-1863	192	23	prove	prove	VERB
ap-1863	192	24	for	for	ADP
ap-1863	192	25	n+	n+	PRON
ap-1863	192	26	1	1	X
ap-1863	192	27	.	.	PUNCT
ap-1863	193	1	it	it	PRON
ap-1863	193	2	follows	follow	VERB
ap-1863	193	3	from	from	ADP
ap-1863	193	4	the	the	DET
ap-1863	193	5	preceeding	preceeding	NOUN
ap-1863	193	6	lemma	lemma	PROPN
ap-1863	193	7	that	that	SCONJ
ap-1863	193	8	it	it	PRON
ap-1863	193	9	is	be	AUX
ap-1863	193	10	sufficient	sufficient	ADJ
ap-1863	193	11	to	to	PART
ap-1863	193	12	consider	consider	VERB
ap-1863	193	13	v	v	ADP
ap-1863	193	14	∈	∈	PROPN
ap-1863	193	15	u(a−n+1	u(a−n+1	NUM
ap-1863	193	16	)	)	PUNCT
ap-1863	193	17	such	such	ADJ
ap-1863	193	18	that	that	SCONJ
ap-1863	193	19	452	452	NUM
ap-1863	193	20	vol	vol	NOUN
ap-1863	193	21	.	.	PUNCT
ap-1863	194	1	53	53	NUM
ap-1863	194	2	no	no	NOUN
ap-1863	194	3	.	.	PUNCT
ap-1863	195	1	5/2013	5/2013	NUM
ap-1863	195	2	note	note	NOUN
ap-1863	195	3	on	on	ADP
ap-1863	195	4	verma	verma	PROPN
ap-1863	195	5	bases	basis	NOUN
ap-1863	195	6	for	for	ADP
ap-1863	195	7	representations	representation	NOUN
ap-1863	195	8	of	of	ADP
ap-1863	195	9	simple	simple	ADJ
ap-1863	195	10	lie	lie	NOUN
ap-1863	195	11	algebras	algebra	NOUN
ap-1863	195	12	it	it	PRON
ap-1863	195	13	can	can	AUX
ap-1863	195	14	be	be	AUX
ap-1863	195	15	written	write	VERB
ap-1863	195	16	as	as	ADP
ap-1863	195	17	v1f	v1f	X
ap-1863	195	18	r	r	PROPN
ap-1863	195	19	n+1v2	n+1v2	PROPN
ap-1863	195	20	,	,	PUNCT
ap-1863	195	21	where	where	SCONJ
ap-1863	195	22	v1	v1	NOUN
ap-1863	195	23	,	,	PUNCT
ap-1863	195	24	v2	v2	PROPN
ap-1863	195	25	∈	∈	PROPN
ap-1863	195	26	u(a−n	u(a−n	PROPN
ap-1863	195	27	)	)	PUNCT
ap-1863	195	28	and	and	CCONJ
ap-1863	195	29	v1	v1	NOUN
ap-1863	195	30	is	be	AUX
ap-1863	195	31	a	a	DET
ap-1863	195	32	verma	verma	PROPN
ap-1863	195	33	monomial	monomial	NOUN
ap-1863	195	34	of	of	ADP
ap-1863	195	35	the	the	DET
ap-1863	195	36	form	form	NOUN
ap-1863	195	37	v1	v1	NOUN
ap-1863	196	1	=	=	SYM
ap-1863	196	2	fk1n	fk1n	PROPN
ap-1863	196	3	1	1	NUM
ap-1863	196	4	fk2n	fk2n	PROPN
ap-1863	196	5	2	2	NUM
ap-1863	196	6	·	·	PUNCT
ap-1863	196	7	·	·	PUNCT
ap-1863	196	8	·	·	PUNCT
ap-1863	196	9	fknn	fknn	PROPN
ap-1863	196	10	n	n	CCONJ
ap-1863	196	11	f	f	PROPN
ap-1863	196	12	k1,n−1	k1,n−1	ADJ
ap-1863	196	13	1	1	NUM
ap-1863	196	14	f	f	NOUN
ap-1863	196	15	k2,n−1	k2,n−1	PROPN
ap-1863	196	16	2	2	NUM
ap-1863	196	17	.	.	PUNCT
ap-1863	196	18	.	.	PUNCT
ap-1863	196	19	.	.	PUNCT
ap-1863	197	1	×	×	PROPN
ap-1863	197	2	fkn−1,n−1	fkn−1,n−1	PROPN
ap-1863	197	3	n−1	n−1	PROPN
ap-1863	197	4	.	.	PUNCT
ap-1863	197	5	.	.	PUNCT
ap-1863	197	6	.	.	PUNCT
ap-1863	198	1	fk12	fk12	PROPN
ap-1863	198	2	1	1	NUM
ap-1863	198	3	fk22	fk22	PROPN
ap-1863	198	4	2	2	NUM
ap-1863	198	5	fk11	fk11	PROPN
ap-1863	198	6	1	1	NUM
ap-1863	198	7	.	.	PUNCT
ap-1863	199	1	therefore	therefore	ADV
ap-1863	199	2	v1f	v1f	VERB
ap-1863	199	3	r	r	NOUN
ap-1863	199	4	n+1v2	n+1v2	NOUN
ap-1863	199	5	=	=	PUNCT
ap-1863	199	6	fk1n	fk1n	PROPN
ap-1863	199	7	1	1	NUM
ap-1863	199	8	fk2n	fk2n	PROPN
ap-1863	199	9	2	2	NUM
ap-1863	199	10	·	·	PUNCT
ap-1863	199	11	·	·	PUNCT
ap-1863	199	12	·	·	PUNCT
ap-1863	199	13	fknn	fknn	PROPN
ap-1863	199	14	n	n	PRON
ap-1863	199	15	frn+1	frn+1	PROPN
ap-1863	199	16	×	×	NOUN
ap-1863	199	17	fk1,n−1	fk1,n−1	PROPN
ap-1863	199	18	1	1	NUM
ap-1863	199	19	f	f	NOUN
ap-1863	199	20	k2,n−1	k2,n−1	PROPN
ap-1863	199	21	2	2	NUM
ap-1863	199	22	·	·	PUNCT
ap-1863	199	23	·	·	PUNCT
ap-1863	199	24	·	·	PUNCT
ap-1863	200	1	fkn−1,n−1	fkn−1,n−1	PROPN
ap-1863	200	2	n−1	n−1	PROPN
ap-1863	200	3	.	.	PUNCT
ap-1863	200	4	.	.	PUNCT
ap-1863	200	5	.	.	PUNCT
ap-1863	201	1	fk12	fk12	PROPN
ap-1863	201	2	1	1	NUM
ap-1863	201	3	fk22	fk22	PROPN
ap-1863	201	4	2	2	NUM
ap-1863	201	5	fk11	fk11	PROPN
ap-1863	201	6	1	1	NUM
ap-1863	201	7	v2︸	v2︸	PROPN
ap-1863	201	8	︷︷	︷︷	PROPN
ap-1863	201	9	︸	︸	ADP
ap-1863	201	10	v′	v′	PROPN
ap-1863	201	11	and	and	CCONJ
ap-1863	201	12	,	,	PUNCT
ap-1863	201	13	due	due	ADP
ap-1863	201	14	to	to	ADP
ap-1863	201	15	the	the	DET
ap-1863	201	16	induction	induction	NOUN
ap-1863	201	17	hypothesis	hypothesis	NOUN
ap-1863	201	18	,	,	PUNCT
ap-1863	201	19	v′	v′	PROPN
ap-1863	201	20	is	be	AUX
ap-1863	201	21	a	a	DET
ap-1863	201	22	linear	linear	ADJ
ap-1863	201	23	combination	combination	NOUN
ap-1863	201	24	of	of	ADP
ap-1863	201	25	verma	verma	PROPN
ap-1863	201	26	monomials	monomial	NOUN
ap-1863	201	27	.	.	PUNCT
ap-1863	202	1	now	now	ADV
ap-1863	202	2	if	if	SCONJ
ap-1863	202	3	r	r	NOUN
ap-1863	202	4	≥	≥	AUX
ap-1863	202	5	knn	knn	PROPN
ap-1863	202	6	,	,	PUNCT
ap-1863	202	7	then	then	ADV
ap-1863	202	8	the	the	DET
ap-1863	202	9	product	product	NOUN
ap-1863	202	10	fk1n	fk1n	VERB
ap-1863	202	11	1	1	NUM
ap-1863	202	12	fk2n	fk2n	PROPN
ap-1863	202	13	2	2	NUM
ap-1863	202	14	·	·	PUNCT
ap-1863	202	15	·	·	PUNCT
ap-1863	202	16	·	·	PUNCT
ap-1863	202	17	fknn	fknn	PROPN
ap-1863	202	18	n	n	PRON
ap-1863	202	19	frn+1	frn+1	NOUN
ap-1863	202	20	is	be	AUX
ap-1863	202	21	already	already	ADV
ap-1863	202	22	a	a	DET
ap-1863	202	23	verma	verma	PROPN
ap-1863	202	24	monomial	monomial	NOUN
ap-1863	202	25	and	and	CCONJ
ap-1863	202	26	the	the	DET
ap-1863	202	27	proof	proof	NOUN
ap-1863	202	28	is	be	AUX
ap-1863	202	29	finished	finish	VERB
ap-1863	202	30	.	.	PUNCT
ap-1863	203	1	when	when	SCONJ
ap-1863	203	2	r	r	NOUN
ap-1863	203	3	<	<	X
ap-1863	203	4	knn	knn	PROPN
ap-1863	203	5	,	,	PUNCT
ap-1863	203	6	we	we	PRON
ap-1863	203	7	rewrite	rewrite	VERB
ap-1863	203	8	the	the	DET
ap-1863	203	9	product	product	NOUN
ap-1863	203	10	fknn	fknn	PROPN
ap-1863	203	11	n	n	PRON
ap-1863	203	12	frn+1	frn+1	NOUN
ap-1863	203	13	using	use	VERB
ap-1863	203	14	(	(	PUNCT
ap-1863	203	15	2	2	NUM
ap-1863	203	16	)	)	PUNCT
ap-1863	203	17	from	from	ADP
ap-1863	203	18	lemma	lemma	PROPN
ap-1863	203	19	3.1	3.1	NUM
ap-1863	203	20	to	to	ADP
ap-1863	203	21	the	the	DET
ap-1863	203	22	form	form	NOUN
ap-1863	203	23	fknn	fknn	PROPN
ap-1863	203	24	n	n	CCONJ
ap-1863	203	25	frn+1	frn+1	NOUN
ap-1863	203	26	=	=	SYM
ap-1863	203	27	a0f	a0f	ADP
ap-1863	203	28	r	r	NOUN
ap-1863	203	29	n	n	NUM
ap-1863	203	30	f	f	NOUN
ap-1863	203	31	r	r	NOUN
ap-1863	203	32	n+1f	n+1f	PROPN
ap-1863	203	33	knn−r	knn−r	PROPN
ap-1863	203	34	n	n	PROPN
ap-1863	203	35	+	+	CCONJ
ap-1863	203	36	a1f	a1f	PROPN
ap-1863	203	37	r−1	r−1	PROPN
ap-1863	203	38	n	n	ADV
ap-1863	203	39	frn+1f	frn+1f	VERB
ap-1863	203	40	knn−r+1	knn−r+1	PROPN
ap-1863	203	41	n	n	PROPN
ap-1863	203	42	+	+	CCONJ
ap-1863	203	43	·	·	PUNCT
ap-1863	203	44	·	·	PUNCT
ap-1863	203	45	·	·	PUNCT
ap-1863	203	46	+	+	NUM
ap-1863	203	47	arf	arf	NOUN
ap-1863	203	48	r	r	NOUN
ap-1863	203	49	n+1f	n+1f	PROPN
ap-1863	203	50	knn	knn	PROPN
ap-1863	203	51	n	n	CCONJ
ap-1863	203	52	,	,	PUNCT
ap-1863	203	53	ai	ai	AUX
ap-1863	203	54	being	be	AUX
ap-1863	203	55	suitable	suitable	ADJ
ap-1863	203	56	complex	complex	ADJ
ap-1863	203	57	constants	constant	NOUN
ap-1863	203	58	.	.	PUNCT
ap-1863	204	1	from	from	ADP
ap-1863	204	2	this	this	PRON
ap-1863	204	3	we	we	PRON
ap-1863	204	4	conclude	conclude	VERB
ap-1863	204	5	that	that	SCONJ
ap-1863	204	6	fk1n	fk1n	PROPN
ap-1863	204	7	1	1	NUM
ap-1863	204	8	fk2n	fk2n	PROPN
ap-1863	204	9	2	2	NUM
ap-1863	204	10	·	·	PUNCT
ap-1863	204	11	·	·	PUNCT
ap-1863	204	12	·	·	PUNCT
ap-1863	204	13	fknn	fknn	PROPN
ap-1863	204	14	n	n	PRON
ap-1863	204	15	frn+1	frn+1	PROPN
ap-1863	204	16	∈	∈	PROPN
ap-1863	204	17	span{u1f	span{u1f	NOUN
ap-1863	204	18	r	r	NOUN
ap-1863	204	19	n+1w1	n+1w1	PROPN
ap-1863	204	20	,	,	PUNCT
ap-1863	204	21	u2f	u2f	ADJ
ap-1863	204	22	r	r	NOUN
ap-1863	204	23	n+1w2	n+1w2	NOUN
ap-1863	204	24	,	,	PUNCT
ap-1863	204	25	.	.	PUNCT
ap-1863	204	26	.	.	PUNCT
ap-1863	204	27	.	.	PUNCT
ap-1863	205	1	,	,	PUNCT
ap-1863	205	2	unf	unf	INTJ
ap-1863	205	3	r	r	NOUN
ap-1863	205	4	n+1wn	n+1wn	NOUN
ap-1863	205	5	}	}	PUNCT
ap-1863	205	6	,	,	PUNCT
ap-1863	205	7	(	(	PUNCT
ap-1863	205	8	15	15	NUM
ap-1863	205	9	)	)	PUNCT
ap-1863	205	10	where	where	SCONJ
ap-1863	205	11	ui	ui	PROPN
ap-1863	205	12	,	,	PUNCT
ap-1863	205	13	wi	wi	PROPN
ap-1863	205	14	are	be	AUX
ap-1863	205	15	verma	verma	PROPN
ap-1863	205	16	monomials	monomial	NOUN
ap-1863	205	17	from	from	ADP
ap-1863	205	18	u(a−n	u(a−n	PROPN
ap-1863	205	19	)	)	PUNCT
ap-1863	205	20	and	and	CCONJ
ap-1863	205	21	the	the	DET
ap-1863	205	22	highest	high	ADJ
ap-1863	205	23	degree	degree	NOUN
ap-1863	205	24	of	of	ADP
ap-1863	205	25	the	the	DET
ap-1863	205	26	simple	simple	ADJ
ap-1863	205	27	root	root	NOUN
ap-1863	205	28	fn	fn	NOUN
ap-1863	205	29	in	in	ADP
ap-1863	205	30	vi	vi	PROPN
ap-1863	205	31	is	be	AUX
ap-1863	205	32	less	less	ADV
ap-1863	205	33	or	or	CCONJ
ap-1863	205	34	equal	equal	ADJ
ap-1863	205	35	to	to	ADP
ap-1863	205	36	r.	r.	PROPN
ap-1863	205	37	therefore	therefore	ADV
ap-1863	205	38	the	the	DET
ap-1863	205	39	product	product	NOUN
ap-1863	205	40	(	(	PUNCT
ap-1863	205	41	15	15	NUM
ap-1863	205	42	)	)	PUNCT
ap-1863	205	43	is	be	AUX
ap-1863	205	44	a	a	DET
ap-1863	205	45	linear	linear	ADJ
ap-1863	205	46	combination	combination	NOUN
ap-1863	205	47	of	of	ADP
ap-1863	205	48	verma	verma	PROPN
ap-1863	205	49	monomials	monomial	NOUN
ap-1863	205	50	from	from	ADP
ap-1863	205	51	u(a−n+1	u(a−n+1	NOUN
ap-1863	205	52	)	)	PUNCT
ap-1863	205	53	,	,	PUNCT
ap-1863	205	54	as	as	SCONJ
ap-1863	205	55	desired	desire	VERB
ap-1863	205	56	.	.	PUNCT
ap-1863	206	1	linear	linear	ADJ
ap-1863	206	2	independence	independence	NOUN
ap-1863	206	3	of	of	ADP
ap-1863	206	4	verma	verma	PROPN
ap-1863	206	5	monomials	monomial	NOUN
ap-1863	206	6	can	can	AUX
ap-1863	206	7	be	be	AUX
ap-1863	206	8	shown	show	VERB
ap-1863	206	9	as	as	SCONJ
ap-1863	206	10	follows	follow	VERB
ap-1863	206	11	.	.	PUNCT
ap-1863	207	1	we	we	PRON
ap-1863	207	2	make	make	VERB
ap-1863	207	3	use	use	NOUN
ap-1863	207	4	of	of	ADP
ap-1863	207	5	commuting	commute	VERB
ap-1863	207	6	operators	operator	NOUN
ap-1863	207	7	adhi	adhi	VERB
ap-1863	207	8	:	:	PUNCT
ap-1863	208	1	u(a−n	u(a−n	PROPN
ap-1863	208	2	)	)	PUNCT
ap-1863	208	3	→	→	SYM
ap-1863	208	4	u(a−n	u(a−n	PROPN
ap-1863	208	5	)	)	PUNCT
ap-1863	208	6	defined	define	VERB
ap-1863	208	7	by	by	ADP
ap-1863	208	8	adhiv	adhiv	PROPN
ap-1863	208	9	=	=	PUNCT
ap-1863	209	1	[	[	X
ap-1863	209	2	hi	hi	INTJ
ap-1863	209	3	,	,	PUNCT
ap-1863	209	4	v	v	ADP
ap-1863	209	5	]	]	PUNCT
ap-1863	209	6	,	,	PUNCT
ap-1863	209	7	i	i	PRON
ap-1863	209	8	=	=	NOUN
ap-1863	209	9	1	1	NUM
ap-1863	209	10	,	,	PUNCT
ap-1863	209	11	.	.	PUNCT
ap-1863	209	12	.	.	PUNCT
ap-1863	209	13	.	.	PUNCT
ap-1863	210	1	,	,	PUNCT
ap-1863	210	2	n.	n.	NOUN
ap-1863	210	3	(	(	PUNCT
ap-1863	210	4	16	16	NUM
ap-1863	210	5	)	)	PUNCT
ap-1863	210	6	the	the	DET
ap-1863	210	7	algebra	algebra	PROPN
ap-1863	210	8	u(a−n	u(a−n	X
ap-1863	210	9	)	)	PUNCT
ap-1863	210	10	decomposes	decompose	VERB
ap-1863	210	11	into	into	ADP
ap-1863	210	12	the	the	DET
ap-1863	210	13	direct	direct	ADJ
ap-1863	210	14	sum	sum	NOUN
ap-1863	210	15	u(a−n	u(a−n	PROPN
ap-1863	210	16	)	)	PUNCT
ap-1863	210	17	=	=	PUNCT
ap-1863	210	18	⊕	⊕	PROPN
ap-1863	210	19	z1,	z1,	NOUN
ap-1863	210	20	...	...	PUNCT
ap-1863	210	21	,zn	,zn	PUNCT
ap-1863	210	22	v	v	X
ap-1863	210	23	(	(	PUNCT
ap-1863	210	24	z1	z1	PROPN
ap-1863	210	25	,	,	PUNCT
ap-1863	210	26	.	.	PUNCT
ap-1863	210	27	.	.	PUNCT
ap-1863	211	1	.	.	PUNCT
ap-1863	212	1	,	,	PUNCT
ap-1863	212	2	zn	zn	X
ap-1863	212	3	)	)	PUNCT
ap-1863	212	4	of	of	ADP
ap-1863	212	5	common	common	ADJ
ap-1863	212	6	eigenspaces	eigenspace	NOUN
ap-1863	212	7	of	of	ADP
ap-1863	212	8	operators	operator	NOUN
ap-1863	212	9	adhi	adhi	VERB
ap-1863	212	10	v	v	ADP
ap-1863	212	11	(	(	PUNCT
ap-1863	212	12	z1	z1	PROPN
ap-1863	212	13	,	,	PUNCT
ap-1863	212	14	.	.	PUNCT
ap-1863	212	15	.	.	PUNCT
ap-1863	213	1	.	.	PUNCT
ap-1863	214	1	,	,	PUNCT
ap-1863	214	2	zn	zn	X
