id	sid	tid	token	lemma	pos
ap-1261	1	1	ap-5-10.dvi	ap-5-10.dvi	PROPN
ap-1261	1	2	acta	acta	PROPN
ap-1261	1	3	polytechnica	polytechnica	PROPN
ap-1261	1	4	vol	vol	NOUN
ap-1261	1	5	.	.	PROPN
ap-1261	2	1	50	50	NUM
ap-1261	2	2	no	no	NOUN
ap-1261	2	3	.	.	PUNCT
ap-1261	3	1	5/2010	5/2010	NUM
ap-1261	3	2	on	on	ADP
ap-1261	3	3	representations	representation	NOUN
ap-1261	3	4	of	of	ADP
ap-1261	3	5	sl(n	sl(n	ADJ
ap-1261	3	6	,	,	PUNCT
ap-1261	3	7	c	c	NOUN
ap-1261	3	8	)	)	PUNCT
ap-1261	3	9	compatible	compatible	ADJ
ap-1261	3	10	with	with	ADP
ap-1261	3	11	a	a	DET
ap-1261	3	12	z2	z2	NOUN
ap-1261	3	13	-	-	PUNCT
ap-1261	3	14	grading	grade	VERB
ap-1261	3	15	m.	m.	NOUN
ap-1261	3	16	havlíček	havlíček	PROPN
ap-1261	3	17	,	,	PUNCT
ap-1261	3	18	e.	e.	PROPN
ap-1261	3	19	pelantová	pelantová	PROPN
ap-1261	3	20	,	,	PUNCT
ap-1261	3	21	j.	j.	PROPN
ap-1261	3	22	tolar	tolar	PROPN
ap-1261	3	23	abstract	abstract	NOUN
ap-1261	3	24	this	this	DET
ap-1261	3	25	paper	paper	NOUN
ap-1261	3	26	extends	extend	VERB
ap-1261	3	27	existing	exist	VERB
ap-1261	3	28	lie	lie	NOUN
ap-1261	3	29	algebra	algebra	NOUN
ap-1261	3	30	representation	representation	NOUN
ap-1261	3	31	theory	theory	NOUN
ap-1261	3	32	related	relate	VERB
ap-1261	3	33	to	to	PART
ap-1261	3	34	lie	lie	VERB
ap-1261	3	35	algebra	algebra	NOUN
ap-1261	3	36	gradings	grading	NOUN
ap-1261	3	37	.	.	PUNCT
ap-1261	4	1	the	the	DET
ap-1261	4	2	notion	notion	NOUN
ap-1261	4	3	of	of	ADP
ap-1261	4	4	a	a	DET
ap-1261	4	5	representation	representation	NOUN
ap-1261	4	6	compatible	compatible	ADJ
ap-1261	4	7	with	with	ADP
ap-1261	4	8	a	a	DET
ap-1261	4	9	given	give	VERB
ap-1261	4	10	grading	grading	NOUN
ap-1261	4	11	is	be	AUX
ap-1261	4	12	applied	apply	VERB
ap-1261	4	13	to	to	ADP
ap-1261	4	14	finite	finite	ADJ
ap-1261	4	15	-	-	ADJ
ap-1261	4	16	dimensional	dimensional	ADJ
ap-1261	4	17	representations	representation	NOUN
ap-1261	4	18	of	of	ADP
ap-1261	4	19	sl(n	sl(n	ADJ
ap-1261	4	20	,	,	PUNCT
ap-1261	4	21	c	c	NOUN
ap-1261	4	22	)	)	PUNCT
ap-1261	4	23	in	in	ADP
ap-1261	4	24	relation	relation	NOUN
ap-1261	4	25	to	to	ADP
ap-1261	4	26	its	its	PRON
ap-1261	4	27	z2	z2	NUM
ap-1261	4	28	-	-	PUNCT
ap-1261	4	29	gradings	grading	NOUN
ap-1261	4	30	.	.	PUNCT
ap-1261	5	1	for	for	ADP
ap-1261	5	2	representation	representation	NOUN
ap-1261	5	3	theory	theory	NOUN
ap-1261	5	4	of	of	ADP
ap-1261	5	5	sl(n	sl(n	PROPN
ap-1261	5	6	,	,	PUNCT
ap-1261	5	7	c	c	X
ap-1261	5	8	)	)	PUNCT