ap-1863	214	3	)	)	PUNCT
ap-1863	214	4	=	=	PRON
ap-1863	214	5	{	{	PUNCT
ap-1863	214	6	v	v	NUM
ap-1863	214	7	∈	∈	PROPN
ap-1863	214	8	u(a−n	u(a−n	PROPN
ap-1863	214	9	)	)	PUNCT
ap-1863	214	10	∣∣	∣∣	X
ap-1863	214	11	adhiv	adhiv	PROPN
ap-1863	214	12	=	=	SYM
ap-1863	214	13	ziv	ziv	PROPN
ap-1863	214	14	,	,	PUNCT
ap-1863	214	15	i	i	NOUN
ap-1863	214	16	=	=	NOUN
ap-1863	214	17	1	1	NUM
ap-1863	214	18	,	,	PUNCT
ap-1863	214	19	.	.	PUNCT
ap-1863	214	20	.	.	PUNCT
ap-1863	215	1	.	.	PUNCT
ap-1863	216	1	,	,	PUNCT
ap-1863	216	2	n	n	CCONJ
ap-1863	216	3	}	}	PUNCT
ap-1863	216	4	.	.	PUNCT
ap-1863	217	1	two	two	NUM
ap-1863	217	2	vectors	vector	NOUN
ap-1863	217	3	belonging	belong	VERB
ap-1863	217	4	to	to	ADP
ap-1863	217	5	different	different	ADJ
ap-1863	217	6	subspaces	subspace	NOUN
ap-1863	217	7	are	be	AUX
ap-1863	217	8	linearly	linearly	ADV
ap-1863	217	9	independent	independent	ADJ
ap-1863	217	10	.	.	PUNCT
ap-1863	218	1	lemma	lemma	PROPN
ap-1863	218	2	3.4	3.4	NUM
ap-1863	218	3	.	.	PUNCT
ap-1863	219	1	(	(	PUNCT
ap-1863	219	2	1	1	NUM
ap-1863	219	3	.	.	NUM
ap-1863	219	4	)	)	PUNCT
ap-1863	219	5	pbwmonomials	pbwmonomial	NOUN
ap-1863	219	6	(	(	PUNCT
ap-1863	219	7	8)	8)	NUM
ap-1863	219	8	of	of	ADP
ap-1863	219	9	u(a−n	u(a−n	PROPN
ap-1863	219	10	)	)	PUNCT
ap-1863	219	11	are	be	AUX
ap-1863	219	12	eigenvectors	eigenvector	NOUN
ap-1863	219	13	of	of	ADP
ap-1863	219	14	all	all	DET
ap-1863	219	15	adhi	adhi	PROPN
ap-1863	219	16	.	.	PUNCT
ap-1863	220	1	(	(	PUNCT
ap-1863	220	2	2	2	NUM
ap-1863	220	3	.	.	PUNCT
ap-1863	220	4	)	)	PUNCT
ap-1863	220	5	v	v	ADP
ap-1863	220	6	∈	∈	PROPN
ap-1863	220	7	v	v	NOUN
ap-1863	220	8	(	(	PUNCT
ap-1863	220	9	z1	z1	PROPN
ap-1863	220	10	,	,	PUNCT
ap-1863	220	11	.	.	PUNCT
ap-1863	220	12	.	.	PUNCT
ap-1863	220	13	.	.	PUNCT
ap-1863	221	1	,	,	PUNCT
ap-1863	221	2	zn	zn	X
ap-1863	221	3	)	)	PUNCT
ap-1863	221	4	iff	iff	PROPN
ap-1863	221	5	s12	s12	PROPN
ap-1863	221	6	+	+	CCONJ
ap-1863	221	7	s13	s13	NOUN
ap-1863	221	8	+	+	CCONJ
ap-1863	221	9	·	·	PUNCT
ap-1863	221	10	·	·	PUNCT
ap-1863	221	11	·	·	PUNCT
ap-1863	222	1	+	+	NUM
ap-1863	222	2	s1,n+1	s1,n+1	PROPN
ap-1863	222	3	=	=	SYM
ap-1863	222	4	m1	m1	NOUN
ap-1863	222	5	,	,	PUNCT
ap-1863	222	6	s23	s23	NOUN
ap-1863	222	7	+	+	X
ap-1863	222	8	·	·	PUNCT
ap-1863	222	9	·	·	PUNCT
ap-1863	222	10	·	·	PUNCT
ap-1863	222	11	+	+	NUM
ap-1863	222	12	s2,n+1	s2,n+1	PROPN
ap-1863	222	13	=	=	SYM
ap-1863	222	14	m2	m2	PROPN
ap-1863	222	15	+	+	CCONJ
ap-1863	222	16	s12	s12	PROPN
ap-1863	222	17	,	,	PUNCT
ap-1863	222	18	...	...	PUNCT
ap-1863	223	1	sn	sn	INTJ
ap-1863	223	2	,	,	PUNCT
ap-1863	223	3	n+1	n+1	PROPN
ap-1863	223	4	=	=	SYM
ap-1863	223	5	mn	mn	PROPN
ap-1863	223	6	+	+	CCONJ
ap-1863	223	7	s1n	s1n	VERB
ap-1863	223	8	+	+	CCONJ
ap-1863	223	9	s2n	s2n	PROPN
ap-1863	223	10	+	+	NUM
ap-1863	223	11	·	·	PUNCT
ap-1863	223	12	·	·	PUNCT
ap-1863	223	13	·	·	PUNCT
ap-1863	224	1	+	+	NUM
ap-1863	224	2	sn−1,n	sn−1,n	NOUN
ap-1863	224	3	,	,	PUNCT
ap-1863	224	4	(	(	PUNCT
ap-1863	224	5	17	17	NUM
ap-1863	224	6	)	)	PUNCT
ap-1863	224	7	where	where	SCONJ
ap-1863	224	8	m	m	VERB
ap-1863	224	9	=	=	SYM
ap-1863	224	10	−	−	PROPN
ap-1863	224	11	1	1	NUM
ap-1863	224	12	n+	n+	NUM
ap-1863	224	13	1c1z	1c1z	NUM
ap-1863	224	14	,	,	PUNCT
ap-1863	224	15	(	(	PUNCT
ap-1863	224	16	18	18	NUM
ap-1863	224	17	)	)	PUNCT
ap-1863	224	18	and	and	CCONJ
ap-1863	224	19	m	m	NOUN
ap-1863	224	20	=	=	SYM
ap-1863	224	21			ADJ
ap-1863	224	22	m1	m1	NOUN
ap-1863	224	23	m2	m2	PROPN
ap-1863	224	24	m3	m3	PROPN
ap-1863	224	25	...	...	PUNCT
ap-1863	225	1	mn−1	mn−1	PROPN
ap-1863	225	2	mn	mn	PROPN
ap-1863	225	3			PROPN
ap-1863	225	4	,	,	PUNCT
ap-1863	225	5	c1	c1	PROPN
ap-1863	225	6	=	=	PUNCT
ap-1863	225	7			PROPN
ap-1863	225	8	−n	−n	ADV
ap-1863	225	9	−(n−	−(n−	VERB
ap-1863	225	10	1	1	NUM
ap-1863	225	11	)	)	PUNCT
ap-1863	225	12	−(n−	−(n−	NOUN
ap-1863	225	13	2	2	NUM
ap-1863	225	14	)	)	PUNCT
ap-1863	225	15	·	·	PUNCT
ap-1863	225	16	·	·	PUNCT
ap-1863	225	17	·	·	PUNCT
ap-1863	226	1	−2	−2	X
ap-1863	226	2	−1	−1	NOUN
ap-1863	226	3	1	1	NUM
ap-1863	226	4	−(n−	−(n−	ADJ
ap-1863	226	5	1	1	NUM
ap-1863	226	6	)	)	PUNCT
ap-1863	226	7	−(n−	−(n−	NOUN
ap-1863	226	8	2	2	NUM
ap-1863	226	9	)	)	PUNCT
ap-1863	226	10	·	·	PUNCT
ap-1863	226	11	·	·	PUNCT
ap-1863	226	12	·	·	PUNCT
ap-1863	227	1	−2	−2	X
ap-1863	227	2	−1	−1	NOUN
ap-1863	227	3	1	1	NUM
ap-1863	227	4	2	2	NUM
ap-1863	227	5	−(n−	−(n−	NOUN
ap-1863	227	6	2	2	NUM
ap-1863	227	7	)	)	PUNCT
ap-1863	227	8	·	·	PUNCT
ap-1863	227	9	·	·	PUNCT
ap-1863	227	10	·	·	PUNCT
ap-1863	228	1	−2	−2	X
ap-1863	228	2	−1	−1	NOUN
ap-1863	228	3	...	...	PUNCT
ap-1863	228	4	...	...	PUNCT
ap-1863	228	5	...	...	PUNCT
ap-1863	228	6	...	...	PUNCT
ap-1863	228	7	...	...	PUNCT
ap-1863	229	1	1	1	NUM
ap-1863	229	2	2	2	NUM
ap-1863	229	3	3	3	NUM
ap-1863	229	4	·	·	PUNCT
ap-1863	229	5	·	·	PUNCT
ap-1863	229	6	·	·	PUNCT
ap-1863	230	1	−2	−2	X
ap-1863	230	2	−1	−1	NOUN
ap-1863	230	3	1	1	NUM
ap-1863	230	4	2	2	NUM
ap-1863	230	5	3	3	NUM
ap-1863	230	6	·	·	PUNCT
ap-1863	230	7	·	·	PUNCT
ap-1863	230	8	·	·	PUNCT
ap-1863	231	1	(	(	PUNCT
ap-1863	231	2	n−	n−	NOUN
ap-1863	231	3	1	1	NUM
ap-1863	231	4	)	)	PUNCT
ap-1863	231	5	−1	−1	NOUN
ap-1863	231	6			NOUN
ap-1863	231	7	,	,	PUNCT
ap-1863	231	8	z	z	NOUN
ap-1863	231	9	=	=	SYM
ap-1863	231	10			ADJ
ap-1863	231	11	z1	z1	ADJ
ap-1863	231	12	z2	z2	PROPN
ap-1863	231	13	z3	z3	PROPN
ap-1863	231	14	...	...	PUNCT
ap-1863	232	1	zn−1	zn−1	PROPN
ap-1863	232	2	zn	zn	NUM
ap-1863	232	3			PROPN
ap-1863	232	4	.	.	PUNCT
ap-1863	233	1	proof	proof	NOUN
ap-1863	233	2	.	.	PUNCT
ap-1863	234	1	(	(	PUNCT
ap-1863	234	2	1	1	NUM
ap-1863	234	3	.	.	PUNCT
ap-1863	234	4	)	)	PUNCT
ap-1863	235	1	the	the	DET
ap-1863	235	2	assertion	assertion	NOUN
ap-1863	235	3	is	be	AUX
ap-1863	235	4	direct	direct	ADJ
ap-1863	235	5	consequence	consequence	NOUN
ap-1863	235	6	of	of	ADP
ap-1863	235	7	the	the	DET
ap-1863	235	8	fact	fact	NOUN
ap-1863	235	9	that	that	SCONJ
ap-1863	235	10	generators	generator	NOUN
ap-1863	235	11	ejk	ejk	PROPN
ap-1863	235	12	,	,	PUNCT
ap-1863	235	13	j	j	PROPN
ap-1863	235	14	<	<	X
ap-1863	235	15	k	k	PROPN
ap-1863	235	16	are	be	AUX
ap-1863	235	17	eigenvectors	eigenvector	NOUN
ap-1863	235	18	of	of	ADP
ap-1863	235	19	adhi	adhi	PROPN
ap-1863	235	20	.	.	PUNCT
ap-1863	236	1	(	(	PUNCT
ap-1863	236	2	2	2	NUM
ap-1863	236	3	.	.	NUM
ap-1863	236	4	)	)	PUNCT
ap-1863	236	5	system	system	NOUN
ap-1863	236	6	(	(	PUNCT
ap-1863	236	7	17	17	NUM
ap-1863	236	8	)	)	PUNCT
ap-1863	236	9	was	be	AUX
ap-1863	236	10	obtained	obtain	VERB
ap-1863	236	11	using	use	VERB
ap-1863	236	12	generators	generator	NOUN
ap-1863	236	13	eii	eii	PROPN
ap-1863	236	14	,	,	PUNCT
ap-1863	236	15	eii	eii	PROPN
ap-1863	236	16	=	=	PROPN
ap-1863	236	17	1	1	NUM
ap-1863	236	18	n+	n+	SYM
ap-1863	236	19	1	1	NUM
ap-1863	236	20	(	(	PUNCT
ap-1863	236	21	c1	c1	PROPN
ap-1863	236	22	−	−	PROPN
ap-1863	236	23	n+1−i∑	n+1−i∑	PROPN
ap-1863	236	24	j=1	j=1	PROPN
ap-1863	236	25	jhn+1−j+	jhn+1−j+	PROPN
ap-1863	236	26	n∑	n∑	PROPN
ap-1863	236	27	j	j	PROPN
ap-1863	236	28	=	=	X
ap-1863	236	29	n+2−i	n+2−i	PROPN
ap-1863	236	30	(	(	PUNCT
ap-1863	236	31	n+	n+	NUM
ap-1863	236	32	1−	1−	NUM
ap-1863	236	33	j)hn+1−j	j)hn+1−j	NUM
ap-1863	236	34	)	)	PUNCT
ap-1863	236	35	,	,	PUNCT
ap-1863	236	36	ad	ad	NOUN
ap-1863	236	37	eiiv	eiiv	NOUN
ap-1863	236	38	=	=	SYM
ap-1863	236	39	1	1	NUM
ap-1863	236	40	n+	n+	SYM
ap-1863	236	41	1	1	NUM
ap-1863	236	42	(	(	PUNCT
ap-1863	236	43	−	−	PROPN
ap-1863	236	44	n+1−j∑	n+1−j∑	NUM
ap-1863	236	45	j=1	j=1	NOUN
ap-1863	237	1	jzn+1−j+	jzn+1−j+	PROPN
ap-1863	237	2	n∑	n∑	PROPN
ap-1863	237	3	j	j	PROPN
ap-1863	237	4	=	=	X
ap-1863	237	5	n+2−i	n+2−i	PROPN
ap-1863	237	6	(	(	PUNCT
ap-1863	237	7	n+	n+	NUM
ap-1863	237	8	1−	1−	NUM
ap-1863	237	9	j)zn+1−j	j)zn+1−j	PROPN
ap-1863	237	10	)	)	PUNCT
ap-1863	237	11	v	v	ADP
ap-1863	237	12	≡	≡	PROPN
ap-1863	237	13	miv	miv	PROPN
ap-1863	237	14	.	.	PUNCT
ap-1863	238	1	c1	c1	PROPN
ap-1863	238	2	=	=	PUNCT
ap-1863	238	3	e11	e11	PROPN
ap-1863	238	4	+	+	CCONJ
ap-1863	238	5	·	·	PUNCT
ap-1863	238	6	·	·	PUNCT
ap-1863	238	7	·	·	PUNCT
ap-1863	238	8	+	+	NOUN
ap-1863	238	9	enn	enn	PROPN
ap-1863	238	10	stands	stand	VERB
ap-1863	238	11	for	for	ADP
ap-1863	238	12	the	the	DET
ap-1863	238	13	casimir	casimir	NOUN
ap-1863	238	14	operator	operator	NOUN
ap-1863	238	15	.	.	PUNCT
ap-1863	239	1	note	note	VERB
ap-1863	239	2	that	that	SCONJ
ap-1863	239	3	the	the	DET
ap-1863	239	4	matrix	matrix	NOUN
ap-1863	239	5	which	which	PRON
ap-1863	239	6	appears	appear	VERB
ap-1863	239	7	in	in	ADP
ap-1863	239	8	(	(	PUNCT
ap-1863	239	9	18	18	NUM
ap-1863	239	10	)	)	PUNCT
ap-1863	239	11	is	be	AUX
ap-1863	239	12	the	the	DET
ap-1863	239	13	inverse	inverse	NOUN
ap-1863	239	14	of	of	ADP
ap-1863	239	15	the	the	DET
ap-1863	239	16	cartan	cartan	ADJ
ap-1863	239	17	matrix	matrix	NOUN
ap-1863	239	18	of	of	ADP
ap-1863	239	19	the	the	DET
ap-1863	239	20	algebra	algebra	NOUN
ap-1863	239	21	an	an	PROPN
ap-1863	239	22	.	.	NOUN
ap-1863	239	23	from	from	ADP
ap-1863	239	24	equations	equation	NOUN
ap-1863	239	25	(	(	PUNCT
ap-1863	239	26	17	17	NUM
ap-1863	239	27	)	)	PUNCT
ap-1863	239	28	we	we	PRON
ap-1863	239	29	see	see	VERB
ap-1863	239	30	that	that	SCONJ
ap-1863	239	31	mi	mi	PROPN
ap-1863	239	32	are	be	AUX
ap-1863	239	33	all	all	PRON
ap-1863	239	34	nonnegative	nonnegative	ADJ
ap-1863	239	35	453	453	NUM
ap-1863	239	36	s.	s.	PROPN
ap-1863	239	37	pošta	pošta	PROPN
ap-1863	239	38	,	,	PUNCT
ap-1863	239	39	m.	m.	PROPN
ap-1863	239	40	havlíček	havlíček	PROPN
ap-1863	239	41	acta	acta	PROPN
ap-1863	239	42	polytechnica	polytechnica	PROPN
ap-1863	239	43	integers	integer	NOUN
ap-1863	239	44	.	.	PUNCT
ap-1863	240	1	the	the	DET
ap-1863	240	2	dimension	dimension	NOUN
ap-1863	240	3	of	of	ADP
ap-1863	240	4	v	v	NOUN
ap-1863	240	5	(	(	PUNCT
ap-1863	240	6	z1	z1	PROPN
ap-1863	240	7	,	,	PUNCT
ap-1863	240	8	.	.	PUNCT
ap-1863	240	9	.	.	PUNCT
ap-1863	240	10	.	.	PUNCT
ap-1863	241	1	,	,	PUNCT
ap-1863	241	2	zn	zn	X
ap-1863	241	3	)	)	PUNCT
ap-1863	241	4	is	be	AUX
ap-1863	241	5	finite	finite	ADJ
ap-1863	241	6	since	since	SCONJ
ap-1863	241	7	for	for	ADP
ap-1863	241	8	fixed	fix	VERB
ap-1863	241	9	right	right	ADJ
ap-1863	241	10	hand	hand	NOUN
ap-1863	241	11	sides	side	NOUN
ap-1863	241	12	of	of	ADP
ap-1863	241	13	equations	equation	NOUN
ap-1863	241	14	(	(	PUNCT
ap-1863	241	15	18	18	NUM
ap-1863	241	16	)	)	PUNCT
ap-1863	241	17	there	there	PRON
ap-1863	241	18	is	be	VERB
ap-1863	241	19	only	only	ADV
ap-1863	241	20	a	a	DET
ap-1863	241	21	finite	finite	ADJ
ap-1863	241	22	number	number	NOUN
ap-1863	241	23	of	of	ADP
ap-1863	241	24	decompositions	decomposition	NOUN
ap-1863	241	25	of	of	ADP
ap-1863	241	26	m1	m1	NOUN
ap-1863	241	27	into	into	ADP
ap-1863	241	28	the	the	DET
ap-1863	241	29	sum	sum	NOUN
ap-1863	241	30	of	of	ADP
ap-1863	241	31	s12	s12	PROPN
ap-1863	241	32	,	,	PUNCT
ap-1863	241	33	s13	s13	NOUN
ap-1863	241	34	,	,	PUNCT
ap-1863	241	35	.	.	PUNCT
ap-1863	241	36	.	.	PUNCT
ap-1863	242	1	.	.	PUNCT
ap-1863	243	1	,	,	PUNCT
ap-1863	243	2	s1,n+1	s1,n+1	ADJ
ap-1863	243	3	,	,	PUNCT
ap-1863	243	4	etc	etc	X
ap-1863	243	5	.	.	X
ap-1863	243	6	for	for	ADP
ap-1863	243	7	each	each	PRON
ap-1863	243	8	of	of	ADP
ap-1863	243	9	the	the	DET
ap-1863	243	10	possibilities	possibility	NOUN
ap-1863	243	11	(	(	PUNCT
ap-1863	243	12	s12	s12	NOUN
ap-1863	243	13	,	,	PUNCT
ap-1863	243	14	.	.	PUNCT
ap-1863	243	15	.	.	PUNCT
ap-1863	244	1	.	.	PUNCT
ap-1863	245	1	,	,	PUNCT
ap-1863	245	2	s1,n+1	s1,n+1	ADJ
ap-1863	245	3	,	,	PUNCT
ap-1863	245	4	s21	s21	NOUN
ap-1863	245	5	,	,	PUNCT
ap-1863	245	6	.	.	PUNCT
ap-1863	245	7	.	.	PUNCT
ap-1863	246	1	.	.	PUNCT
ap-1863	247	1	,	,	PUNCT
ap-1863	247	2	s2,n+1	s2,n+1	PROPN
ap-1863	247	3	,	,	PUNCT
ap-1863	247	4	.	.	PUNCT
ap-1863	247	5	.	.	PUNCT
ap-1863	248	1	.	.	PUNCT
ap-1863	249	1	,	,	PUNCT
ap-1863	249	2	.	.	PUNCT
ap-1863	249	3	.	.	PUNCT
ap-1863	250	1	.	.	PUNCT
ap-1863	251	1	,	,	PUNCT
ap-1863	251	2	sn	sn	PROPN
ap-1863	251	3	,	,	PUNCT
ap-1863	251	4	n+1	n+1	PROPN
ap-1863	251	5	)	)	PUNCT
ap-1863	251	6	(	(	PUNCT
ap-1863	251	7	19	19	NUM
ap-1863	251	8	)	)	PUNCT
ap-1863	251	9	we	we	PRON
ap-1863	251	10	obtain	obtain	VERB
ap-1863	251	11	a	a	DET
ap-1863	251	12	basis	basis	NOUN
ap-1863	251	13	vector	vector	NOUN
ap-1863	251	14	v	v	ADP
ap-1863	251	15	∈	∈	PROPN
ap-1863	251	16	v	v	NOUN
ap-1863	251	17	(	(	PUNCT
ap-1863	251	18	z1	z1	PROPN
ap-1863	251	19	,	,	PUNCT
ap-1863	251	20	.	.	PUNCT
ap-1863	251	21	.	.	PUNCT
ap-1863	252	1	.	.	PUNCT
ap-1863	253	1	,	,	PUNCT
ap-1863	253	2	zn	zn	X
ap-1863	253	3	)	)	PUNCT
ap-1863	253	4	.	.	PUNCT
ap-1863	254	1	by	by	ADP
ap-1863	254	2	exhausting	exhaust	VERB
ap-1863	254	3	all	all	DET
ap-1863	254	4	these	these	DET
ap-1863	254	5	possibilities	possibility	NOUN
ap-1863	254	6	we	we	PRON
ap-1863	254	7	obtain	obtain	VERB
ap-1863	254	8	the	the	DET
ap-1863	254	9	basis	basis	NOUN
ap-1863	254	10	of	of	ADP
ap-1863	254	11	v	v	PROPN
ap-1863	254	12	(	(	PUNCT
ap-1863	254	13	z1	z1	PROPN
ap-1863	254	14	,	,	PUNCT
ap-1863	254	15	.	.	PUNCT
ap-1863	254	16	.	.	PUNCT
ap-1863	254	17	.	.	PUNCT
ap-1863	255	1	,	,	PUNCT
ap-1863	255	2	zn	zn	X
ap-1863	255	3	)	)	PUNCT
ap-1863	255	4	.	.	PUNCT
ap-1863	256	1	lemma	lemma	PROPN
ap-1863	256	2	3.5	3.5	NUM
ap-1863	256	3	.	.	PUNCT
ap-1863	257	1	verma	verma	PROPN
ap-1863	257	2	monomial	monomial	PROPN
ap-1863	257	3	v	v	PROPN
ap-1863	257	4	=	=	PUNCT
ap-1863	257	5	(	(	PUNCT
ap-1863	257	6	f	f	X
ap-1863	257	7	l1n	l1n	PROPN
ap-1863	257	8	1	1	NUM
ap-1863	257	9	·	·	PUNCT
ap-1863	257	10	·	·	PUNCT
ap-1863	257	11	·	·	PUNCT
ap-1863	258	1	f	f	X
ap-1863	258	2	ln−1,n	ln−1,n	NUM
ap-1863	259	1	n−1	n−1	PROPN
ap-1863	259	2	fkn	fkn	INTJ
ap-1863	259	3	n	n	PROPN
ap-1863	259	4	)	)	PUNCT
ap-1863	259	5	(	(	PUNCT
ap-1863	259	6	f	f	PROPN
ap-1863	259	7	l1,n−1	l1,n−1	PROPN
ap-1863	259	8	1	1	NUM
ap-1863	259	9	·	·	PUNCT
ap-1863	259	10	·	·	PUNCT
ap-1863	259	11	·	·	PUNCT
ap-1863	260	1	f	f	X
ap-1863	260	2	ln−2,n−1	ln−2,n−1	PROPN
ap-1863	260	3	n−2	n−2	PROPN
ap-1863	260	4	f	f	PROPN
ap-1863	260	5	kn−1	kn−1	PROPN
ap-1863	260	6	n−1	n−1	PROPN
ap-1863	260	7	)	)	PUNCT
ap-1863	260	8	·	·	PUNCT
ap-1863	260	9	·	·	PUNCT
ap-1863	260	10	·	·	PUNCT
ap-1863	261	1	(	(	PUNCT
ap-1863	261	2	f	f	X
ap-1863	261	3	l12	l12	NOUN
ap-1863	261	4	1	1	NUM
ap-1863	261	5	fk2	fk2	NOUN
ap-1863	261	6	2	2	NUM
ap-1863	261	7	)	)	PUNCT
ap-1863	261	8	(	(	PUNCT
ap-1863	261	9	fk1	fk1	NOUN
ap-1863	261	10	1	1	NUM
ap-1863	261	11	)	)	PUNCT
ap-1863	261	12	∈	∈	PROPN
ap-1863	261	13	v	v	NOUN
ap-1863	261	14	(	(	PUNCT
ap-1863	261	15	z1	z1	PROPN
ap-1863	261	16	,	,	PUNCT
ap-1863	261	17	.	.	PUNCT
ap-1863	261	18	.	.	PUNCT
ap-1863	261	19	.	.	PUNCT
ap-1863	262	1	,	,	PUNCT
ap-1863	262	2	zn	zn	X
ap-1863	262	3	)	)	PUNCT
ap-1863	262	4	(	(	PUNCT
ap-1863	262	5	20	20	X
ap-1863	262	6	)	)	PUNCT
ap-1863	262	7	iff	iff	PROPN
ap-1863	262	8			ADJ
ap-1863	262	9	z1	z1	PROPN
ap-1863	262	10	z2	z2	PROPN
ap-1863	262	11	...	...	PUNCT
ap-1863	263	1	zn−1	zn−1	PROPN
ap-1863	263	2	zn	zn	NOUN
ap-1863	263	3			PUNCT
ap-1863	264	1	=	=	PRON
ap-1863	264	2			ADJ
ap-1863	264	3	−2	−2	NOUN
ap-1863	264	4	−1	−1	NOUN
ap-1863	264	5	0	0	PUNCT
ap-1863	264	6	·	·	PUNCT
ap-1863	264	7	·	·	PUNCT
ap-1863	264	8	·	·	PUNCT
ap-1863	264	9	0	0	NUM
ap-1863	264	10	0	0	NUM
ap-1863	264	11	−1	−1	NOUN
ap-1863	264	12	−2	−2	NOUN
ap-1863	264	13	−1	−1	NOUN
ap-1863	264	14	·	·	PUNCT
ap-1863	264	15	·	·	PUNCT
ap-1863	264	16	·	·	PUNCT
ap-1863	264	17	0	0	NUM
ap-1863	264	18	0	0	NUM
ap-1863	264	19	...	...	PUNCT
ap-1863	264	20	...	...	PUNCT
ap-1863	264	21	...	...	PUNCT
ap-1863	264	22	...	...	PUNCT
ap-1863	264	23	...	...	PUNCT
ap-1863	265	1	0	0	NUM
ap-1863	265	2	0	0	NUM
ap-1863	265	3	0	0	NUM
ap-1863	265	4	·	·	PUNCT
ap-1863	265	5	·	·	PUNCT
ap-1863	265	6	·	·	PUNCT
ap-1863	266	1	−2	−2	X
ap-1863	266	2	−1	−1	NOUN
ap-1863	266	3	0	0	NUM
ap-1863	266	4	0	0	NUM
ap-1863	266	5	0	0	NUM
ap-1863	266	6	·	·	PUNCT
ap-1863	266	7	·	·	PUNCT
ap-1863	266	8	·	·	PUNCT
ap-1863	267	1	−1	−1	NOUN
ap-1863	267	2	−2	−2	NOUN
ap-1863	267	3			DET
ap-1863	267	4	×	×	NOUN
ap-1863	267	5			ADJ
ap-1863	267	6	l1n	l1n	NOUN
ap-1863	267	7	+	+	CCONJ
ap-1863	267	8	l1,n−1	l1,n−1	PROPN
ap-1863	267	9	+	+	CCONJ
ap-1863	267	10	·	·	PUNCT
ap-1863	267	11	·	·	PUNCT
ap-1863	267	12	·	·	PUNCT
ap-1863	267	13	+	+	NUM
ap-1863	267	14	l12	l12	NOUN
ap-1863	267	15	+	+	CCONJ
ap-1863	267	16	k1	k1	NOUN
ap-1863	267	17	l2n	l2n	NOUN
ap-1863	267	18	+	+	CCONJ
ap-1863	267	19	l2,n−1	l2,n−1	ADJ
ap-1863	267	20	+	+	X
ap-1863	267	21	·	·	PUNCT
ap-1863	267	22	·	·	PUNCT
ap-1863	267	23	·	·	PUNCT
ap-1863	267	24	+	+	PUNCT
ap-1863	268	1	l2,3	l2,3	NOUN
ap-1863	268	2	+	+	CCONJ
ap-1863	268	3	k2	k2	ADJ
ap-1863	268	4	...	...	PUNCT
ap-1863	268	5	ln−1,n	ln−1,n	X
ap-1863	269	1	+	+	CCONJ
ap-1863	269	2	kn−1	kn−1	PROPN
ap-1863	269	3	kn	kn	PROPN
ap-1863	269	4			PROPN
ap-1863	269	5	.	.	PUNCT
ap-1863	270	1	(	(	PUNCT
ap-1863	270	2	21	21	NUM
ap-1863	270	3	)	)	PUNCT
ap-1863	270	4	proof	proof	NOUN
ap-1863	270	5	.	.	PUNCT
ap-1863	271	1	by	by	ADP
ap-1863	271	2	direct	direct	ADJ
ap-1863	271	3	calculation	calculation	NOUN
ap-1863	271	4	using	use	VERB
ap-1863	271	5	relations	relation	NOUN
ap-1863	271	6	[	[	X
ap-1863	271	7	fi	fi	NOUN
ap-1863	271	8	,	,	PUNCT
ap-1863	271	9	hj	hj	X
ap-1863	271	10	]	]	PUNCT
ap-1863	271	11	=	=	SYM
ap-1863	271	12	cijfi	cijfi	PROPN
ap-1863	271	13	,	,	PUNCT
ap-1863	271	14	cij	cij	PROPN
ap-1863	271	15	=	=	SYM
ap-1863	271	16	2δij	2δij	PROPN
ap-1863	271	17	−	−	NOUN
ap-1863	271	18	δi	δi	NOUN
ap-1863	271	19	,	,	PUNCT
ap-1863	271	20	j+1	j+1	PROPN
ap-1863	271	21	−	−	NOUN
ap-1863	271	22	δi	δi	NOUN
ap-1863	271	23	,	,	PUNCT
ap-1863	271	24	j−1	j−1	PROPN
ap-1863	271	25	,	,	PUNCT
ap-1863	271	26	cij	cij	PROPN
ap-1863	271	27	=	=	PROPN
ap-1863	271	28	0	0	NUM
ap-1863	271	29	for	for	ADP
ap-1863	271	30	|i−	|i−	NOUN
ap-1863	271	31	j|	j|	PROPN
ap-1863	271	32	>	>	X
ap-1863	271	33	1	1	NUM
ap-1863	271	34	and	and	CCONJ
ap-1863	271	35	,	,	PUNCT
ap-1863	271	36	consequently	consequently	ADV
ap-1863	271	37	[	[	X
ap-1863	271	38	fαi	fαi	X
ap-1863	271	39	,	,	PUNCT
ap-1863	271	40	hj	hj	X
ap-1863	271	41	]	]	PUNCT
ap-1863	271	42	=	=	PUNCT
ap-1863	271	43	αcijf	αcijf	X
ap-1863	271	44	α	α	INTJ
ap-1863	271	45	i	i	PRON
ap-1863	271	46	.	.	PUNCT
ap-1863	272	1	note	note	VERB
ap-1863	272	2	that	that	SCONJ
ap-1863	272	3	inverting	invert	VERB
ap-1863	272	4	the	the	DET
ap-1863	272	5	cartan	cartan	ADJ
ap-1863	272	6	matrix	matrix	NOUN
ap-1863	272	7	and	and	CCONJ
ap-1863	272	8	matrix	matrix	NOUN
ap-1863	272	9	from	from	ADP
ap-1863	272	10	eq	eq	PROPN
ap-1863	272	11	.	.	PUNCT
ap-1863	273	1	(	(	PUNCT
ap-1863	273	2	21	21	NUM
ap-1863	273	3	)	)	PUNCT
ap-1863	273	4	we	we	PRON
ap-1863	273	5	can	can	AUX
ap-1863	273	6	rewrite	rewrite	VERB
ap-1863	273	7	system	system	NOUN
ap-1863	273	8	(	(	PUNCT
ap-1863	273	9	21	21	NUM
ap-1863	273	10	)	)	PUNCT
ap-1863	273	11	to	to	ADP
ap-1863	273	12	the	the	DET
ap-1863	273	13	form	form	NOUN
ap-1863	273	14	l1n	l1n	NOUN
ap-1863	273	15	+	+	CCONJ
ap-1863	273	16	l1,n−1	l1,n−1	PROPN
ap-1863	273	17	+	+	CCONJ
ap-1863	273	18	·	·	PUNCT
ap-1863	273	19	·	·	PUNCT
ap-1863	273	20	·	·	PUNCT
ap-1863	274	1	+	+	NUM
ap-1863	274	2	l12	l12	ADJ
ap-1863	274	3	+	+	CCONJ
ap-1863	274	4	k1	k1	NOUN
ap-1863	274	5	=	=	SYM
ap-1863	274	6	m1	m1	NOUN
ap-1863	274	7	,	,	PUNCT
ap-1863	274	8	l2n	l2n	PROPN
ap-1863	274	9	+	+	CCONJ
ap-1863	274	10	l2,n−1	l2,n−1	ADJ
ap-1863	274	11	+	+	X
ap-1863	274	12	·	·	PUNCT
ap-1863	274	13	·	·	PUNCT
ap-1863	274	14	·	·	PUNCT
ap-1863	274	15	+	+	NUM
ap-1863	274	16	k2	k2	X
ap-1863	274	17	=	=	SYM
ap-1863	274	18	m1	m1	PROPN
ap-1863	274	19	+	+	PROPN
ap-1863	274	20	m2	m2	PROPN
ap-1863	274	21	,	,	PUNCT
ap-1863	274	22	...	...	PUNCT
ap-1863	275	1	ln−1,n	ln−1,n	X
ap-1863	275	2	+	+	CCONJ
ap-1863	275	3	kn−1	kn−1	PROPN
ap-1863	275	4	=	=	SYM
ap-1863	275	5	m1	m1	PROPN
ap-1863	276	1	+	+	PROPN
ap-1863	276	2	m2	m2	PROPN
ap-1863	276	3	+	+	CCONJ
ap-1863	277	1	·	·	PUNCT
ap-1863	277	2	·	·	PUNCT
ap-1863	277	3	·	·	PUNCT
ap-1863	277	4	+	+	SYM
ap-1863	277	5	mn−1	mn−1	ADJ
ap-1863	277	6	,	,	PUNCT
ap-1863	277	7	kn	kn	NOUN
ap-1863	277	8	=	=	SYM
ap-1863	277	9	m1	m1	PROPN
ap-1863	277	10	+	+	PROPN
ap-1863	277	11	m2	m2	PROPN
ap-1863	277	12	+	+	CCONJ
ap-1863	277	13	·	·	PUNCT
ap-1863	277	14	·	·	PUNCT
ap-1863	277	15	·	·	PUNCT
ap-1863	277	16	+	+	PROPN
ap-1863	277	17	mn	mn	PROPN
ap-1863	277	18	.	.	PUNCT
ap-1863	278	1	(	(	PUNCT
ap-1863	278	2	22	22	NUM
ap-1863	278	3	)	)	PUNCT
ap-1863	278	4	theorem	theorem	VERB
ap-1863	278	5	3.6	3.6	NUM
ap-1863	278	6	.	.	PUNCT
ap-1863	279	1	if	if	SCONJ
ap-1863	279	2	the	the	DET
ap-1863	279	3	numbers	number	NOUN
ap-1863	279	4	m1	m1	PROPN
ap-1863	279	5	,	,	PUNCT
ap-1863	279	6	.	.	PUNCT
ap-1863	279	7	.	.	PUNCT
ap-1863	280	1	.	.	PUNCT
ap-1863	281	1	,	,	PUNCT
ap-1863	281	2	mn	mn	PROPN
ap-1863	281	3	are	be	AUX
ap-1863	281	4	fixed	fix	VERB
ap-1863	281	5	,	,	PUNCT
ap-1863	281	6	then	then	ADV
ap-1863	281	7	there	there	PRON
ap-1863	281	8	is	be	VERB
ap-1863	281	9	a	a	DET
ap-1863	281	10	bijective	bijective	ADJ
ap-1863	281	11	mapping	mapping	NOUN
ap-1863	281	12	between	between	ADP
ap-1863	281	13	the	the	DET
ap-1863	281	14	set	set	NOUN
ap-1863	281	15	of	of	ADP
ap-1863	281	16	all	all	DET
ap-1863	281	17	solutions	solution	NOUN
ap-1863	281	18	(	(	PUNCT
ap-1863	281	19	19	19	NUM
ap-1863	281	20	)	)	PUNCT
ap-1863	281	21	of	of	ADP
ap-1863	281	22	(	(	PUNCT
ap-1863	281	23	17	17	NUM
ap-1863	281	24	)	)	PUNCT
ap-1863	281	25	and	and	CCONJ
ap-1863	281	26	the	the	DET
ap-1863	281	27	set	set	NOUN
ap-1863	281	28	of	of	ADP
ap-1863	281	29	all	all	DET
ap-1863	281	30	solutions	solution	NOUN
ap-1863	281	31	(	(	PUNCT
ap-1863	281	32	l1n	l1n	NOUN
ap-1863	281	33	,	,	PUNCT
ap-1863	281	34	l1,n−1	l1,n−1	ADJ
ap-1863	281	35	,	,	PUNCT
ap-1863	281	36	.	.	PUNCT
ap-1863	281	37	.	.	PUNCT
ap-1863	282	1	.	.	PUNCT
ap-1863	283	1	,	,	PUNCT
ap-1863	283	2	l12	l12	NOUN
ap-1863	283	3	,	,	PUNCT
ap-1863	283	4	k1	k1	NOUN
ap-1863	283	5	,	,	PUNCT
ap-1863	283	6	l2n	l2n	PROPN
ap-1863	283	7	,	,	PUNCT
ap-1863	283	8	l2,n−1	l2,n−1	ADJ
ap-1863	283	9	,	,	PUNCT
ap-1863	283	10	.	.	PUNCT
ap-1863	283	11	.	.	PUNCT
ap-1863	283	12	.	.	PUNCT
ap-1863	284	1	,	,	PUNCT
ap-1863	284	2	l23	l23	NOUN
ap-1863	284	3	,	,	PUNCT
ap-1863	284	4	k2	k2	NOUN
ap-1863	284	5	,	,	PUNCT
ap-1863	284	6	.	.	PUNCT
ap-1863	284	7	.	.	PUNCT
ap-1863	285	1	.	.	PUNCT
ap-1863	286	1	,	,	PUNCT
ap-1863	286	2	.	.	PUNCT
ap-1863	286	3	.	.	PUNCT
ap-1863	287	1	.	.	PUNCT
ap-1863	288	1	,	,	PUNCT
ap-1863	288	2	ln−1,n	ln−1,n	PROPN
ap-1863	288	3	,	,	PUNCT
ap-1863	288	4	kn−1	kn−1	PROPN
ap-1863	288	5	)	)	PUNCT
ap-1863	288	6	of	of	ADP
ap-1863	288	7	the	the	DET
ap-1863	288	8	system	system	NOUN
ap-1863	288	9	(	(	PUNCT
ap-1863	288	10	22	22	NUM
ap-1863	288	11	)	)	PUNCT
ap-1863	288	12	.	.	PUNCT
ap-1863	289	1	proof	proof	NOUN
ap-1863	289	2	.	.	PUNCT
ap-1863	290	1	the	the	DET
ap-1863	290	2	explicit	explicit	ADJ
ap-1863	290	3	form	form	NOUN
ap-1863	290	4	of	of	ADP
ap-1863	290	5	this	this	DET
ap-1863	290	6	bijection	bijection	NOUN
ap-1863	290	7	is	be	AUX
ap-1863	290	8	s12	s12	NOUN
ap-1863	290	9	=	=	SYM
ap-1863	290	10	k1	k1	NOUN
ap-1863	290	11	s1	s1	PROPN
ap-1863	290	12	t	t	PROPN
ap-1863	290	13	=	=	SYM
ap-1863	290	14	l1,t−1	l1,t−1	PROPN
ap-1863	290	15	,	,	PUNCT
ap-1863	290	16	t	t	PROPN
ap-1863	290	17	=	=	SYM
ap-1863	290	18	3	3	NUM
ap-1863	290	19	,	,	PUNCT
ap-1863	290	20	.	.	PUNCT
ap-1863	290	21	.	.	PUNCT
ap-1863	290	22	.	.	PUNCT
ap-1863	291	1	,	,	PUNCT
ap-1863	291	2	n+	n+	ADP
ap-1863	291	3	1	1	NUM
ap-1863	291	4	,	,	PUNCT