ap-1261	5	9	the	the	DET
ap-1261	5	10	gel’fand	gel’fand	NOUN
ap-1261	5	11	-	-	PUNCT
ap-1261	5	12	tseitlin	tseitlin	NOUN
ap-1261	5	13	method	method	NOUN
ap-1261	5	14	turned	turn	VERB
ap-1261	5	15	out	out	ADP
ap-1261	5	16	very	very	ADV
ap-1261	5	17	efficient	efficient	ADJ
ap-1261	5	18	.	.	PUNCT
ap-1261	6	1	we	we	PRON
ap-1261	6	2	show	show	VERB
ap-1261	6	3	that	that	SCONJ
ap-1261	6	4	it	it	PRON
ap-1261	6	5	is	be	AUX
ap-1261	6	6	not	not	PART
ap-1261	6	7	generally	generally	ADV
ap-1261	6	8	true	true	ADJ
ap-1261	6	9	that	that	SCONJ
ap-1261	6	10	every	every	DET
ap-1261	6	11	irreducible	irreducible	ADJ
ap-1261	6	12	representation	representation	NOUN
ap-1261	6	13	can	can	AUX
ap-1261	6	14	be	be	AUX
ap-1261	6	15	compatibly	compatibly	ADV
ap-1261	6	16	graded	grade	VERB
ap-1261	6	17	.	.	PUNCT
ap-1261	7	1	1	1	NUM
ap-1261	7	2	introduction	introduction	NOUN
ap-1261	7	3	contractions	contraction	NOUN
ap-1261	7	4	of	of	ADP
ap-1261	7	5	lie	lie	NOUN
ap-1261	7	6	algebras	algebra	NOUN
ap-1261	7	7	,	,	PUNCT
ap-1261	7	8	of	of	ADP
ap-1261	7	9	interest	interest	NOUN
ap-1261	7	10	in	in	ADP
ap-1261	7	11	connecting	connect	VERB
ap-1261	7	12	physical	physical	ADJ
ap-1261	7	13	theories	theory	NOUN
ap-1261	7	14	,	,	PUNCT
ap-1261	7	15	are	be	AUX
ap-1261	7	16	traditionally	traditionally	ADV
ap-1261	7	17	understood	understand	VERB
ap-1261	7	18	as	as	ADP
ap-1261	7	19	limit	limit	NOUN
ap-1261	7	20	procedures	procedure	NOUN
ap-1261	7	21	through	through	ADP
ap-1261	7	22	which	which	PRON
ap-1261	7	23	lie	lie	NOUN
ap-1261	7	24	algebras	algebra	NOUN
ap-1261	7	25	are	be	AUX
ap-1261	7	26	modified	modify	VERB
ap-1261	7	27	into	into	ADP
ap-1261	7	28	different	different	ADJ
ap-1261	7	29	,	,	PUNCT
ap-1261	7	30	non	non	ADJ
ap-1261	7	31	-	-	ADJ
ap-1261	7	32	isomorphic	isomorphic	ADJ
ap-1261	7	33	lie	lie	NOUN
ap-1261	7	34	algebras	algebra	NOUN
ap-1261	7	35	[	[	X
ap-1261	7	36	5	5	NUM
ap-1261	7	37	,	,	PUNCT
ap-1261	7	38	8	8	NUM
ap-1261	7	39	]	]	PUNCT
ap-1261	7	40	.	.	PUNCT
ap-1261	8	1	nevertheless	nevertheless	ADV
ap-1261	8	2	,	,	PUNCT
ap-1261	8	3	for	for	ADP
ap-1261	8	4	many	many	ADJ
ap-1261	8	5	physical	physical	ADJ
ap-1261	8	6	applications	application	NOUN
ap-1261	8	7	,	,	PUNCT
ap-1261	8	8	especially	especially	ADV
ap-1261	8	9	in	in	ADP
ap-1261	8	10	quantum	quantum	ADJ
ap-1261	8	11	theory	theory	NOUN
ap-1261	8	12	,	,	PUNCT
ap-1261	8	13	representations	representation	NOUN
ap-1261	8	14	of	of	ADP