ap-1863	291	5	sr	sr	PROPN
ap-1863	291	6	,	,	PUNCT
ap-1863	291	7	r+1	r+1	PROPN
ap-1863	291	8	=	=	PUNCT
ap-1863	291	9	kr	kr	PROPN
ap-1863	291	10	−	−	PROPN
ap-1863	291	11	lr−1,r	lr−1,r	PROPN
ap-1863	291	12	,	,	PUNCT
ap-1863	291	13	srt	srt	NOUN
ap-1863	291	14	=	=	SYM
ap-1863	291	15	lr	lr	PROPN
ap-1863	291	16	,	,	PUNCT
ap-1863	291	17	t−1	t−1	PROPN
ap-1863	291	18	−	−	PROPN
ap-1863	291	19	lr−1,t−1	lr−1,t−1	PROPN
ap-1863	291	20	,	,	PUNCT
ap-1863	291	21	t	t	NOUN
ap-1863	291	22	=	=	SYM
ap-1863	291	23	r	r	NOUN
ap-1863	291	24	+	+	NUM
ap-1863	291	25	2	2	NUM
ap-1863	291	26	,	,	PUNCT
ap-1863	291	27	.	.	PUNCT
ap-1863	291	28	.	.	PUNCT
ap-1863	291	29	.	.	PUNCT
ap-1863	292	1	,	,	PUNCT
ap-1863	292	2	n+	n+	ADP
ap-1863	292	3	1	1	NUM
ap-1863	292	4	,	,	PUNCT
ap-1863	292	5	sn	sn	INTJ
ap-1863	292	6	,	,	PUNCT
ap-1863	292	7	n+1	n+1	PROPN
ap-1863	292	8	=	=	SYM
ap-1863	292	9	mn	mn	PROPN
ap-1863	292	10	+	+	CCONJ
ap-1863	292	11	kn−1	kn−1	PROPN
ap-1863	292	12	.	.	PROPN
ap-1863	292	13	bijectivity	bijectivity	PROPN
ap-1863	292	14	is	be	AUX
ap-1863	292	15	the	the	DET
ap-1863	292	16	consequence	consequence	NOUN
ap-1863	292	17	of	of	ADP
ap-1863	292	18	the	the	DET
ap-1863	292	19	fact	fact	NOUN
ap-1863	292	20	that	that	SCONJ
ap-1863	292	21	verma	verma	PROPN
ap-1863	292	22	monomials	monomial	VERB
ap-1863	292	23	form	form	VERB
ap-1863	292	24	the	the	DET
ap-1863	292	25	spanning	span	VERB
ap-1863	292	26	set	set	NOUN
ap-1863	292	27	of	of	ADP
ap-1863	292	28	u(a−n	u(a−n	PROPN
ap-1863	292	29	)	)	PUNCT
ap-1863	292	30	.	.	PUNCT
ap-1863	293	1	corollary	corollary	ADJ
ap-1863	293	2	3.7	3.7	NUM
ap-1863	293	3	.	.	PUNCT
ap-1863	294	1	all	all	DET
ap-1863	294	2	verma	verma	PROPN
ap-1863	294	3	monomials	monomial	NOUN
ap-1863	294	4	are	be	AUX
ap-1863	294	5	linearly	linearly	ADV
ap-1863	294	6	independent	independent	ADJ
ap-1863	294	7	.	.	PUNCT
ap-1863	295	1	4	4	X
ap-1863	295	2	.	.	X
ap-1863	295	3	conclusions	conclusion	NOUN
ap-1863	295	4	problems	problem	NOUN
ap-1863	295	5	of	of	ADP
ap-1863	295	6	unified	unified	ADJ
ap-1863	295	7	construction	construction	NOUN
ap-1863	295	8	of	of	ADP
ap-1863	295	9	verma	verma	PROPN
ap-1863	295	10	bases	basis	NOUN
ap-1863	295	11	for	for	ADP
ap-1863	295	12	other	other	ADJ
ap-1863	295	13	series	series	NOUN
ap-1863	295	14	of	of	ADP
ap-1863	295	15	simple	simple	ADJ
ap-1863	295	16	lie	lie	NOUN
ap-1863	295	17	algebras	algebra	NOUN
ap-1863	295	18	(	(	PUNCT
ap-1863	295	19	namely	namely	ADV
ap-1863	295	20	orthogonal	orthogonal	ADJ
ap-1863	295	21	and	and	CCONJ
ap-1863	295	22	symplectic	symplectic	ADJ
ap-1863	295	23	)	)	PUNCT
ap-1863	295	24	and	and	CCONJ
ap-1863	295	25	of	of	ADP
ap-1863	295	26	an	an	DET
ap-1863	295	27	effective	effective	ADJ
ap-1863	295	28	determination	determination	NOUN
ap-1863	295	29	of	of	ADP
ap-1863	295	30	matrix	matrix	NOUN
ap-1863	295	31	elements	element	NOUN
ap-1863	295	32	in	in	ADP
ap-1863	295	33	these	these	DET
ap-1863	295	34	cases	case	NOUN
ap-1863	295	35	are	be	AUX
ap-1863	295	36	still	still	ADV
ap-1863	295	37	open	open	ADJ
ap-1863	295	38	.	.	PUNCT
ap-1863	296	1	in	in	ADP
ap-1863	296	2	[	[	X
ap-1863	296	3	50	50	NUM
ap-1863	296	4	,	,	PUNCT
ap-1863	296	5	51	51	NUM
ap-1863	296	6	]	]	PUNCT
ap-1863	296	7	,	,	PUNCT
ap-1863	296	8	kang	kang	PROPN
ap-1863	296	9	and	and	CCONJ
ap-1863	296	10	lee	lee	PROPN
ap-1863	296	11	developed	develop	VERB
ap-1863	296	12	the	the	DET
ap-1863	296	13	notion	notion	NOUN
ap-1863	296	14	of	of	ADP
ap-1863	296	15	gröbnershirshov	gröbnershirshov	PROPN
ap-1863	296	16	pairs	pair	NOUN
ap-1863	296	17	.	.	PUNCT
ap-1863	297	1	in	in	ADP
ap-1863	297	2	this	this	DET
ap-1863	297	3	way	way	NOUN
ap-1863	297	4	,	,	PUNCT
ap-1863	297	5	the	the	DET
ap-1863	297	6	reduction	reduction	NOUN
ap-1863	297	7	problem	problem	NOUN
ap-1863	297	8	in	in	ADP
ap-1863	297	9	representation	representation	NOUN
ap-1863	297	10	theory	theory	NOUN
ap-1863	297	11	was	be	AUX
ap-1863	297	12	solved	solve	VERB
ap-1863	297	13	and	and	CCONJ
ap-1863	297	14	monomial	monomial	ADJ
ap-1863	297	15	bases	basis	NOUN
ap-1863	297	16	of	of	ADP
ap-1863	297	17	representations	representation	NOUN
ap-1863	297	18	of	of	ADP
ap-1863	297	19	various	various	ADJ
ap-1863	297	20	associative	associative	ADJ
ap-1863	297	21	algebras	algebra	NOUN
ap-1863	297	22	could	could	AUX
ap-1863	297	23	be	be	AUX
ap-1863	297	24	constructed	construct	VERB
ap-1863	297	25	.	.	PUNCT
ap-1863	298	1	the	the	DET
ap-1863	298	2	algebra	algebra	NOUN
ap-1863	298	3	an	an	PRON
ap-1863	298	4	was	be	AUX
ap-1863	298	5	among	among	ADP
ap-1863	298	6	the	the	DET
ap-1863	298	7	first	first	ADJ
ap-1863	298	8	examples	example	NOUN
ap-1863	298	9	.	.	PUNCT
ap-1863	299	1	note	note	VERB
ap-1863	299	2	that	that	SCONJ
ap-1863	299	3	the	the	DET
ap-1863	299	4	bases	basis	NOUN
ap-1863	299	5	obtained	obtain	VERB
ap-1863	299	6	there	there	PRON
ap-1863	299	7	are	be	AUX
ap-1863	299	8	different	different	ADJ
ap-1863	299	9	from	from	ADP
ap-1863	299	10	verma	verma	PROPN
ap-1863	299	11	bases	basis	NOUN
ap-1863	299	12	.	.	PUNCT
ap-1863	300	1	it	it	PRON
ap-1863	300	2	is	be	AUX
ap-1863	300	3	an	an	DET
ap-1863	300	4	interesting	interesting	ADJ
ap-1863	300	5	question	question	NOUN
ap-1863	300	6	whether	whether	SCONJ
ap-1863	300	7	verma	verma	PROPN
ap-1863	300	8	bases	basis	NOUN
ap-1863	300	9	can	can	AUX
ap-1863	300	10	be	be	AUX
ap-1863	300	11	derived	derive	VERB
ap-1863	300	12	this	this	DET
ap-1863	300	13	way	way	NOUN
ap-1863	300	14	.	.	PUNCT
ap-1863	301	1	acknowledgements	acknowledgement	NOUN
ap-1863	301	2	s.	s.	PROPN
ap-1863	301	3	p.	p.	PROPN
ap-1863	301	4	acknowledges	acknowledge	VERB
ap-1863	301	5	support	support	NOUN
ap-1863	301	6	from	from	ADP
ap-1863	301	7	grant	grant	PROPN
ap-1863	301	8	no	no	PROPN
ap-1863	301	9	.	.	PUNCT
ap-1863	302	1	p201/10/1509	p201/10/1509	PROPN
ap-1863	302	2	,	,	PUNCT
ap-1863	302	3	a	a	DET
ap-1863	302	4	project	project	NOUN
ap-1863	302	5	of	of	ADP
ap-1863	302	6	the	the	DET
ap-1863	302	7	grant	grant	NOUN
ap-1863	302	8	agency	agency	NOUN
ap-1863	302	9	of	of	ADP
ap-1863	302	10	the	the	DET
ap-1863	302	11	czech	czech	PROPN
ap-1863	302	12	republic	republic	NOUN
ap-1863	302	13	.	.	PUNCT
ap-1863	303	1	references	reference	NOUN
ap-1863	303	2	[	[	X
ap-1863	303	3	1	1	NUM
ap-1863	303	4	]	]	PUNCT
ap-1863	303	5	p.	p.	NOUN
ap-1863	303	6	littelmann	littelmann	PROPN
ap-1863	303	7	.	.	PUNCT
ap-1863	304	1	an	an	DET
ap-1863	304	2	algorithm	algorithm	NOUN
ap-1863	304	3	to	to	PART
ap-1863	304	4	compute	compute	VERB
ap-1863	304	5	bases	basis	NOUN
ap-1863	304	6	and	and	CCONJ
ap-1863	304	7	representation	representation	NOUN
ap-1863	304	8	matrices	matrix	NOUN
ap-1863	304	9	for	for	ADP
ap-1863	304	10	sln+1	sln+1	NOUN
ap-1863	304	11	-	-	PUNCT
ap-1863	304	12	representations	representation	NOUN
ap-1863	304	13	.	.	PUNCT
ap-1863	305	1	j	j	PROPN
ap-1863	305	2	pure	pure	ADJ
ap-1863	305	3	appl	appl	PROPN
ap-1863	305	4	algebra	algebra	PROPN
ap-1863	305	5	117/118:447–468	117/118:447–468	NUM
ap-1863	305	6	,	,	PUNCT
ap-1863	305	7	1997	1997	NUM
ap-1863	305	8	.	.	PUNCT
ap-1863	306	1	algorithms	algorithm	NOUN
ap-1863	306	2	for	for	ADP
ap-1863	306	3	algebra	algebra	NOUN
ap-1863	306	4	(	(	PUNCT
ap-1863	306	5	eindhoven	eindhoven	NOUN
ap-1863	306	6	,	,	PUNCT
ap-1863	306	7	1996	1996	NUM
ap-1863	306	8	)	)	PUNCT
ap-1863	306	9	.	.	PUNCT
ap-1863	307	1	[	[	X
ap-1863	307	2	2	2	X
ap-1863	307	3	]	]	X
ap-1863	307	4	n.	n.	NOUN
ap-1863	307	5	bourbaki	bourbaki	PROPN
ap-1863	307	6	.	.	PUNCT
ap-1863	308	1	éléments	éléments	PROPN
ap-1863	308	2	de	de	PROPN
ap-1863	308	3	mathématique	mathématique	PROPN
ap-1863	308	4	.	.	PUNCT
ap-1863	309	1	fasc	fasc	PROPN
ap-1863	309	2	.	.	PROPN
ap-1863	310	1	xxxiv	xxxiv	PROPN
ap-1863	310	2	.	.	PUNCT
ap-1863	311	1	groupes	groupe	NOUN
ap-1863	311	2	et	et	PROPN
ap-1863	311	3	algèbres	algèbre	VERB
ap-1863	311	4	de	de	ADP
ap-1863	311	5	lie	lie	NOUN
ap-1863	311	6	.	.	PUNCT
ap-1863	312	1	chapitre	chapitre	PROPN
ap-1863	312	2	iv	iv	NUM
ap-1863	312	3	:	:	PUNCT
ap-1863	312	4	groupes	groupes	X
ap-1863	312	5	de	de	X
ap-1863	312	6	coxeter	coxeter	X
ap-1863	312	7	et	et	PROPN
ap-1863	312	8	systèmes	systèmes	X
ap-1863	312	9	de	de	X
ap-1863	312	10	tits	tit	NOUN
ap-1863	312	11	.	.	PUNCT
ap-1863	313	1	chapitre	chapitre	PROPN
ap-1863	313	2	v	v	PROPN
ap-1863	313	3	:	:	PUNCT
ap-1863	313	4	groupes	groupe	NOUN
ap-1863	313	5	engendrés	engendrés	PROPN
ap-1863	313	6	par	par	PROPN
ap-1863	313	7	des	des	PROPN
ap-1863	313	8	réflexions	réflexion	NOUN
ap-1863	313	9	.	.	PUNCT
ap-1863	314	1	chapitre	chapitre	PROPN
ap-1863	314	2	vi	vi	PROPN
ap-1863	314	3	:	:	PUNCT
ap-1863	314	4	systèmes	systèmes	PROPN
ap-1863	314	5	de	de	PROPN
ap-1863	314	6	racines	racines	PROPN
ap-1863	314	7	.	.	PUNCT
ap-1863	315	1	actualités	actualités	PROPN
ap-1863	315	2	scientifiques	scientifique	NOUN
ap-1863	315	3	et	et	NOUN
ap-1863	315	4	industrielles	industrielle	NOUN
ap-1863	315	5	,	,	PUNCT
ap-1863	315	6	no	no	INTJ
ap-1863	315	7	.	.	NOUN
ap-1863	315	8	1337	1337	NUM
ap-1863	315	9	.	.	PUNCT
ap-1863	316	1	hermann	hermann	PROPN
ap-1863	316	2	,	,	PUNCT
ap-1863	316	3	paris	paris	PROPN
ap-1863	316	4	,	,	PUNCT
ap-1863	316	5	1968	1968	NUM
ap-1863	316	6	.	.	PUNCT
ap-1863	317	1	[	[	X
ap-1863	317	2	3	3	X
ap-1863	317	3	]	]	X
ap-1863	317	4	j.	j.	PROPN
ap-1863	317	5	dixmier	dixmier	PROPN
ap-1863	317	6	.	.	PUNCT
ap-1863	318	1	algèbres	algèbre	NOUN
ap-1863	318	2	enveloppantes	enveloppante	NOUN
ap-1863	318	3	.	.	PUNCT
ap-1863	319	1	les	les	PROPN
ap-1863	319	2	grands	grands	X
ap-1863	319	3	classiques	classique	NOUN
ap-1863	319	4	gauthier	gauthier	NOUN
ap-1863	319	5	-	-	PUNCT
ap-1863	319	6	villars	villar	NOUN
ap-1863	319	7	.	.	PUNCT
ap-1863	320	1	[	[	X
ap-1863	320	2	gauthier	gauthier	NOUN
ap-1863	320	3	-	-	PUNCT
ap-1863	320	4	villars	villar	NOUN
ap-1863	320	5	great	great	ADJ
ap-1863	320	6	classics	classic	NOUN
ap-1863	320	7	]	]	PUNCT
ap-1863	320	8	.	.	PUNCT
ap-1863	321	1	éditions	éditions	PROPN
ap-1863	321	2	jacques	jacques	PROPN
ap-1863	321	3	gabay	gabay	PROPN
ap-1863	321	4	,	,	PUNCT
ap-1863	321	5	paris	paris	PROPN
ap-1863	321	6	,	,	PUNCT
ap-1863	321	7	1996	1996	NUM
ap-1863	321	8	.	.	PUNCT
ap-1863	322	1	reprint	reprint	NOUN
ap-1863	322	2	of	of	ADP
ap-1863	322	3	the	the	DET
ap-1863	322	4	1974	1974	NUM
ap-1863	322	5	original	original	NOUN
ap-1863	322	6	.	.	PUNCT
ap-1863	323	1	[	[	X
ap-1863	323	2	4	4	X
ap-1863	323	3	]	]	PUNCT
ap-1863	323	4	j.	j.	PROPN
ap-1863	323	5	e.	e.	PROPN
ap-1863	323	6	humphreys	humphreys	PROPN
ap-1863	323	7	.	.	PUNCT
ap-1863	324	1	introduction	introduction	NOUN
ap-1863	324	2	to	to	PART
ap-1863	324	3	lie	lie	VERB
ap-1863	324	4	algebras	algebra	NOUN
ap-1863	324	5	and	and	CCONJ
ap-1863	324	6	representation	representation	NOUN
ap-1863	324	7	theory	theory	NOUN
ap-1863	324	8	,	,	PUNCT
ap-1863	324	9	vol	vol	NOUN
ap-1863	324	10	.	.	PROPN
ap-1863	324	11	9	9	NUM
ap-1863	324	12	of	of	ADP
ap-1863	324	13	graduate	graduate	ADJ
ap-1863	324	14	texts	text	NOUN
ap-1863	324	15	in	in	ADP
ap-1863	324	16	mathematics	mathematic	NOUN
ap-1863	324	17	.	.	PUNCT
ap-1863	325	1	springer	springer	NOUN
ap-1863	325	2	-	-	PUNCT
ap-1863	325	3	verlag	verlag	PROPN
ap-1863	325	4	,	,	PUNCT
ap-1863	325	5	new	new	PROPN
ap-1863	325	6	york	york	PROPN
ap-1863	325	7	,	,	PUNCT
ap-1863	325	8	1978	1978	NUM
ap-1863	325	9	.	.	PUNCT
ap-1863	326	1	second	second	ADJ
ap-1863	326	2	printing	printing	NOUN
ap-1863	326	3	,	,	PUNCT
ap-1863	326	4	revised	revise	VERB
ap-1863	326	5	.	.	PUNCT
ap-1863	327	1	[	[	X
ap-1863	327	2	5	5	X
ap-1863	327	3	]	]	PUNCT
ap-1863	327	4	k.	k.	PROPN
ap-1863	327	5	erdmann	erdmann	PROPN
ap-1863	327	6	,	,	PUNCT
ap-1863	327	7	et	et	PROPN
ap-1863	327	8	al	al	PROPN
ap-1863	327	9	.	.	PROPN
ap-1863	327	10	introduction	introduction	NOUN
ap-1863	327	11	to	to	PART
ap-1863	327	12	lie	lie	VERB
ap-1863	327	13	algebras	algebras	PROPN
ap-1863	327	14	.	.	PUNCT
ap-1863	328	1	springer	springer	PROPN
ap-1863	328	2	undergraduate	undergraduate	NOUN
ap-1863	328	3	mathematics	mathematics	PROPN
ap-1863	328	4	series	series	PROPN
ap-1863	328	5	.	.	PUNCT
ap-1863	329	1	springer	springer	NOUN
ap-1863	329	2	-	-	PUNCT
ap-1863	329	3	verlag	verlag	PROPN
ap-1863	329	4	london	london	PROPN
ap-1863	329	5	ltd	ltd	PROPN
ap-1863	329	6	.	.	PROPN
ap-1863	329	7	,	,	PUNCT
ap-1863	329	8	london	london	PROPN
ap-1863	329	9	,	,	PUNCT
ap-1863	329	10	2006	2006	NUM
ap-1863	329	11	.	.	PUNCT
ap-1863	330	1	[	[	X
ap-1863	330	2	6	6	NUM
ap-1863	330	3	]	]	PUNCT
ap-1863	330	4	i.	i.	PROPN
ap-1863	330	5	m.	m.	PROPN
ap-1863	330	6	gel′fand	gel′fand	PROPN
ap-1863	330	7	,	,	PUNCT
ap-1863	330	8	et	et	PROPN
ap-1863	330	9	al	al	PROPN
ap-1863	330	10	.	.	PUNCT
ap-1863	331	1	finite	finite	ADJ
ap-1863	331	2	-	-	ADJ
ap-1863	331	3	dimensional	dimensional	ADJ
ap-1863	331	4	representations	representation	NOUN
ap-1863	331	5	of	of	ADP
ap-1863	331	6	the	the	DET
ap-1863	331	7	group	group	NOUN
ap-1863	331	8	of	of	ADP
ap-1863	331	9	unimodular	unimodular	ADJ
ap-1863	331	10	matrices	matrix	NOUN
ap-1863	331	11	.	.	PUNCT
ap-1863	332	1	doklady	doklady	ADJ
ap-1863	332	2	akad	akad	NOUN
ap-1863	332	3	nauk	nauk	NOUN
ap-1863	332	4	sssr	sssr	NOUN
ap-1863	332	5	(	(	PUNCT
ap-1863	332	6	ns	ns	ADJ
ap-1863	332	7	)	)	PUNCT
ap-1863	332	8	71:825–828	71:825–828	NOUN
ap-1863	332	9	,	,	PUNCT
ap-1863	332	10	1950	1950	NUM
ap-1863	332	11	.	.	PUNCT
ap-1863	333	1	454	454	NUM
ap-1863	333	2	vol	vol	NOUN
ap-1863	333	3	.	.	PUNCT
ap-1863	334	1	53	53	NUM
ap-1863	334	2	no	no	NOUN
ap-1863	334	3	.	.	PUNCT
ap-1863	335	1	5/2013	5/2013	NUM
ap-1863	335	2	note	note	NOUN
ap-1863	335	3	on	on	ADP
ap-1863	335	4	verma	verma	PROPN
ap-1863	335	5	bases	basis	NOUN
ap-1863	335	6	for	for	ADP
ap-1863	335	7	representations	representation	NOUN
ap-1863	335	8	of	of	ADP
ap-1863	335	9	simple	simple	ADJ
ap-1863	335	10	lie	lie	NOUN
ap-1863	335	11	algebras	algebra	NOUN
ap-1863	335	12	[	[	X
ap-1863	335	13	7	7	NUM
ap-1863	335	14	]	]	X
ap-1863	335	15	i.	i.	PROPN
ap-1863	335	16	m.	m.	PROPN
ap-1863	335	17	gel′fand	gel′fand	PROPN
ap-1863	335	18	,	,	PUNCT
ap-1863	335	19	et	et	PROPN
ap-1863	335	20	al	al	PROPN
ap-1863	335	21	.	.	PUNCT
ap-1863	336	1	finite	finite	ADJ
ap-1863	336	2	-	-	ADJ
ap-1863	336	3	dimensional	dimensional	ADJ
ap-1863	336	4	representations	representation	NOUN
ap-1863	336	5	of	of	ADP
ap-1863	336	6	groups	group	NOUN
ap-1863	336	7	of	of	ADP
ap-1863	336	8	orthogonal	orthogonal	ADJ
ap-1863	336	9	matrices	matrix	NOUN
ap-1863	336	10	.	.	PUNCT
ap-1863	337	1	doklady	doklady	ADJ
ap-1863	337	2	akad	akad	NOUN
ap-1863	337	3	nauk	nauk	NOUN
ap-1863	337	4	sssr	sssr	NOUN
ap-1863	337	5	(	(	PUNCT
ap-1863	337	6	ns	ns	ADJ
ap-1863	337	7	)	)	PUNCT
ap-1863	337	8	71:1017–1020	71:1017–1020	NOUN
ap-1863	337	9	,	,	PUNCT
ap-1863	337	10	1950	1950	NUM
ap-1863	337	11	.	.	PUNCT
ap-1863	338	1	[	[	X
ap-1863	338	2	8	8	NUM
ap-1863	338	3	]	]	PUNCT
ap-1863	338	4	a.	a.	NOUN
ap-1863	338	5	i.	i.	PROPN
ap-1863	338	6	molev	molev	PROPN
ap-1863	338	7	.	.	PUNCT
ap-1863	339	1	gelfand	gelfand	PROPN
ap-1863	339	2	-	-	PUNCT
ap-1863	339	3	tsetlin	tsetlin	PROPN
ap-1863	339	4	bases	basis	NOUN
ap-1863	339	5	for	for	ADP
ap-1863	339	6	classical	classical	ADJ
ap-1863	339	7	lie	lie	NOUN
ap-1863	339	8	algebras	algebra	NOUN
ap-1863	339	9	.	.	PUNCT
ap-1863	340	1	in	in	ADP
ap-1863	340	2	handbook	handbook	NOUN
ap-1863	340	3	of	of	ADP
ap-1863	340	4	algebra	algebra	PROPN
ap-1863	340	5	.	.	PUNCT
ap-1863	341	1	vol	vol	NOUN
ap-1863	341	2	.	.	PROPN
ap-1863	342	1	4	4	NUM
ap-1863	342	2	,	,	PUNCT
ap-1863	342	3	vol	vol	NOUN
ap-1863	342	4	.	.	NOUN
ap-1863	342	5	4	4	NUM
ap-1863	342	6	of	of	ADP
ap-1863	342	7	handb	handb	NOUN
ap-1863	342	8	.	.	PUNCT
ap-1863	343	1	algebr	algebr	PROPN
ap-1863	343	2	.	.	PUNCT
ap-1863	344	1	,	,	PUNCT
ap-1863	344	2	pp	pp	ADP
ap-1863	344	3	.	.	PUNCT
ap-1863	345	1	109–170	109–170	NUM
ap-1863	345	2	.	.	PUNCT
ap-1863	346	1	elsevier	elsevier	NOUN
ap-1863	346	2	/	/	SYM
ap-1863	346	3	north	north	PROPN
ap-1863	346	4	-	-	PUNCT
ap-1863	346	5	holland	holland	PROPN
ap-1863	346	6	,	,	PUNCT
ap-1863	346	7	amsterdam	amsterdam	PROPN
ap-1863	346	8	,	,	PUNCT
ap-1863	346	9	2006	2006	NUM
ap-1863	346	10	.	.	PUNCT
ap-1863	347	1	[	[	X
ap-1863	347	2	9	9	NUM
ap-1863	347	3	]	]	SYM
ap-1863	347	4	l.	l.	PROPN
ap-1863	347	5	c.	c.	PROPN
ap-1863	347	6	biedenharn	biedenharn	PROPN
ap-1863	347	7	.	.	PUNCT
ap-1863	348	1	on	on	ADP
ap-1863	348	2	the	the	DET
ap-1863	348	3	representations	representation	NOUN
ap-1863	348	4	of	of	ADP
ap-1863	348	5	the	the	DET
ap-1863	348	6	semisimple	semisimple	NOUN
ap-1863	348	7	lie	lie	NOUN
ap-1863	348	8	groups	group	NOUN
ap-1863	348	9	.	.	PUNCT
ap-1863	349	1	i.	i.	PROPN
ap-1863	349	2	the	the	DET
ap-1863	349	3	explicit	explicit	ADJ
ap-1863	349	4	construction	construction	NOUN
ap-1863	349	5	of	of	ADP
ap-1863	349	6	invariants	invariant	NOUN
ap-1863	349	7	for	for	ADP
ap-1863	349	8	the	the	DET
ap-1863	349	9	unimodular	unimodular	ADJ
ap-1863	349	10	unitary	unitary	ADJ
ap-1863	349	11	group	group	NOUN
ap-1863	349	12	in	in	ADP
ap-1863	349	13	n	n	DET
ap-1863	349	14	dimensions	dimension	NOUN
ap-1863	349	15	.	.	PUNCT
ap-1863	350	1	j	j	PROPN
ap-1863	350	2	math	math	PROPN
ap-1863	350	3	phys	phys	PROPN
ap-1863	350	4	4:436–445	4:436–445	PROPN
ap-1863	350	5	,	,	PUNCT
ap-1863	350	6	1963	1963	NUM
ap-1863	350	7	.	.	PUNCT
ap-1863	351	1	[	[	X
ap-1863	351	2	10	10	NUM
ap-1863	351	3	]	]	X
ap-1863	351	4	g.	g.	PROPN
ap-1863	351	5	e.	e.	PROPN
ap-1863	351	6	baird	baird	PROPN
ap-1863	351	7	,	,	PUNCT
ap-1863	351	8	et	et	PROPN
ap-1863	351	9	al	al	PROPN
ap-1863	351	10	.	.	PROPN
ap-1863	352	1	on	on	ADP
ap-1863	352	2	the	the	DET
ap-1863	352	3	representations	representation	NOUN
ap-1863	352	4	of	of	ADP
ap-1863	352	5	the	the	DET
ap-1863	352	6	semisimple	semisimple	NOUN
ap-1863	352	7	lie	lie	NOUN
ap-1863	352	8	groups	group	NOUN
ap-1863	352	9	.	.	PUNCT
ap-1863	353	1	ii	ii	PROPN
ap-1863	353	2	.	.	PUNCT
ap-1863	354	1	j	j	PROPN
ap-1863	354	2	math	math	PROPN
ap-1863	354	3	phys	phy	NOUN
ap-1863	354	4	4:1449–1466	4:1449–1466	NUM
ap-1863	354	5	,	,	PUNCT
ap-1863	354	6	1963	1963	NUM
ap-1863	354	7	.	.	PUNCT
ap-1863	355	1	[	[	X
ap-1863	355	2	11	11	NUM
ap-1863	355	3	]	]	X
ap-1863	355	4	d.	d.	PROPN
ap-1863	355	5	p.	p.	PROPN
ap-1863	355	6	želobenko	želobenko	PROPN
ap-1863	355	7	.	.	PUNCT
ap-1863	356	1	compact	compact	ADJ
ap-1863	356	2	lie	lie	NOUN
ap-1863	356	3	groups	group	NOUN
ap-1863	356	4	and	and	CCONJ
ap-1863	356	5	their	their	PRON
ap-1863	356	6	representations	representation	NOUN
ap-1863	356	7	.	.	PUNCT
ap-1863	357	1	american	american	PROPN
ap-1863	357	2	mathematical	mathematical	PROPN
ap-1863	357	3	society	society	NOUN
ap-1863	357	4	,	,	PUNCT
ap-1863	357	5	providence	providence	NOUN
ap-1863	357	6	,	,	PUNCT
ap-1863	357	7	r.i	r.i	PROPN
ap-1863	357	8	.	.	PROPN
ap-1863	357	9	,	,	PUNCT
ap-1863	357	10	1973	1973	NUM
ap-1863	357	11	.	.	PUNCT
ap-1863	358	1	translated	translate	VERB
ap-1863	358	2	from	from	ADP
ap-1863	358	3	the	the	DET
ap-1863	358	4	russian	russian	NOUN
ap-1863	358	5	by	by	ADP
ap-1863	358	6	the	the	DET
ap-1863	358	7	israel	israel	PROPN
ap-1863	358	8	program	program	NOUN
ap-1863	358	9	for	for	ADP
ap-1863	358	10	scientific	scientific	ADJ
ap-1863	358	11	translations	translation	NOUN
ap-1863	358	12	,	,	PUNCT
ap-1863	358	13	translations	translation	NOUN
ap-1863	358	14	of	of	ADP
ap-1863	358	15	mathematical	mathematical	ADJ
ap-1863	358	16	monographs	monograph	NOUN
ap-1863	358	17	,	,	PUNCT
ap-1863	358	18	vol	vol	NOUN
ap-1863	358	19	.	.	PROPN
ap-1863	359	1	40	40	NUM
ap-1863	359	2	.	.	PUNCT
ap-1863	360	1	[	[	X
ap-1863	360	2	12	12	NUM
ap-1863	360	3	]	]	PUNCT
ap-1863	360	4	j.	j.	PROPN
ap-1863	360	5	g.	g.	PROPN
ap-1863	360	6	nagel	nagel	PROPN
ap-1863	360	7	,	,	PUNCT
ap-1863	360	8	et	et	PROPN
ap-1863	360	9	al	al	PROPN
ap-1863	360	10	.	.	PUNCT
ap-1863	360	11	operators	operator	NOUN
ap-1863	360	12	that	that	PRON
ap-1863	360	13	lower	low	ADJ
ap-1863	360	14	or	or	CCONJ
ap-1863	360	15	raise	raise	VERB
ap-1863	360	16	the	the	DET
ap-1863	360	17	irreducible	irreducible	ADJ
ap-1863	360	18	vector	vector	NOUN
ap-1863	360	19	spaces	space	NOUN
ap-1863	360	20	of	of	ADP
ap-1863	360	21	un−1	un−1	PROPN
ap-1863	360	22	contained	contain	VERB
ap-1863	360	23	in	in	ADP
ap-1863	360	24	an	an	DET
ap-1863	360	25	irreducible	irreducible	ADJ
ap-1863	360	26	vector	vector	NOUN
ap-1863	360	27	space	space	NOUN
ap-1863	360	28	of	of	ADP
ap-1863	360	29	un	un	PROPN
ap-1863	360	30	.	.	PROPN
ap-1863	361	1	j	j	PROPN
ap-1863	361	2	math	math	PROPN
ap-1863	361	3	phys	phy	NOUN
ap-1863	361	4	6:682–694	6:682–694	ADV
ap-1863	361	5	,	,	PUNCT
ap-1863	361	6	1965	1965	NUM
ap-1863	361	7	.	.	PUNCT
ap-1863	362	1	[	[	X
ap-1863	362	2	13	13	NUM
ap-1863	362	3	]	]	X
ap-1863	362	4	h.	h.	PROPN
ap-1863	362	5	pei	pei	PROPN
ap-1863	362	6	-	-	PUNCT
ap-1863	362	7	yu	yu	PROPN
ap-1863	362	8	.	.	PUNCT
ap-1863	362	9	orthonormal	orthonormal	ADJ
ap-1863	362	10	bases	basis	NOUN
ap-1863	362	11	and	and	CCONJ
ap-1863	362	12	infinitesimal	infinitesimal	ADJ
ap-1863	362	13	operators	operator	NOUN
ap-1863	362	14	of	of	ADP
ap-1863	362	15	the	the	DET
ap-1863	362	16	irreducible	irreducible	ADJ
ap-1863	362	17	representations	representation	NOUN
ap-1863	362	18	of	of	ADP
ap-1863	362	19	group	group	NOUN
ap-1863	362	20	un	un	PROPN
ap-1863	362	21	.	.	PROPN
ap-1863	362	22	sci	sci	PROPN
ap-1863	362	23	sinica	sinica	PROPN
ap-1863	362	24	15:763–772	15:763–772	PROPN
ap-1863	362	25	,	,	PUNCT
ap-1863	362	26	1966	1966	NUM
ap-1863	362	27	.	.	PUNCT
ap-1863	363	1	[	[	X
ap-1863	363	2	14	14	NUM
ap-1863	363	3	]	]	X
ap-1863	363	4	f.	f.	PROPN
ap-1863	363	5	lemire	lemire	PROPN
ap-1863	363	6	,	,	PUNCT
ap-1863	363	7	et	et	PROPN
ap-1863	363	8	al	al	PROPN
ap-1863	363	9	.	.	PUNCT
ap-1863	364	1	formal	formal	ADJ
ap-1863	364	2	analytic	analytic	ADJ
ap-1863	364	3	continuation	continuation	NOUN
ap-1863	364	4	of	of	ADP
ap-1863	364	5	gel′fand	gel′fand	PROPN
ap-1863	364	6	’s	’s	PART
ap-1863	364	7	finite	finite	ADJ
ap-1863	364	8	-	-	ADJ
ap-1863	364	9	dimensional	dimensional	ADJ
ap-1863	364	10	representations	representation	NOUN
ap-1863	364	11	of	of	ADP
ap-1863	364	12	gl(n	gl(n	NUM
ap-1863	364	13	,	,	PUNCT
ap-1863	364	14	c	c	NOUN
ap-1863	364	15	)	)	PUNCT
ap-1863	364	16	.	.	PUNCT
ap-1863	365	1	j	j	PROPN
ap-1863	365	2	math	math	PROPN
ap-1863	365	3	phys	phy	NOUN
ap-1863	365	4	20(5):820–829	20(5):820–829	PROPN
ap-1863	365	5	,	,	PUNCT
ap-1863	365	6	1979	1979	NUM
ap-1863	365	7	.	.	PUNCT
ap-1863	366	1	[	[	X
ap-1863	366	2	15	15	NUM
ap-1863	366	3	]	]	X
ap-1863	366	4	m.	m.	NOUN
ap-1863	366	5	d.	d.	PROPN
ap-1863	366	6	gould	gould	PROPN
ap-1863	366	7	.	.	PUNCT
ap-1863	367	1	the	the	DET
ap-1863	367	2	characteristic	characteristic	ADJ
ap-1863	367	3	identities	identity	NOUN
ap-1863	367	4	and	and	CCONJ
ap-1863	367	5	reduced	reduced	ADJ
ap-1863	367	6	matrix	matrix	NOUN
ap-1863	367	7	elements	element	NOUN
ap-1863	367	8	of	of	ADP
ap-1863	367	9	the	the	DET
ap-1863	367	10	unitary	unitary	ADJ
ap-1863	367	11	and	and	CCONJ
ap-1863	367	12	orthogonal	orthogonal	ADJ
ap-1863	367	13	groups	group	NOUN
ap-1863	367	14	.	.	PUNCT
ap-1863	368	1	j	j	PROPN
ap-1863	368	2	austral	austral	PROPN
ap-1863	368	3	math	math	PROPN
ap-1863	368	4	soc	soc	PROPN
ap-1863	368	5	ser	ser	PROPN
ap-1863	368	6	b	b	PROPN
ap-1863	368	7	20(4):401–433	20(4):401–433	PROPN
ap-1863	368	8	,	,	PUNCT
ap-1863	368	9	1977/78	1977/78	NUM
ap-1863	368	10	.	.	PUNCT
ap-1863	369	1	[	[	X
ap-1863	369	2	16	16	NUM
ap-1863	369	3	]	]	PUNCT
ap-1863	369	4	m.	m.	PROPN