ap-1261	8	15	lie	lie	NOUN
ap-1261	8	16	algebras	algebra	NOUN
ap-1261	8	17	are	be	AUX
ap-1261	8	18	important	important	ADJ
ap-1261	8	19	.	.	PUNCT
ap-1261	9	1	it	it	PRON
ap-1261	9	2	should	should	AUX
ap-1261	9	3	be	be	AUX
ap-1261	9	4	noted	note	VERB
ap-1261	9	5	that	that	SCONJ
ap-1261	9	6	contractions	contraction	NOUN
ap-1261	9	7	usually	usually	ADV
ap-1261	9	8	produce	produce	VERB
ap-1261	9	9	non	non	ADJ
ap-1261	9	10	-	-	ADJ
ap-1261	9	11	compact	compact	ADJ
ap-1261	9	12	lie	lie	NOUN
ap-1261	9	13	algebras	algebra	NOUN
ap-1261	9	14	whose	whose	DET
ap-1261	9	15	unitary	unitary	ADJ
ap-1261	9	16	representations	representation	NOUN
ap-1261	9	17	are	be	AUX
ap-1261	9	18	infinite	infinite	ADJ
ap-1261	9	19	-	-	PUNCT
ap-1261	9	20	dimensional	dimensional	ADJ
ap-1261	9	21	.	.	PUNCT
ap-1261	10	1	remaining	remain	VERB
ap-1261	10	2	inside	inside	ADP
ap-1261	10	3	the	the	DET
ap-1261	10	4	framework	framework	NOUN
ap-1261	10	5	of	of	ADP
ap-1261	10	6	lie	lie	NOUN
ap-1261	10	7	algebras	algebra	NOUN
ap-1261	10	8	,	,	PUNCT
ap-1261	10	9	a	a	DET
ap-1261	10	10	completely	completely	ADV
ap-1261	10	11	different	different	ADJ
ap-1261	10	12	notion	notion	NOUN
ap-1261	10	13	of	of	ADP
ap-1261	10	14	graded	grade	VERB
ap-1261	10	15	contractions	contraction	NOUN
ap-1261	10	16	was	be	AUX
ap-1261	10	17	proposed	propose	VERB
ap-1261	10	18	in	in	ADP
ap-1261	10	19	[	[	X
ap-1261	10	20	11	11	NUM
ap-1261	10	21	]	]	PUNCT
ap-1261	10	22	.	.	PUNCT
ap-1261	11	1	in	in	ADP
ap-1261	11	2	a	a	DET
ap-1261	11	3	seminal	seminal	ADJ
ap-1261	11	4	paper	paper	NOUN
ap-1261	11	5	[	[	X
ap-1261	11	6	13	13	NUM
ap-1261	11	7	]	]	PUNCT
ap-1261	11	8	,	,	PUNCT
ap-1261	11	9	r.	r.	PROPN
ap-1261	11	10	v.	v.	PROPN
ap-1261	11	11	moody	moody	PROPN
ap-1261	11	12	and	and	CCONJ
ap-1261	11	13	j.	j.	PROPN
ap-1261	11	14	patera	patera	PROPN
ap-1261	11	15	pushed	push	VERB
ap-1261	11	16	the	the	DET
ap-1261	11	17	theory	theory	NOUN
ap-1261	11	18	of	of	ADP
ap-1261	11	19	graded	grade	VERB
ap-1261	11	20	contractions	contraction	NOUN
ap-1261	11	21	of	of	ADP
ap-1261	11	22	lie	lie	NOUN
ap-1261	11	23	algebras	algebra	VERB
ap-1261	11	24	further	far	ADV
ap-1261	11	25	with	with	ADP
ap-1261	11	26	graded	grade	VERB
ap-1261	11	27	contractions	contraction	NOUN
ap-1261	11	28	of	of	ADP
ap-1261	11	29	representations	representation	NOUN
ap-1261	11	30	of	of	ADP
ap-1261	11	31	lie	lie	NOUN
ap-1261	11	32	algebras	algebra	NOUN
ap-1261	11	33	.	.	PUNCT
ap-1261	12	1	by	by	ADP
ap-1261	12	2	considering	consider	VERB
ap-1261	12	3	along	along	ADP
ap-1261	12	4	with	with	ADP
ap-1261	12	5	graded	grade	VERB
ap-1261	12	6	lie	lie	NOUN
ap-1261	12	7	algebras	algebra	VERB
ap-1261	12	8	their	their	PRON
ap-1261	12	9	compatibly	compatibly	ADV
ap-1261	12	10	graded	grade	VERB
ap-1261	12	11	finite	finite	ADJ
ap-1261	12	12	-	-	ADJ
ap-1261	12	13	dimensional	dimensional	ADJ
ap-1261	12	14	representations	representation	NOUN
ap-1261	12	15	,	,	PUNCT
ap-1261	12	16	they	they	PRON
ap-1261	12	17	obtained	obtain	VERB
ap-1261	12	18	a	a	DET
ap-1261	12	19	theory	theory	NOUN
ap-1261	12	20	of	of	ADP
ap-1261	12	21	contractions	contraction	NOUN
ap-1261	12	22	of	of	ADP
ap-1261	12	23	representations	representation	NOUN
ap-1261	12	24	that	that	PRON
ap-1261	12	25	contains	contain	VERB
ap-1261	12	26	the	the	DET
ap-1261	12	27	lie	lie	NOUN
ap-1261	12	28	algebra	algebra	NOUN
ap-1261	12	29	contractions	contraction	NOUN
ap-1261	12	30	as	as	ADP
ap-1261	12	31	a	a	DET
ap-1261	12	32	special	special	ADJ
ap-1261	12	33	case	case	NOUN
ap-1261	12	34	for	for	ADP
ap-1261	12	35	adjoint	adjoint	NOUN
ap-1261	12	36	representation	representation	NOUN
ap-1261	12	37	.	.	PUNCT
ap-1261	13	1	this	this	PRON
ap-1261	13	2	is	be	AUX
ap-1261	13	3	unfortunately	unfortunately	ADV
ap-1261	13	4	the	the	DET
ap-1261	13	5	only	only	ADJ
ap-1261	13	6	existing	exist	VERB
ap-1261	13	7	mathematical	mathematical	ADJ
ap-1261	13	8	theory	theory	NOUN
ap-1261	13	9	of	of	ADP
ap-1261	13	10	this	this	DET
ap-1261	13	11	matter	matter	NOUN
ap-1261	13	12	,	,	PUNCT
ap-1261	13	13	and	and	CCONJ
ap-1261	13	14	moreover	moreover	ADV
ap-1261	13	15	it	it	PRON
ap-1261	13	16	is	be	AUX
ap-1261	13	17	not	not	PART
ap-1261	13	18	concerned	concern	VERB
ap-1261	13	19	with	with	ADP
ap-1261	13	20	the	the	DET
ap-1261	13	21	question	question	NOUN
ap-1261	13	22	of	of	ADP
ap-1261	13	23	which	which	PRON
ap-1261	13	24	representations	representation	NOUN
ap-1261	13	25	can	can	AUX
ap-1261	13	26	be	be	AUX
ap-1261	13	27	compatibly	compatibly	ADV
ap-1261	13	28	graded	grade	VERB
ap-1261	13	29	.	.	PUNCT
ap-1261	14	1	namely	namely	ADV
ap-1261	14	2	,	,	PUNCT
ap-1261	14	3	compatibly	compatibly	ADV
ap-1261	14	4	graded	grade	VERB
ap-1261	14	5	finite	finite	ADJ
ap-1261	14	6	-	-	ADJ
ap-1261	14	7	dimensional	dimensional	ADJ
ap-1261	14	8	representations	representation	NOUN
ap-1261	14	9	were	be	AUX
ap-1261	14	10	assumed	assume	VERB