ap-1863	369	5	d.	d.	PROPN
ap-1863	369	6	gould	gould	PROPN
ap-1863	369	7	,	,	PUNCT
ap-1863	369	8	et	et	PROPN
ap-1863	369	9	al	al	PROPN
ap-1863	369	10	.	.	PUNCT
ap-1863	369	11	characteristic	characteristic	ADJ
ap-1863	369	12	identities	identity	NOUN
ap-1863	369	13	for	for	ADP
ap-1863	369	14	kacmoody	kacmoody	PROPN
ap-1863	369	15	algebras	algebra	VERB
ap-1863	369	16	.	.	PUNCT
ap-1863	370	1	lett	lett	PROPN
ap-1863	370	2	math	math	PROPN
ap-1863	370	3	phys	phys	PROPN
ap-1863	370	4	22(2):91–100	22(2):91–100	NUM
ap-1863	370	5	,	,	PUNCT
ap-1863	370	6	1991	1991	NUM
ap-1863	370	7	.	.	PUNCT
ap-1863	371	1	[	[	X
ap-1863	371	2	17	17	NUM
ap-1863	371	3	]	]	X
ap-1863	371	4	r.	r.	PROPN
ap-1863	371	5	m.	m.	PROPN
ap-1863	371	6	ašerova	ašerova	PROPN
ap-1863	371	7	,	,	PUNCT
ap-1863	371	8	et	et	PROPN
ap-1863	371	9	al	al	PROPN
ap-1863	371	10	.	.	PROPN
ap-1863	372	1	projection	projection	NOUN
ap-1863	372	2	operators	operator	NOUN
ap-1863	372	3	for	for	ADP
ap-1863	372	4	simple	simple	ADJ
ap-1863	372	5	lie	lie	NOUN
ap-1863	372	6	groups	group	NOUN
ap-1863	372	7	.	.	PUNCT
ap-1863	373	1	ii	ii	PROPN
ap-1863	373	2	.	.	PUNCT
ap-1863	373	3	general	general	ADJ
ap-1863	373	4	scheme	scheme	NOUN
ap-1863	373	5	for	for	ADP
ap-1863	373	6	the	the	DET
ap-1863	373	7	construction	construction	NOUN
ap-1863	373	8	of	of	ADP
ap-1863	373	9	lowering	lower	VERB
ap-1863	373	10	operators	operator	NOUN
ap-1863	373	11	.	.	PUNCT
ap-1863	374	1	the	the	DET
ap-1863	374	2	case	case	NOUN
ap-1863	374	3	of	of	ADP
ap-1863	374	4	the	the	DET
ap-1863	374	5	groups	group	NOUN
ap-1863	374	6	su(n	su(n	NOUN
ap-1863	374	7	)	)	PUNCT
ap-1863	374	8	.	.	PUNCT
ap-1863	375	1	teoret	teoret	PROPN
ap-1863	375	2	mat	mat	PROPN
ap-1863	375	3	fiz	fiz	PROPN
ap-1863	375	4	15(1):107–119	15(1):107–119	PROPN
ap-1863	375	5	,	,	PUNCT
ap-1863	375	6	1973	1973	NUM
ap-1863	375	7	.	.	PUNCT
ap-1863	376	1	[	[	X
ap-1863	376	2	18	18	NUM
ap-1863	376	3	]	]	X
ap-1863	376	4	r.	r.	PROPN
ap-1863	376	5	m.	m.	PROPN
ap-1863	376	6	ašerova	ašerova	PROPN
ap-1863	376	7	,	,	PUNCT
ap-1863	376	8	et	et	PROPN
ap-1863	376	9	al	al	PROPN
ap-1863	376	10	.	.	PROPN
ap-1863	377	1	projection	projection	NOUN
ap-1863	377	2	operators	operator	NOUN
ap-1863	377	3	for	for	ADP
ap-1863	377	4	simple	simple	ADJ
ap-1863	377	5	lie	lie	NOUN
ap-1863	377	6	groups	group	NOUN
ap-1863	377	7	.	.	PUNCT
ap-1863	378	1	teoret	teoret	PROPN
ap-1863	378	2	mat	mat	PROPN
ap-1863	378	3	fiz	fiz	PROPN
ap-1863	378	4	8(2):255–271	8(2):255–271	NUM
ap-1863	378	5	,	,	PUNCT
ap-1863	378	6	1971	1971	NUM
ap-1863	378	7	.	.	PUNCT
ap-1863	379	1	[	[	X
ap-1863	379	2	19	19	NUM
ap-1863	379	3	]	]	X
ap-1863	379	4	y.	y.	PROPN
ap-1863	379	5	f.	f.	PROPN
ap-1863	379	6	smirnov	smirnov	PROPN
ap-1863	379	7	.	.	PROPN
ap-1863	380	1	projection	projection	NOUN
ap-1863	380	2	operators	operator	NOUN
ap-1863	380	3	for	for	ADP
ap-1863	380	4	lie	lie	NOUN
ap-1863	380	5	algebras	algebra	NOUN
ap-1863	380	6	,	,	PUNCT
ap-1863	380	7	superalgebras	superalgebra	NOUN
ap-1863	380	8	,	,	PUNCT
ap-1863	380	9	and	and	CCONJ
ap-1863	380	10	quantum	quantum	NOUN
ap-1863	380	11	algebras	algebra	NOUN
ap-1863	380	12	.	.	PUNCT
ap-1863	381	1	in	in	ADP
ap-1863	381	2	latin	latin	ADJ
ap-1863	381	3	-	-	PUNCT
ap-1863	381	4	american	american	ADJ
ap-1863	381	5	school	school	PROPN
ap-1863	381	6	of	of	ADP
ap-1863	381	7	physics	physics	PROPN
ap-1863	381	8	xxx	xxx	PROPN
ap-1863	381	9	elaf	elaf	PROPN
ap-1863	381	10	(	(	PUNCT
ap-1863	381	11	mexico	mexico	PROPN
ap-1863	381	12	city	city	NOUN
ap-1863	381	13	,	,	PUNCT
ap-1863	381	14	1995	1995	NUM
ap-1863	381	15	)	)	PUNCT
ap-1863	381	16	,	,	PUNCT
ap-1863	381	17	vol	vol	NOUN
ap-1863	381	18	.	.	PROPN
ap-1863	381	19	365	365	NUM
ap-1863	381	20	of	of	ADP
ap-1863	381	21	aip	aip	PROPN
ap-1863	381	22	conf	conf	PROPN
ap-1863	381	23	.	.	PUNCT
ap-1863	382	1	proc	proc	PROPN
ap-1863	382	2	.	.	PROPN
ap-1863	382	3	,	,	PUNCT
ap-1863	383	1	pp	pp	ADP
ap-1863	383	2	.	.	PUNCT
ap-1863	384	1	99–116	99–116	INTJ
ap-1863	384	2	.	.	PUNCT
ap-1863	385	1	amer	amer	PROPN
ap-1863	385	2	.	.	PROPN
ap-1863	385	3	inst	inst	PROPN
ap-1863	385	4	.	.	PUNCT
ap-1863	386	1	phys	phy	NOUN
ap-1863	386	2	.	.	PUNCT
ap-1863	387	1	press	press	PROPN
ap-1863	387	2	,	,	PUNCT
ap-1863	387	3	woodbury	woodbury	PROPN
ap-1863	387	4	,	,	PUNCT
ap-1863	387	5	ny	ny	PROPN
ap-1863	387	6	,	,	PUNCT
ap-1863	387	7	1996	1996	NUM
ap-1863	387	8	.	.	PUNCT
ap-1863	388	1	[	[	X
ap-1863	388	2	20	20	NUM
ap-1863	388	3	]	]	PUNCT
ap-1863	388	4	m.	m.	NOUN
ap-1863	388	5	nazarov	nazarov	PROPN
ap-1863	388	6	,	,	PUNCT
ap-1863	388	7	et	et	PROPN
ap-1863	388	8	al	al	PROPN
ap-1863	388	9	.	.	PUNCT
ap-1863	388	10	representations	representation	NOUN
ap-1863	388	11	of	of	ADP
ap-1863	388	12	yangians	yangian	NOUN
ap-1863	388	13	with	with	ADP
ap-1863	388	14	gelfand	gelfand	PROPN
ap-1863	388	15	-	-	PUNCT
ap-1863	388	16	zetlin	zetlin	PROPN
ap-1863	388	17	bases	basis	NOUN
ap-1863	388	18	.	.	PUNCT
ap-1863	389	1	j	j	PROPN
ap-1863	389	2	reine	reine	PROPN
ap-1863	389	3	angew	angew	PROPN
ap-1863	389	4	math	math	PROPN
ap-1863	389	5	496:181–212	496:181–212	NUM
ap-1863	389	6	,	,	PUNCT
ap-1863	389	7	1998	1998	NUM
ap-1863	389	8	.	.	PUNCT
ap-1863	390	1	[	[	X
ap-1863	390	2	21	21	NUM
ap-1863	390	3	]	]	X
ap-1863	390	4	h.	h.	PROPN
ap-1863	390	5	weyl	weyl	PROPN
ap-1863	390	6	.	.	PUNCT
ap-1863	391	1	the	the	DET
ap-1863	391	2	classical	classical	ADJ
ap-1863	391	3	groups	group	NOUN
ap-1863	391	4	.	.	PUNCT
ap-1863	392	1	their	their	PRON
ap-1863	392	2	invariants	invariant	NOUN
ap-1863	392	3	and	and	CCONJ
ap-1863	392	4	representations	representation	NOUN
ap-1863	392	5	.	.	PUNCT
ap-1863	393	1	princeton	princeton	PROPN
ap-1863	393	2	university	university	PROPN
ap-1863	393	3	press	press	PROPN
ap-1863	393	4	,	,	PUNCT
ap-1863	393	5	princeton	princeton	PROPN
ap-1863	393	6	,	,	PUNCT
ap-1863	393	7	n.j	n.j	PROPN
ap-1863	393	8	.	.	PROPN
ap-1863	393	9	,	,	PUNCT
ap-1863	393	10	1939	1939	NUM
ap-1863	393	11	.	.	PUNCT
ap-1863	394	1	[	[	X
ap-1863	394	2	22	22	NUM
ap-1863	394	3	]	]	PUNCT
ap-1863	394	4	r.	r.	PROPN
ap-1863	394	5	c.	c.	PROPN
ap-1863	394	6	king	king	PROPN
ap-1863	394	7	,	,	PUNCT
ap-1863	394	8	et	et	PROPN
ap-1863	394	9	al	al	PROPN
ap-1863	394	10	.	.	PROPN
ap-1863	394	11	standard	standard	ADJ
ap-1863	394	12	young	young	ADJ
ap-1863	394	13	tableaux	tableau	NOUN
ap-1863	394	14	and	and	CCONJ
ap-1863	394	15	weight	weight	NOUN
ap-1863	394	16	multiplicities	multiplicity	NOUN
ap-1863	394	17	of	of	ADP
ap-1863	394	18	the	the	DET
ap-1863	394	19	classical	classical	ADJ
ap-1863	394	20	lie	lie	NOUN
ap-1863	394	21	groups	group	NOUN
ap-1863	394	22	.	.	PUNCT
ap-1863	395	1	j	j	PROPN
ap-1863	395	2	phys	phy	NOUN
ap-1863	395	3	a	a	DET
ap-1863	395	4	16(14):3153–3177	16(14):3153–3177	NUM
ap-1863	395	5	,	,	PUNCT
ap-1863	395	6	1983	1983	NUM
ap-1863	395	7	.	.	PUNCT
ap-1863	396	1	[	[	X
ap-1863	396	2	23	23	NUM
ap-1863	396	3	]	]	PUNCT
ap-1863	396	4	a.	a.	NOUN
ap-1863	396	5	berele	berele	PROPN
ap-1863	396	6	.	.	PUNCT
ap-1863	397	1	construction	construction	NOUN
ap-1863	397	2	of	of	ADP
ap-1863	397	3	sp	sp	NOUN
ap-1863	397	4	-	-	PUNCT
ap-1863	397	5	modules	module	NOUN
ap-1863	397	6	by	by	ADP
ap-1863	397	7	tableaux	tableau	NOUN
ap-1863	397	8	.	.	PUNCT
ap-1863	398	1	linear	linear	PROPN
ap-1863	398	2	and	and	CCONJ
ap-1863	398	3	multilinear	multilinear	PROPN
ap-1863	398	4	algebra	algebra	PROPN
ap-1863	398	5	19(4):299–307	19(4):299–307	PROPN
ap-1863	398	6	,	,	PUNCT
ap-1863	398	7	1986	1986	NUM
ap-1863	398	8	.	.	PUNCT
ap-1863	399	1	[	[	X
ap-1863	399	2	24	24	NUM
ap-1863	399	3	]	]	PUNCT
ap-1863	399	4	r.	r.	PROPN
ap-1863	399	5	c.	c.	PROPN
ap-1863	399	6	king	king	PROPN
ap-1863	399	7	,	,	PUNCT
ap-1863	399	8	et	et	PROPN
ap-1863	399	9	al	al	PROPN
ap-1863	399	10	.	.	PUNCT
ap-1863	399	11	construction	construction	NOUN
ap-1863	399	12	of	of	ADP
ap-1863	399	13	orthogonal	orthogonal	ADJ
ap-1863	399	14	group	group	NOUN
ap-1863	399	15	modules	module	NOUN
ap-1863	399	16	using	use	VERB
ap-1863	399	17	tableaux	tableaux	ADV
ap-1863	399	18	.	.	PUNCT
ap-1863	400	1	linear	linear	VERB
ap-1863	400	2	and	and	CCONJ
ap-1863	400	3	multilinear	multilinear	PROPN
ap-1863	400	4	algebra	algebra	PROPN
ap-1863	400	5	33(3	33(3	NOUN
ap-1863	400	6	-	-	PUNCT
ap-1863	400	7	4):251–283	4):251–283	NUM
ap-1863	400	8	,	,	PUNCT
ap-1863	400	9	1993	1993	NUM
ap-1863	400	10	.	.	PUNCT
ap-1863	401	1	[	[	X
ap-1863	401	2	25	25	NUM
ap-1863	401	3	]	]	PUNCT
ap-1863	401	4	k.	k.	PROPN
ap-1863	401	5	koike	koike	PROPN
ap-1863	401	6	,	,	PUNCT
ap-1863	401	7	et	et	PROPN
ap-1863	401	8	al	al	PROPN
ap-1863	401	9	.	.	PUNCT
ap-1863	402	1	young	young	ADJ
ap-1863	402	2	-	-	PUNCT
ap-1863	402	3	diagrammatic	diagrammatic	ADJ
ap-1863	402	4	methods	method	NOUN
ap-1863	402	5	for	for	ADP
ap-1863	402	6	the	the	DET
ap-1863	402	7	representation	representation	NOUN
ap-1863	402	8	theory	theory	NOUN
ap-1863	402	9	of	of	ADP
ap-1863	402	10	the	the	DET
ap-1863	402	11	classical	classical	ADJ
ap-1863	402	12	groups	group	NOUN
ap-1863	402	13	of	of	ADP
ap-1863	402	14	type	type	NOUN
ap-1863	402	15	bn	bn	PROPN
ap-1863	402	16	,	,	PUNCT
ap-1863	402	17	cn	cn	PROPN
ap-1863	402	18	,	,	PUNCT
ap-1863	402	19	dn	dn	PROPN
ap-1863	402	20	.	.	PUNCT
ap-1863	403	1	j	j	PROPN
ap-1863	403	2	algebra	algebra	PROPN
ap-1863	403	3	107(2):466–511	107(2):466–511	NUM
ap-1863	403	4	,	,	PUNCT
ap-1863	403	5	1987	1987	NUM
ap-1863	403	6	.	.	PUNCT
ap-1863	404	1	[	[	X
ap-1863	404	2	26	26	NUM
ap-1863	404	3	]	]	PUNCT
ap-1863	404	4	p.	p.	NOUN
ap-1863	404	5	exner	exner	PROPN
ap-1863	404	6	,	,	PUNCT
ap-1863	404	7	et	et	PROPN
ap-1863	404	8	al	al	PROPN
ap-1863	404	9	.	.	PUNCT
ap-1863	404	10	canonical	canonical	ADJ
ap-1863	404	11	realizations	realization	NOUN
ap-1863	404	12	of	of	ADP
ap-1863	404	13	classical	classical	ADJ
ap-1863	404	14	lie	lie	NOUN
ap-1863	404	15	algebras	algebra	NOUN
ap-1863	404	16	.	.	PUNCT
ap-1863	405	1	czech	czech	PROPN
ap-1863	405	2	j	j	PROPN
ap-1863	405	3	phys	phy	NOUN
ap-1863	405	4	26b(11):1213–1228	26b(11):1213–1228	NUM
ap-1863	405	5	,	,	PUNCT
ap-1863	405	6	1976	1976	NUM
ap-1863	405	7	.	.	PUNCT
ap-1863	406	1	[	[	X
ap-1863	406	2	27	27	NUM
ap-1863	406	3	]	]	X
ap-1863	406	4	c.	c.	PROPN
ap-1863	406	5	de	de	PROPN
ap-1863	406	6	concini	concini	PROPN
ap-1863	406	7	,	,	PUNCT
ap-1863	406	8	et	et	PROPN
ap-1863	406	9	al	al	PROPN
ap-1863	406	10	.	.	PROPN
ap-1863	406	11	special	special	ADJ
ap-1863	406	12	bases	basis	NOUN
ap-1863	406	13	for	for	ADP
ap-1863	406	14	sn	sn	PROPN
ap-1863	406	15	and	and	CCONJ
ap-1863	406	16	gl(n	gl(n	NUM
ap-1863	406	17	)	)	PUNCT
ap-1863	406	18	.	.	PUNCT
ap-1863	407	1	israel	israel	PROPN
ap-1863	407	2	j	j	PROPN
ap-1863	407	3	math	math	PROPN
ap-1863	407	4	40(3	40(3	PROPN
ap-1863	407	5	-	-	SYM
ap-1863	407	6	4):275–290	4):275–290	NUM
ap-1863	407	7	(	(	PUNCT
ap-1863	407	8	1982	1982	NUM
ap-1863	407	9	)	)	PUNCT
ap-1863	407	10	,	,	PUNCT
ap-1863	407	11	1981	1981	NUM
ap-1863	407	12	.	.	PUNCT
ap-1863	408	1	[	[	X
ap-1863	408	2	28	28	NUM
ap-1863	408	3	]	]	X
ap-1863	408	4	n.	n.	PROPN
ap-1863	408	5	h.	h.	PROPN
ap-1863	408	6	xi	xi	PROPN
ap-1863	408	7	.	.	PUNCT
ap-1863	409	1	special	special	ADJ
ap-1863	409	2	bases	basis	NOUN
ap-1863	409	3	of	of	ADP
ap-1863	409	4	irreducible	irreducible	ADJ
ap-1863	409	5	modules	module	NOUN
ap-1863	409	6	of	of	ADP
ap-1863	409	7	the	the	DET
ap-1863	409	8	quantized	quantize	VERB
ap-1863	409	9	universal	universal	ADJ
ap-1863	409	10	enveloping	enveloping	NOUN
ap-1863	409	11	algebra	algebra	NOUN
ap-1863	409	12	uv(gl(n	uv(gl(n	PROPN
ap-1863	409	13	)	)	PUNCT
ap-1863	409	14	)	)	PUNCT
ap-1863	409	15	.	.	PUNCT
ap-1863	410	1	j	j	PROPN
ap-1863	410	2	algebra	algebra	PROPN
ap-1863	410	3	154(2):377–386	154(2):377–386	NUM
ap-1863	410	4	,	,	PUNCT