ap-1261	14	11	throughout	throughout	ADP
ap-1261	14	12	the	the	DET
ap-1261	14	13	paper	paper	NOUN
ap-1261	15	1	[	[	X
ap-1261	15	2	13	13	NUM
ap-1261	15	3	]	]	PUNCT
ap-1261	15	4	,	,	PUNCT
ap-1261	15	5	eqs	eqs	X
ap-1261	15	6	.	.	PUNCT
ap-1261	16	1	(	(	PUNCT
ap-1261	16	2	2.10	2.10	NUM
ap-1261	16	3	)	)	PUNCT
ap-1261	16	4	and	and	CCONJ
ap-1261	16	5	(	(	PUNCT
ap-1261	16	6	2.11	2.11	NUM
ap-1261	16	7	)	)	PUNCT
ap-1261	16	8	which	which	PRON
ap-1261	16	9	is	be	AUX
ap-1261	16	10	a	a	DET
ap-1261	16	11	valid	valid	ADJ
ap-1261	16	12	assumption	assumption	NOUN
ap-1261	16	13	if	if	SCONJ
ap-1261	16	14	the	the	DET
ap-1261	16	15	grading	grading	NOUN
ap-1261	16	16	is	be	AUX
ap-1261	16	17	induced	induce	VERB
ap-1261	16	18	by	by	ADP
ap-1261	16	19	an	an	DET
ap-1261	16	20	inner	inner	ADJ
ap-1261	16	21	automorphism	automorphism	NOUN
ap-1261	16	22	.	.	PUNCT
ap-1261	17	1	in	in	ADP
ap-1261	17	2	this	this	DET
ap-1261	17	3	respect	respect	NOUN
ap-1261	17	4	they	they	PRON
ap-1261	17	5	also	also	ADV
ap-1261	17	6	provided	provide	VERB
ap-1261	17	7	a	a	DET
ap-1261	17	8	recipe	recipe	NOUN
ap-1261	17	9	for	for	ADP
ap-1261	17	10	finding	find	VERB
ap-1261	17	11	the	the	DET
ap-1261	17	12	corresponding	correspond	VERB
ap-1261	17	13	grading	grading	NOUN
ap-1261	17	14	of	of	ADP
ap-1261	17	15	vector	vector	NOUN
ap-1261	17	16	space	space	NOUN
ap-1261	17	17	v	v	NOUN
ap-1261	17	18	on	on	ADP
ap-1261	17	19	which	which	PRON
ap-1261	17	20	the	the	DET
ap-1261	17	21	representation	representation	NOUN
ap-1261	17	22	is	be	AUX
ap-1261	17	23	acting	act	VERB
ap-1261	17	24	(	(	PUNCT
ap-1261	17	25	5	5	NUM
ap-1261	17	26	)	)	PUNCT
ap-1261	17	27	.	.	PUNCT
ap-1261	18	1	one	one	PRON
ap-1261	18	2	should	should	AUX
ap-1261	18	3	also	also	ADV
ap-1261	18	4	mention	mention	VERB
ap-1261	18	5	a	a	DET
ap-1261	18	6	short	short	ADJ
ap-1261	18	7	note	note	NOUN
ap-1261	19	1	[	[	X
ap-1261	19	2	15	15	NUM
ap-1261	19	3	]	]	PUNCT
ap-1261	19	4	on	on	ADP
ap-1261	19	5	the	the	DET
ap-1261	19	6	subject	subject	NOUN
ap-1261	19	7	,	,	PUNCT
ap-1261	19	8	but	but	CCONJ
ap-1261	19	9	up	up	ADP
ap-1261	19	10	to	to	ADP
ap-1261	19	11	now	now	ADV
ap-1261	19	12	nobody	nobody	PRON
ap-1261	19	13	has	have	AUX
ap-1261	19	14	gone	go	VERB
ap-1261	19	15	ahead	ahead	ADV
ap-1261	19	16	with	with	ADP
ap-1261	19	17	a	a	DET
ap-1261	19	18	further	further	ADJ
ap-1261	19	19	study	study	NOUN
ap-1261	19	20	of	of	ADP
ap-1261	19	21	representations	representation	NOUN
ap-1261	19	22	of	of	ADP
ap-1261	19	23	lie	lie	NOUN
ap-1261	19	24	algebras	algebra	NOUN
ap-1261	19	25	related	relate	VERB
ap-1261	19	26	to	to	ADP
ap-1261	19	27	their	their	PRON
ap-1261	19	28	gradings	grading	NOUN
ap-1261	19	29	,	,	PUNCT
ap-1261	19	30	especially	especially	ADV
ap-1261	19	31	when	when	SCONJ
ap-1261	19	32	the	the	DET
ap-1261	19	33	gradings	grading	NOUN
ap-1261	19	34	are	be	AUX
ap-1261	19	35	induced	induce	VERB
ap-1261	19	36	by	by	ADP
ap-1261	19	37	outer	outer	ADJ
ap-1261	19	38	automorphisms	automorphism	NOUN
ap-1261	19	39	.	.	PUNCT
ap-1261	20	1	we	we	PRON
ap-1261	20	2	are	be	AUX
ap-1261	20	3	aware	aware	ADJ
ap-1261	20	4	that	that	SCONJ
ap-1261	20	5	finite	finite	ADJ
ap-1261	20	6	-	-	ADJ
ap-1261	20	7	dimensional	dimensional	ADJ
ap-1261	20	8	representations	representation	NOUN
ap-1261	20	9	of	of	ADP
ap-1261	20	10	contracted	contract	VERB
ap-1261	20	11	lie	lie	NOUN
ap-1261	20	12	algebras	algebra	NOUN
ap-1261	20	13	can	can	AUX
ap-1261	20	14	only	only	ADV
ap-1261	20	15	be	be	AUX
ap-1261	20	16	non	non	ADJ
ap-1261	20	17	-	-	ADJ
ap-1261	20	18	unitary	unitary	ADJ
ap-1261	20	19	.	.	PUNCT
ap-1261	21	1	however	however	ADV
ap-1261	21	2	,	,	PUNCT
ap-1261	21	3	such	such	ADJ
ap-1261	21	4	representations	representation	NOUN
ap-1261	21	5	,	,	PUNCT
ap-1261	21	6	usually	usually	ADV
ap-1261	21	7	indecomposable	indecomposable	ADJ
ap-1261	21	8	,	,	PUNCT
ap-1261	21	9	also	also	ADV
ap-1261	21	10	have	have	VERB
ap-1261	21	11	some	some	DET
ap-1261	21	12	interest	interest	NOUN
ap-1261	21	13	in	in	ADP
ap-1261	21	14	physics	physics	NOUN
ap-1261	21	15	.	.	PUNCT
ap-1261	22	1	our	our	PRON
ap-1261	22	2	paper	paper	NOUN
ap-1261	22	3	,	,	PUNCT
ap-1261	22	4	as	as	ADP
ap-1261	22	5	a	a	DET
ap-1261	22	6	starting	starting	NOUN
ap-1261	22	7	point	point	NOUN
ap-1261	22	8	for	for	ADP
ap-1261	22	9	such	such	DET
ap-1261	22	10	an	an	DET
ap-1261	22	11	investigation	investigation	NOUN
ap-1261	22	12	,	,	PUNCT
ap-1261	22	13	gives	give	VERB
ap-1261	22	14	answers	answer	NOUN
ap-1261	22	15	under	under	ADP
ap-1261	22	16	the	the	DET
ap-1261	22	17	restrictive	restrictive	ADJ
ap-1261	22	18	assumptions	assumption	NOUN
ap-1261	22	19	used	use	VERB
ap-1261	22	20	in	in	ADP
ap-1261	22	21	[	[	X
ap-1261	22	22	13	13	NUM
ap-1261	22	23	]	]	PUNCT
ap-1261	22	24	.	.	PUNCT
ap-1261	23	1	thus	thus	ADV
ap-1261	23	2	we	we	PRON
ap-1261	23	3	restrict	restrict	VERB
ap-1261	23	4	our	our	PRON