ap-1863	410	5	1993	1993	NUM
ap-1863	410	6	.	.	PUNCT
ap-1863	411	1	[	[	X
ap-1863	411	2	29	29	NUM
ap-1863	411	3	]	]	X
ap-1863	411	4	i.	i.	PROPN
ap-1863	411	5	m.	m.	PROPN
ap-1863	411	6	gel′fand	gel′fand	PROPN
ap-1863	411	7	,	,	PUNCT
ap-1863	411	8	et	et	PROPN
ap-1863	411	9	al	al	PROPN
ap-1863	411	10	.	.	PROPN
ap-1863	411	11	multiplicities	multiplicities	PROPN
ap-1863	411	12	and	and	CCONJ
ap-1863	411	13	proper	proper	ADJ
ap-1863	411	14	bases	basis	NOUN
ap-1863	411	15	for	for	ADP
ap-1863	411	16	gln	gln	PROPN
ap-1863	411	17	.	.	PUNCT
ap-1863	412	1	in	in	ADP
ap-1863	412	2	group	group	NOUN
ap-1863	412	3	theoretical	theoretical	ADJ
ap-1863	412	4	methods	method	NOUN
ap-1863	412	5	in	in	ADP
ap-1863	412	6	physics	physics	NOUN
ap-1863	412	7	,	,	PUNCT
ap-1863	412	8	vol	vol	NOUN
ap-1863	412	9	.	.	PUNCT
ap-1863	413	1	ii	ii	PROPN
ap-1863	413	2	(	(	PUNCT
ap-1863	413	3	yurmala	yurmala	PROPN
ap-1863	413	4	,	,	PUNCT
ap-1863	413	5	1985	1985	NUM
ap-1863	413	6	)	)	PUNCT
ap-1863	413	7	,	,	PUNCT
ap-1863	413	8	pp	pp	ADP
ap-1863	413	9	.	.	PUNCT
ap-1863	414	1	147–159	147–159	NUM
ap-1863	414	2	.	.	PUNCT
ap-1863	415	1	vnu	vnu	PROPN
ap-1863	415	2	sci	sci	PROPN
ap-1863	415	3	.	.	PUNCT
ap-1863	416	1	press	press	PROPN
ap-1863	416	2	,	,	PUNCT
ap-1863	416	3	utrecht	utrecht	PROPN
ap-1863	416	4	,	,	PUNCT
ap-1863	416	5	1986	1986	NUM
ap-1863	416	6	.	.	PUNCT
ap-1863	417	1	[	[	X
ap-1863	417	2	30	30	NUM
ap-1863	417	3	]	]	X
ap-1863	417	4	a.	a.	NOUN
ap-1863	417	5	v.	v.	PROPN
ap-1863	417	6	zelevinskĭı	zelevinskĭı	PROPN
ap-1863	417	7	,	,	PUNCT
ap-1863	417	8	et	et	PROPN
ap-1863	417	9	al	al	PROPN
ap-1863	417	10	.	.	PUNCT
ap-1863	418	1	the	the	DET
ap-1863	418	2	fundamental	fundamental	ADJ
ap-1863	418	3	affine	affine	NOUN
ap-1863	418	4	space	space	NOUN
ap-1863	418	5	and	and	CCONJ
ap-1863	418	6	canonical	canonical	ADJ
ap-1863	418	7	basis	basis	NOUN
ap-1863	418	8	in	in	ADP
ap-1863	418	9	irreducible	irreducible	ADJ
ap-1863	418	10	representations	representation	NOUN
ap-1863	418	11	of	of	ADP
ap-1863	418	12	the	the	DET
ap-1863	418	13	group	group	NOUN
ap-1863	418	14	sp4	sp4	PROPN
ap-1863	418	15	.	.	PROPN
ap-1863	418	16	dokl	dokl	PROPN
ap-1863	418	17	akad	akad	PROPN
ap-1863	418	18	nauk	nauk	PROPN
ap-1863	418	19	sssr	sssr	NOUN
ap-1863	418	20	300(1):31–35	300(1):31–35	NUM
ap-1863	418	21	,	,	PUNCT
ap-1863	418	22	1988	1988	NUM
ap-1863	418	23	.	.	PUNCT
ap-1863	419	1	[	[	X
ap-1863	419	2	31	31	NUM
ap-1863	419	3	]	]	X
ap-1863	419	4	o.	o.	PROPN
ap-1863	419	5	mathieu	mathieu	PROPN
ap-1863	419	6	.	.	PUNCT
ap-1863	420	1	good	good	ADJ
ap-1863	420	2	bases	basis	NOUN
ap-1863	420	3	for	for	ADP
ap-1863	420	4	g	g	NOUN
ap-1863	420	5	-	-	PUNCT
ap-1863	420	6	modules	module	NOUN
ap-1863	420	7	.	.	PUNCT
ap-1863	421	1	geom	geom	PROPN
ap-1863	421	2	dedicata	dedicata	PROPN
ap-1863	421	3	36(1):51–66	36(1):51–66	NUM
ap-1863	421	4	,	,	PUNCT
ap-1863	421	5	1990	1990	NUM
ap-1863	421	6	.	.	PUNCT
ap-1863	422	1	[	[	X
ap-1863	422	2	32	32	NUM
ap-1863	422	3	]	]	PUNCT
ap-1863	422	4	g.	g.	PROPN
ap-1863	422	5	lusztig	lusztig	PROPN
ap-1863	422	6	.	.	PUNCT
ap-1863	423	1	canonical	canonical	ADJ
ap-1863	423	2	bases	basis	NOUN
ap-1863	423	3	arising	arise	VERB
ap-1863	423	4	from	from	ADP
ap-1863	423	5	quantized	quantize	VERB
ap-1863	423	6	enveloping	enveloping	NOUN
ap-1863	423	7	algebras	algebra	NOUN
ap-1863	423	8	.	.	PUNCT
ap-1863	424	1	j	j	PROPN
ap-1863	424	2	amer	amer	PROPN
ap-1863	424	3	math	math	PROPN
ap-1863	424	4	soc	soc	PROPN
ap-1863	424	5	3(2):447–498	3(2):447–498	NUM
ap-1863	424	6	,	,	PUNCT
ap-1863	424	7	1990	1990	NUM
ap-1863	424	8	.	.	PUNCT
ap-1863	425	1	[	[	X
ap-1863	425	2	33	33	NUM
ap-1863	425	3	]	]	PUNCT
ap-1863	425	4	g.	g.	PROPN
ap-1863	425	5	lusztig	lusztig	PROPN
ap-1863	425	6	.	.	PUNCT
ap-1863	426	1	canonical	canonical	ADJ
ap-1863	426	2	bases	basis	NOUN
ap-1863	426	3	arising	arise	VERB
ap-1863	426	4	from	from	ADP
ap-1863	426	5	quantized	quantize	VERB
ap-1863	426	6	enveloping	enveloping	NOUN
ap-1863	426	7	algebras	algebra	NOUN
ap-1863	426	8	.	.	PUNCT
ap-1863	427	1	ii	ii	PROPN
ap-1863	427	2	.	.	PUNCT
ap-1863	428	1	progr	progr	VERB
ap-1863	428	2	theoret	theoret	NOUN
ap-1863	428	3	phys	phy	NOUN
ap-1863	428	4	suppl	suppl	ADJ
ap-1863	428	5	(	(	PUNCT
ap-1863	428	6	102):175–201	102):175–201	NUM
ap-1863	428	7	(	(	PUNCT
ap-1863	428	8	1991	1991	NUM
ap-1863	428	9	)	)	PUNCT
ap-1863	428	10	,	,	PUNCT
ap-1863	428	11	1990	1990	NUM
ap-1863	428	12	.	.	PUNCT
ap-1863	429	1	common	common	ADJ
ap-1863	429	2	trends	trend	NOUN
ap-1863	429	3	in	in	ADP
ap-1863	429	4	mathematics	mathematic	NOUN
ap-1863	429	5	and	and	CCONJ
ap-1863	429	6	quantum	quantum	NOUN
ap-1863	429	7	field	field	NOUN
ap-1863	429	8	theories	theory	NOUN
ap-1863	429	9	(	(	PUNCT
ap-1863	429	10	kyoto	kyoto	NOUN
ap-1863	429	11	,	,	PUNCT
ap-1863	429	12	1990	1990	NUM
ap-1863	429	13	)	)	PUNCT
ap-1863	429	14	.	.	PUNCT
ap-1863	430	1	[	[	X
ap-1863	430	2	34	34	NUM
ap-1863	430	3	]	]	PUNCT
ap-1863	430	4	m.	m.	NOUN
ap-1863	430	5	kashiwara	kashiwara	PROPN
ap-1863	430	6	.	.	PUNCT
ap-1863	431	1	crystalizing	crystalize	VERB
ap-1863	431	2	the	the	DET
ap-1863	431	3	q	q	NOUN
ap-1863	431	4	-	-	PUNCT
ap-1863	431	5	analogue	analogue	NOUN
ap-1863	431	6	of	of	ADP
ap-1863	431	7	universal	universal	ADJ
ap-1863	431	8	enveloping	enveloping	NOUN
ap-1863	431	9	algebras	algebra	NOUN
ap-1863	431	10	.	.	PUNCT
ap-1863	432	1	commun	commun	PROPN
ap-1863	432	2	math	math	PROPN
ap-1863	432	3	phys	phy	NOUN
ap-1863	432	4	133(2):249–260	133(2):249–260	NUM
ap-1863	432	5	,	,	PUNCT
ap-1863	432	6	1990	1990	NUM
ap-1863	432	7	.	.	PUNCT
ap-1863	433	1	[	[	X
ap-1863	433	2	35	35	NUM
ap-1863	433	3	]	]	X
ap-1863	433	4	j.	j.	PROPN
ap-1863	433	5	du	du	PROPN
ap-1863	433	6	.	.	PUNCT
ap-1863	433	7	canonical	canonical	ADJ
ap-1863	433	8	bases	basis	NOUN
ap-1863	433	9	for	for	ADP
ap-1863	433	10	irreducible	irreducible	ADJ
ap-1863	433	11	representations	representation	NOUN
ap-1863	433	12	of	of	ADP
ap-1863	433	13	quantum	quantum	ADJ
ap-1863	433	14	gln	gln	NOUN
ap-1863	433	15	.	.	PUNCT
ap-1863	434	1	bull	bull	PROPN
ap-1863	434	2	london	london	PROPN
ap-1863	434	3	math	math	NOUN
ap-1863	434	4	soc	soc	PROPN
ap-1863	434	5	24(4):325–334	24(4):325–334	PROPN
ap-1863	434	6	,	,	PUNCT
ap-1863	434	7	1992	1992	NUM
ap-1863	434	8	.	.	PUNCT
ap-1863	435	1	[	[	X
ap-1863	435	2	36	36	NUM
ap-1863	435	3	]	]	X
ap-1863	435	4	j.	j.	PROPN
ap-1863	435	5	du	du	PROPN
ap-1863	435	6	.	.	PUNCT
ap-1863	435	7	canonical	canonical	ADJ
ap-1863	435	8	bases	basis	NOUN
ap-1863	435	9	for	for	ADP
ap-1863	435	10	irreducible	irreducible	ADJ
ap-1863	435	11	representations	representation	NOUN
ap-1863	435	12	of	of	ADP
ap-1863	435	13	quantum	quantum	PROPN
ap-1863	435	14	gln	gln	PROPN
ap-1863	435	15	.	.	PUNCT
ap-1863	435	16	ii	ii	PROPN
ap-1863	435	17	.	.	PUNCT
ap-1863	436	1	j	j	PROPN
ap-1863	436	2	london	london	PROPN
ap-1863	436	3	math	math	PROPN
ap-1863	436	4	soc	soc	NOUN
ap-1863	436	5	(	(	PUNCT
ap-1863	436	6	2	2	NUM
ap-1863	436	7	)	)	PUNCT
ap-1863	436	8	51(3):461–470	51(3):461–470	PROPN
ap-1863	436	9	,	,	PUNCT
ap-1863	436	10	1995	1995	NUM
ap-1863	436	11	.	.	PUNCT
ap-1863	437	1	[	[	X
ap-1863	437	2	37	37	NUM
ap-1863	437	3	]	]	PUNCT
ap-1863	437	4	s.-j	s.-j	PROPN
ap-1863	437	5	.	.	PUNCT
ap-1863	438	1	kang	kang	PROPN
ap-1863	438	2	.	.	PUNCT
ap-1863	439	1	representations	representation	NOUN
ap-1863	439	2	of	of	ADP
ap-1863	439	3	quantum	quantum	ADJ
ap-1863	439	4	groups	group	NOUN
ap-1863	439	5	and	and	CCONJ
ap-1863	439	6	crystal	crystal	NOUN
ap-1863	439	7	base	base	NOUN
ap-1863	439	8	theory	theory	NOUN
ap-1863	439	9	.	.	PUNCT
ap-1863	440	1	in	in	ADP
ap-1863	440	2	algebra	algebra	NOUN
ap-1863	440	3	and	and	CCONJ
ap-1863	440	4	topology	topology	NOUN
ap-1863	440	5	1992	1992	NUM
ap-1863	440	6	(	(	PUNCT
ap-1863	440	7	taejŏn	taejŏn	PROPN
ap-1863	440	8	)	)	PUNCT
ap-1863	440	9	,	,	PUNCT
ap-1863	440	10	pp	pp	ADP
ap-1863	440	11	.	.	PUNCT
ap-1863	441	1	189–210	189–210	NUM
ap-1863	441	2	.	.	PUNCT
ap-1863	441	3	korea	korea	PROPN
ap-1863	441	4	adv	adv	PROPN
ap-1863	441	5	.	.	PROPN
ap-1863	441	6	inst	inst	PROPN
ap-1863	441	7	.	.	PUNCT
ap-1863	442	1	sci	sci	PROPN
ap-1863	442	2	.	.	PUNCT
ap-1863	442	3	tech	tech	PROPN
ap-1863	442	4	.	.	PUNCT
ap-1863	442	5	,	,	PUNCT
ap-1863	442	6	taejŏn	taejŏn	PROPN
ap-1863	442	7	,	,	PUNCT
ap-1863	442	8	1992	1992	NUM
ap-1863	442	9	.	.	PUNCT
ap-1863	443	1	[	[	X
ap-1863	443	2	38	38	NUM
ap-1863	443	3	]	]	PUNCT
ap-1863	443	4	k.	k.	NOUN
ap-1863	443	5	misra	misra	PROPN
ap-1863	443	6	,	,	PUNCT
ap-1863	443	7	et	et	PROPN
ap-1863	444	1	al	al	PROPN
ap-1863	444	2	.	.	PUNCT
ap-1863	444	3	crystal	crystal	PROPN
ap-1863	444	4	base	base	NOUN
ap-1863	444	5	for	for	ADP
ap-1863	444	6	the	the	DET
ap-1863	444	7	basic	basic	ADJ
ap-1863	444	8	representation	representation	NOUN
ap-1863	444	9	of	of	ADP
ap-1863	444	10	uq(sl(n	uq(sl(n	ADJ
ap-1863	444	11	)	)	PUNCT
ap-1863	444	12	)	)	PUNCT
ap-1863	444	13	.	.	PUNCT
ap-1863	445	1	commun	commun	PROPN
ap-1863	445	2	math	math	PROPN
ap-1863	445	3	phys	phy	NOUN
ap-1863	445	4	134(1):79–88	134(1):79–88	ADV
ap-1863	445	5	,	,	PUNCT
ap-1863	445	6	1990	1990	NUM
ap-1863	445	7	.	.	PUNCT
ap-1863	446	1	[	[	X
ap-1863	446	2	39	39	NUM
ap-1863	446	3	]	]	X
ap-1863	447	1	y.	y.	PROPN
ap-1863	447	2	m.	m.	PROPN
ap-1863	447	3	zou	zou	PROPN
ap-1863	447	4	.	.	PUNCT
ap-1863	448	1	crystal	crystal	NOUN
ap-1863	448	2	bases	basis	NOUN
ap-1863	448	3	for	for	ADP
ap-1863	448	4	uq(sl(2	uq(sl(2	PROPN
ap-1863	448	5	,	,	PUNCT
ap-1863	448	6	1	1	NUM
ap-1863	448	7	)	)	PUNCT
ap-1863	448	8	)	)	PUNCT
ap-1863	448	9	.	.	PUNCT
ap-1863	449	1	proc	proc	PROPN
ap-1863	449	2	amer	amer	PROPN
ap-1863	449	3	math	math	PROPN
ap-1863	449	4	soc	soc	PROPN
ap-1863	449	5	127(8):2213–2223	127(8):2213–2223	NUM
ap-1863	449	6	,	,	PUNCT
ap-1863	449	7	1999	1999	NUM
ap-1863	449	8	.	.	PUNCT
ap-1863	450	1	[	[	X
ap-1863	450	2	40	40	NUM
ap-1863	450	3	]	]	PUNCT
ap-1863	450	4	g.	g.	PROPN
ap-1863	450	5	cliff	cliff	PROPN
ap-1863	450	6	.	.	PUNCT
ap-1863	451	1	crystal	crystal	NOUN
ap-1863	451	2	bases	basis	NOUN
ap-1863	451	3	and	and	CCONJ
ap-1863	451	4	young	young	ADJ
ap-1863	451	5	tableaux	tableau	NOUN
ap-1863	451	6	.	.	PUNCT
ap-1863	452	1	j	j	PROPN
ap-1863	452	2	algebra	algebra	PROPN
ap-1863	452	3	202(1):10–35	202(1):10–35	NUM
ap-1863	452	4	,	,	PUNCT
ap-1863	452	5	1998	1998	NUM
ap-1863	452	6	.	.	PUNCT
ap-1863	453	1	[	[	X
ap-1863	453	2	41	41	NUM
ap-1863	453	3	]	]	X
ap-1863	453	4	d.	d.	PROPN
ap-1863	453	5	p.	p.	PROPN
ap-1863	453	6	zhelobenko	zhelobenko	PROPN
ap-1863	453	7	.	.	PUNCT
ap-1863	454	1	crystal	crystal	NOUN
ap-1863	454	2	bases	basis	NOUN
ap-1863	454	3	and	and	CCONJ
ap-1863	454	4	the	the	DET
ap-1863	454	5	problem	problem	NOUN
ap-1863	454	6	of	of	ADP
ap-1863	454	7	reduction	reduction	NOUN
ap-1863	454	8	in	in	ADP
ap-1863	454	9	classical	classical	ADJ
ap-1863	454	10	and	and	CCONJ
ap-1863	454	11	quantum	quantum	NOUN
ap-1863	454	12	modules	module	NOUN
ap-1863	454	13	.	.	PUNCT
ap-1863	455	1	in	in	ADP
ap-1863	455	2	lie	lie	NOUN
ap-1863	455	3	groups	group	NOUN
ap-1863	455	4	and	and	CCONJ
ap-1863	455	5	lie	lie	VERB
ap-1863	455	6	algebras	algebra	NOUN
ap-1863	455	7	:	:	PUNCT
ap-1863	455	8	e.	e.	PROPN
ap-1863	455	9	b.	b.	PROPN
ap-1863	455	10	dynkin	dynkin	PROPN
ap-1863	455	11	’s	’s	PART
ap-1863	455	12	seminar	seminar	NOUN
ap-1863	455	13	,	,	PUNCT
ap-1863	455	14	vol	vol	NOUN
ap-1863	455	15	.	.	PROPN
ap-1863	455	16	169	169	NUM
ap-1863	455	17	of	of	ADP
ap-1863	455	18	amer	amer	PROPN
ap-1863	455	19	.	.	PUNCT
ap-1863	455	20	math	math	PROPN
ap-1863	455	21	.	.	PUNCT
ap-1863	456	1	soc	soc	PROPN
ap-1863	456	2	.	.	PUNCT
ap-1863	457	1	transl	transl	PROPN
ap-1863	457	2	.	.	PUNCT
ap-1863	458	1	ser	ser	PROPN
ap-1863	458	2	.	.	PROPN