ap-1261	23	5	consideration	consideration	NOUN
ap-1261	23	6	to	to	ADP
ap-1261	23	7	1	1	NUM
ap-1261	23	8	.	.	PUNCT
ap-1261	24	1	complex	complex	ADJ
ap-1261	24	2	lie	lie	NOUN
ap-1261	24	3	algebras	algebra	NOUN
ap-1261	24	4	of	of	ADP
ap-1261	24	5	type	type	NOUN
ap-1261	24	6	a	a	PRON
ap-1261	24	7	,	,	PUNCT
ap-1261	24	8	2	2	NUM
ap-1261	24	9	.	.	X
ap-1261	24	10	finite	finite	ADJ
ap-1261	24	11	-	-	ADJ
ap-1261	24	12	dimensional	dimensional	ADJ
ap-1261	24	13	representations	representation	NOUN
ap-1261	24	14	,	,	PUNCT
ap-1261	24	15	3	3	X
ap-1261	24	16	.	.	PUNCT
ap-1261	24	17	group	group	NOUN
ap-1261	24	18	gradings	grading	NOUN
ap-1261	24	19	with	with	ADP
ap-1261	24	20	the	the	DET
ap-1261	24	21	grading	grade	VERB
ap-1261	24	22	group	group	NOUN
ap-1261	24	23	z2	z2	PROPN
ap-1261	24	24	.	.	PUNCT
ap-1261	25	1	z2	z2	PROPN
ap-1261	25	2	-	-	PUNCT
ap-1261	25	3	gradings	grading	NOUN
ap-1261	25	4	are	be	AUX
ap-1261	25	5	closely	closely	ADV
ap-1261	25	6	related	relate	VERB
ap-1261	25	7	to	to	ADP
ap-1261	25	8	involutive	involutive	ADJ
ap-1261	25	9	(	(	PUNCT
ap-1261	25	10	second	second	ADJ
ap-1261	25	11	order	order	NOUN
ap-1261	25	12	)	)	PUNCT
ap-1261	25	13	automorphisms	automorphism	NOUN
ap-1261	25	14	of	of	ADP
ap-1261	25	15	lie	lie	NOUN
ap-1261	25	16	algebras	algebra	NOUN
ap-1261	25	17	.	.	PUNCT
ap-1261	26	1	in	in	ADP
ap-1261	26	2	physical	physical	ADJ
ap-1261	26	3	applications	application	NOUN
ap-1261	26	4	they	they	PRON
ap-1261	26	5	are	be	AUX
ap-1261	26	6	especially	especially	ADV
ap-1261	26	7	useful	useful	ADJ
ap-1261	26	8	as	as	ADP
ap-1261	26	9	generalized	generalized	ADJ
ap-1261	26	10	parity	parity	NOUN
ap-1261	26	11	transformations	transformation	NOUN
ap-1261	26	12	.	.	PUNCT
ap-1261	27	1	in	in	ADP
ap-1261	27	2	this	this	DET
ap-1261	27	3	connection	connection	NOUN
ap-1261	27	4	our	our	PRON
ap-1261	27	5	earlier	early	ADJ
ap-1261	27	6	paper	paper	NOUN
ap-1261	27	7	[	[	X
ap-1261	27	8	12	12	NUM
ap-1261	27	9	]	]	PUNCT
ap-1261	27	10	dealt	deal	VERB
ap-1261	27	11	with	with	ADP
ap-1261	27	12	the	the	DET
ap-1261	27	13	well	well	ADV
ap-1261	27	14	-	-	PUNCT
ap-1261	27	15	known	know	VERB
ap-1261	27	16	space	space	NOUN
ap-1261	27	17	-	-	PUNCT
ap-1261	27	18	time	time	NOUN
ap-1261	27	19	parity	parity	NOUN
ap-1261	27	20	transformations	transformation	NOUN
ap-1261	27	21	—	—	PUNCT
ap-1261	27	22	space	space	NOUN
ap-1261	27	23	inversion	inversion	NOUN
ap-1261	27	24	and	and	CCONJ