ap-1863	459	1	2	2	NUM
ap-1863	459	2	,	,	PUNCT
ap-1863	459	3	pp	pp	ADJ
ap-1863	459	4	.	.	PUNCT
ap-1863	460	1	183–202	183–202	NUM
ap-1863	460	2	.	.	PUNCT
ap-1863	461	1	amer	amer	PROPN
ap-1863	461	2	.	.	PUNCT
ap-1863	461	3	math	math	PROPN
ap-1863	461	4	.	.	PUNCT
ap-1863	462	1	soc	soc	PROPN
ap-1863	462	2	.	.	PUNCT
ap-1863	462	3	,	,	PUNCT
ap-1863	462	4	providence	providence	NOUN
ap-1863	462	5	,	,	PUNCT
ap-1863	462	6	ri	ri	NOUN
ap-1863	462	7	,	,	PUNCT
ap-1863	462	8	1995	1995	NUM
ap-1863	462	9	.	.	PUNCT
ap-1863	463	1	[	[	X
ap-1863	463	2	42	42	NUM
ap-1863	463	3	]	]	X
ap-1863	463	4	v.	v.	PROPN
ap-1863	463	5	lakshmibai	lakshmibai	PROPN
ap-1863	463	6	,	,	PUNCT
ap-1863	463	7	et	et	PROPN
ap-1863	463	8	al	al	PROPN
ap-1863	463	9	.	.	PROPN
ap-1863	463	10	geometry	geometry	NOUN
ap-1863	463	11	of	of	ADP
ap-1863	463	12	g	g	PROPN
ap-1863	463	13	/	/	SYM
ap-1863	463	14	p	p	NOUN
ap-1863	463	15	.	.	PUNCT
ap-1863	464	1	iv	iv	X
ap-1863	464	2	.	.	PUNCT
ap-1863	464	3	standard	standard	ADJ
ap-1863	464	4	monomial	monomial	ADJ
ap-1863	464	5	theory	theory	NOUN
ap-1863	464	6	for	for	ADP
ap-1863	464	7	classical	classical	ADJ
ap-1863	464	8	types	type	NOUN
ap-1863	464	9	.	.	PUNCT
ap-1863	465	1	proc	proc	PROPN
ap-1863	465	2	indian	indian	PROPN
ap-1863	465	3	acad	acad	PROPN
ap-1863	465	4	sci	sci	PROPN
ap-1863	465	5	sect	sect	PROPN
ap-1863	465	6	a	a	DET
ap-1863	465	7	math	math	NOUN
ap-1863	465	8	sci	sci	PROPN
ap-1863	465	9	88(4):279–362	88(4):279–362	PROPN
ap-1863	465	10	,	,	PUNCT
ap-1863	465	11	1979	1979	NUM
ap-1863	465	12	.	.	PUNCT
ap-1863	466	1	455	455	NUM
ap-1863	466	2	s.	s.	PROPN
ap-1863	466	3	pošta	pošta	PROPN
ap-1863	466	4	,	,	PUNCT
ap-1863	466	5	m.	m.	NOUN
ap-1863	466	6	havlíček	havlíček	PROPN
ap-1863	466	7	acta	acta	PROPN
ap-1863	466	8	polytechnica	polytechnica	PROPN
ap-1863	467	1	[	[	X
ap-1863	467	2	43	43	NUM
ap-1863	467	3	]	]	X
ap-1863	467	4	p.	p.	NOUN
ap-1863	467	5	littelmann	littelmann	PROPN
ap-1863	467	6	.	.	PUNCT
ap-1863	468	1	cones	cone	NOUN
ap-1863	468	2	,	,	PUNCT
ap-1863	468	3	crystals	crystal	NOUN
ap-1863	468	4	,	,	PUNCT
ap-1863	468	5	and	and	CCONJ
ap-1863	468	6	patterns	pattern	NOUN
ap-1863	468	7	.	.	PUNCT
ap-1863	469	1	transform	transform	VERB
ap-1863	469	2	groups	group	NOUN
ap-1863	469	3	3(2):145–179	3(2):145–179	PROPN
ap-1863	469	4	,	,	PUNCT
ap-1863	469	5	1998	1998	NUM
ap-1863	469	6	.	.	PUNCT
ap-1863	470	1	[	[	X
ap-1863	470	2	44	44	NUM
ap-1863	470	3	]	]	PUNCT
ap-1863	470	4	v.	v.	CCONJ
ap-1863	470	5	chari	chari	PROPN
ap-1863	470	6	,	,	PUNCT
ap-1863	470	7	et	et	PROPN
ap-1863	470	8	al	al	PROPN
ap-1863	470	9	.	.	PUNCT
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ap-1863	470	11	bases	basis	NOUN
ap-1863	470	12	of	of	ADP
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ap-1863	470	14	enveloping	enveloping	NOUN
ap-1863	470	15	algebras	algebra	NOUN
ap-1863	470	16	.	.	PUNCT
ap-1863	471	1	in	in	ADP
ap-1863	471	2	recent	recent	ADJ
ap-1863	471	3	developments	development	NOUN
ap-1863	471	4	in	in	ADP
ap-1863	471	5	quantum	quantum	ADJ
ap-1863	471	6	affine	affine	NOUN
ap-1863	471	7	algebras	algebra	NOUN
ap-1863	471	8	and	and	CCONJ
ap-1863	471	9	related	related	ADJ
ap-1863	471	10	topics	topic	NOUN
ap-1863	471	11	(	(	PUNCT
ap-1863	471	12	raleigh	raleigh	PROPN
ap-1863	471	13	,	,	PUNCT
ap-1863	471	14	nc	nc	PROPN
ap-1863	471	15	,	,	PUNCT
ap-1863	471	16	1998	1998	NUM
ap-1863	471	17	)	)	PUNCT
ap-1863	471	18	,	,	PUNCT
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ap-1863	471	20	.	.	PROPN
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ap-1863	472	3	contemp	contemp	NOUN
ap-1863	472	4	.	.	PUNCT
ap-1863	473	1	math	math	NOUN
ap-1863	473	2	.	.	PUNCT
ap-1863	474	1	,	,	PUNCT
ap-1863	474	2	pp	pp	ADJ
ap-1863	474	3	.	.	PUNCT
ap-1863	475	1	69–81	69–81	NUM
ap-1863	475	2	.	.	PUNCT
ap-1863	476	1	amer	amer	PROPN
ap-1863	476	2	.	.	PUNCT
ap-1863	476	3	math	math	PROPN
ap-1863	476	4	.	.	PUNCT
ap-1863	477	1	soc	soc	PROPN
ap-1863	477	2	.	.	PUNCT
ap-1863	477	3	,	,	PUNCT
ap-1863	477	4	providence	providence	NOUN
ap-1863	477	5	,	,	PUNCT
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ap-1863	477	7	,	,	PUNCT
ap-1863	477	8	1999	1999	NUM
ap-1863	477	9	.	.	PUNCT
ap-1863	478	1	[	[	X
ap-1863	478	2	45	45	NUM
ap-1863	478	3	]	]	PUNCT
ap-1863	478	4	s.	s.	PROPN
ap-1863	478	5	p.	p.	PROPN
ap-1863	478	6	li	li	PROPN
ap-1863	478	7	,	,	PUNCT
ap-1863	478	8	et	et	PROPN
ap-1863	478	9	al	al	PROPN
ap-1863	478	10	.	.	PROPN
ap-1863	478	11	verma	verma	PROPN
ap-1863	478	12	bases	basis	NOUN
ap-1863	478	13	for	for	ADP
ap-1863	478	14	representations	representation	NOUN
ap-1863	478	15	of	of	ADP
ap-1863	478	16	classical	classical	ADJ
ap-1863	478	17	simple	simple	ADJ
ap-1863	478	18	lie	lie	NOUN
ap-1863	478	19	algebras	algebra	NOUN
ap-1863	478	20	.	.	PUNCT
ap-1863	479	1	j	j	PROPN
ap-1863	479	2	math	math	PROPN
ap-1863	479	3	phys	phys	PROPN
ap-1863	479	4	27(3):668–677	27(3):668–677	PROPN
ap-1863	479	5	,	,	PUNCT
ap-1863	479	6	1986	1986	NUM
ap-1863	479	7	.	.	PUNCT
ap-1863	480	1	[	[	X
ap-1863	480	2	46	46	NUM
ap-1863	480	3	]	]	X
ap-1863	480	4	j.	j.	PROPN
ap-1863	480	5	patera	patera	PROPN
ap-1863	480	6	.	.	PUNCT
ap-1863	481	1	verma	verma	PROPN
ap-1863	481	2	bases	basis	NOUN
ap-1863	481	3	for	for	ADP
ap-1863	481	4	representations	representation	NOUN
ap-1863	481	5	of	of	ADP
ap-1863	481	6	rank	rank	NOUN
ap-1863	481	7	two	two	NUM
ap-1863	481	8	lie	lie	NOUN
ap-1863	481	9	and	and	CCONJ
ap-1863	481	10	kac	kac	PROPN
ap-1863	481	11	-	-	PUNCT
ap-1863	481	12	moody	moody	PROPN
ap-1863	481	13	algebras	algebra	NOUN
ap-1863	481	14	.	.	PUNCT
ap-1863	482	1	in	in	ADP
ap-1863	482	2	proceedings	proceeding	NOUN
ap-1863	482	3	of	of	ADP
ap-1863	482	4	the	the	DET
ap-1863	482	5	14th	14th	ADJ
ap-1863	482	6	icgtmp	icgtmp	PROPN
ap-1863	482	7	(	(	PUNCT
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ap-1863	482	9	,	,	PUNCT
ap-1863	482	10	1985	1985	NUM
ap-1863	482	11	)	)	PUNCT
ap-1863	482	12	,	,	PUNCT
ap-1863	482	13	pp	pp	ADP
ap-1863	482	14	.	.	PUNCT
ap-1863	483	1	289–292	289–292	NUM
ap-1863	483	2	.	.	PUNCT
ap-1863	484	1	world	world	PROPN
ap-1863	484	2	sci	sci	PROPN
ap-1863	484	3	.	.	PROPN
ap-1863	484	4	publishing	publishing	PROPN
ap-1863	484	5	,	,	PUNCT
ap-1863	484	6	singapore	singapore	PROPN
ap-1863	484	7	,	,	PUNCT
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ap-1863	484	9	.	.	PUNCT
ap-1863	485	1	[	[	X
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ap-1863	485	3	]	]	PUNCT
ap-1863	485	4	m.	m.	PROPN
ap-1863	485	5	e.	e.	PROPN
ap-1863	485	6	hall	hall	PROPN
ap-1863	485	7	.	.	PUNCT
ap-1863	486	1	verma	verma	PROPN
ap-1863	486	2	bases	basis	NOUN
ap-1863	486	3	of	of	ADP
ap-1863	486	4	modules	module	NOUN
ap-1863	486	5	for	for	ADP
ap-1863	486	6	simple	simple	ADJ
ap-1863	486	7	lie	lie	NOUN
ap-1863	486	8	algebras	algebra	NOUN
ap-1863	486	9	.	.	PUNCT
ap-1863	487	1	proquest	proquest	PROPN
ap-1863	487	2	llc	llc	PROPN
ap-1863	487	3	,	,	PUNCT
ap-1863	487	4	ann	ann	PROPN
ap-1863	487	5	arbor	arbor	PROPN
ap-1863	487	6	,	,	PUNCT
ap-1863	487	7	mi	mi	PROPN
ap-1863	487	8	,	,	PUNCT
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ap-1863	487	10	.	.	PUNCT
ap-1863	488	1	thesis	thesis	NOUN
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ap-1863	488	5	of	of	ADP
ap-1863	488	6	wisconsin	wisconsin	PROPN
ap-1863	488	7	madison	madison	PROPN
ap-1863	488	8	.	.	PUNCT
ap-1863	489	1	[	[	X
ap-1863	489	2	48	48	NUM
ap-1863	489	3	]	]	PUNCT
ap-1863	489	4	k.	k.	PROPN
ap-1863	489	5	n.	n.	PROPN
ap-1863	489	6	raghavan	raghavan	PROPN
ap-1863	489	7	,	,	PUNCT
ap-1863	489	8	et	et	PROPN
ap-1863	489	9	al	al	PROPN
ap-1863	489	10	.	.	PROPN
ap-1863	489	11	on	on	ADP
ap-1863	489	12	verma	verma	PROPN
ap-1863	489	13	bases	basis	NOUN
ap-1863	489	14	for	for	ADP
ap-1863	489	15	representations	representation	NOUN
ap-1863	489	16	of	of	ADP
ap-1863	489	17	sl(n	sl(n	NOUN
ap-1863	489	18	,	,	PUNCT
ap-1863	489	19	c.	c.	PROPN
ap-1863	489	20	j	j	PROPN
ap-1863	489	21	math	math	PROPN
ap-1863	489	22	phys	phy	NOUN
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ap-1863	489	24	,	,	PUNCT
ap-1863	489	25	1999	1999	NUM
ap-1863	489	26	.	.	PUNCT
ap-1863	490	1	[	[	X
ap-1863	490	2	49	49	NUM
ap-1863	490	3	]	]	PUNCT
ap-1863	490	4	k.	k.	PROPN
ap-1863	490	5	n.	n.	PROPN
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ap-1863	490	7	,	,	PUNCT
ap-1863	490	8	et	et	PROPN
ap-1863	490	9	al	al	PROPN
ap-1863	490	10	.	.	PUNCT
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ap-1863	490	13	“	"	PUNCT
ap-1863	490	14	on	on	ADP
ap-1863	490	15	verma	verma	PROPN
ap-1863	490	16	bases	basis	NOUN
ap-1863	490	17	for	for	ADP
ap-1863	490	18	representations	representation	NOUN
ap-1863	490	19	of	of	ADP
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ap-1863	490	21	,	,	PUNCT
ap-1863	490	22	c	c	NOUN
ap-1863	490	23	)	)	PUNCT
ap-1863	490	24	”	"	PUNCT
ap-1863	491	1	[	[	X
ap-1863	491	2	j.	j.	PROPN
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ap-1863	491	4	.	.	PUNCT
ap-1863	492	1	phys	phy	NOUN
ap-1863	492	2	.	.	PUNCT
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ap-1863	493	2	(	(	PUNCT
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ap-1863	493	4	)	)	PUNCT
ap-1863	493	5	,	,	PUNCT
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ap-1863	493	8	4	4	NUM
ap-1863	493	9	,	,	PUNCT
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ap-1863	493	11	;	;	PUNCT
ap-1863	493	12	mr1683149	mr1683149	NOUN
ap-1863	493	13	(	(	PUNCT
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ap-1863	493	15	)	)	PUNCT
ap-1863	493	16	]	]	PUNCT
ap-1863	493	17	.	.	PUNCT
ap-1863	494	1	j	j	PROPN
ap-1863	494	2	math	math	PROPN
ap-1863	494	3	phys	phy	NOUN
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ap-1863	494	5	,	,	PUNCT
ap-1863	494	6	2000	2000	NUM
ap-1863	494	7	.	.	PUNCT
ap-1863	495	1	[	[	X
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ap-1863	495	3	]	]	PUNCT
ap-1863	495	4	s.-j	s.-j	PROPN
ap-1863	495	5	.	.	PUNCT
ap-1863	496	1	kang	kang	PROPN
ap-1863	496	2	,	,	PUNCT
ap-1863	496	3	et	et	PROPN
ap-1863	496	4	al	al	PROPN
ap-1863	496	5	.	.	PROPN
ap-1863	496	6	gröbner	gröbner	PROPN
ap-1863	496	7	-	-	PUNCT
ap-1863	496	8	shirshov	shirshov	ADJ
ap-1863	496	9	bases	basis	NOUN
ap-1863	496	10	for	for	ADP
ap-1863	496	11	representation	representation	NOUN
ap-1863	496	12	theory	theory	NOUN
ap-1863	496	13	.	.	PUNCT
ap-1863	497	1	j	j	PROPN
ap-1863	497	2	korean	korean	ADJ
ap-1863	497	3	math	math	PROPN
ap-1863	497	4	soc	soc	PROPN
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ap-1863	497	7	2000	2000	NUM
ap-1863	497	8	.	.	PUNCT
ap-1863	498	1	[	[	X
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ap-1863	498	3	]	]	PUNCT
ap-1863	498	4	s.-j	s.-j	PROPN
ap-1863	498	5	.	.	PUNCT
ap-1863	499	1	kang	kang	PROPN
ap-1863	499	2	,	,	PUNCT
ap-1863	499	3	et	et	PROPN
ap-1863	499	4	al	al	PROPN
ap-1863	499	5	.	.	PROPN
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ap-1863	499	7	-	-	PUNCT
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ap-1863	500	4	,	,	PUNCT
ap-1863	500	5	2000	2000	NUM
ap-1863	500	6	.	.	PUNCT
ap-1863	501	1	456	456	NUM
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ap-1863	501	3	polytechnica	polytechnica	PROPN
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ap-1863	501	5	,	,	PUNCT
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ap-1863	501	7	1	1	NUM
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ap-1863	501	9	2	2	NUM
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ap-1863	501	12	3	3	NUM
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ap-1863	501	16	4	4	NUM
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ap-1863	501	19	references	reference	NOUN