ap-1261	27	25	time	time	NOUN
ap-1261	27	26	reversal	reversal	NOUN
ap-1261	27	27	—	—	PUNCT
ap-1261	27	28	and	and	CCONJ
ap-1261	27	29	the	the	DET
ap-1261	27	30	associated	associate	VERB
ap-1261	27	31	graded	grade	VERB
ap-1261	27	32	contractions	contraction	NOUN
ap-1261	27	33	for	for	ADP
ap-1261	27	34	the	the	DET
ap-1261	27	35	de	de	PROPN
ap-1261	27	36	sitter	sitter	NOUN
ap-1261	27	37	lie	lie	NOUN
ap-1261	27	38	algebras	algebras	PROPN
ap-1261	27	39	(	(	PUNCT
ap-1261	27	40	type	type	NOUN
ap-1261	27	41	b	b	NOUN
ap-1261	27	42	)	)	PUNCT
ap-1261	27	43	.	.	PUNCT
ap-1261	28	1	here	here	ADV
ap-1261	28	2	we	we	PRON
ap-1261	28	3	start	start	VERB
ap-1261	28	4	with	with	ADP
ap-1261	28	5	the	the	DET
ap-1261	28	6	simplest	simple	ADJ
ap-1261	28	7	case	case	NOUN
ap-1261	28	8	of	of	ADP
ap-1261	28	9	finite	finite	ADJ
ap-1261	28	10	-	-	ADJ
ap-1261	28	11	dimensional	dimensional	ADJ
ap-1261	28	12	representations	representation	NOUN
ap-1261	28	13	of	of	ADP
ap-1261	28	14	classical	classical	ADJ
ap-1261	28	15	lie	lie	NOUN
ap-1261	28	16	algebras	algebra	NOUN
ap-1261	28	17	of	of	ADP
ap-1261	28	18	type	type	NOUN
ap-1261	28	19	a.	a.	NOUN
ap-1261	28	20	the	the	DET
ap-1261	28	21	paper	paper	NOUN
ap-1261	28	22	is	be	AUX
ap-1261	28	23	organized	organize	VERB
ap-1261	28	24	as	as	SCONJ
ap-1261	28	25	follows	follow	VERB
ap-1261	28	26	.	.	PUNCT
ap-1261	29	1	section	section	NOUN
ap-1261	29	2	2	2	NUM
ap-1261	29	3	is	be	AUX
ap-1261	29	4	devoted	devote	VERB
ap-1261	29	5	to	to	ADP
ap-1261	29	6	representations	representation	NOUN
ap-1261	29	7	compatible	compatible	ADJ
ap-1261	29	8	with	with	ADP
ap-1261	29	9	a	a	DET
ap-1261	29	10	grading	grading	NOUN
ap-1261	29	11	.	.	PUNCT
ap-1261	30	1	explicit	explicit	ADJ
ap-1261	30	2	results	result	NOUN
ap-1261	30	3	are	be	AUX
ap-1261	30	4	obtained	obtain	VERB
ap-1261	30	5	in	in	ADP
ap-1261	30	6	section	section	NOUN
ap-1261	30	7	3	3	NUM
ap-1261	30	8	for	for	ADP
ap-1261	30	9	finite	finite	ADJ
ap-1261	30	10	-	-	ADJ
ap-1261	30	11	dimensional	dimensional	ADJ
ap-1261	30	12	representations	representation	NOUN
ap-1261	30	13	of	of	ADP
ap-1261	30	14	sl(n	sl(n	ADJ
ap-1261	30	15	,	,	PUNCT
ap-1261	30	16	c	c	NOUN
ap-1261	30	17	)	)	PUNCT
ap-1261	30	18	compatible	compatible	ADJ
ap-1261	30	19	with	with	ADP
ap-1261	30	20	z2	z2	NOUN
ap-1261	30	21	-	-	PUNCT
ap-1261	30	22	gradings	grading	NOUN
ap-1261	30	23	generated	generate	VERB
ap-1261	30	24	either	either	CCONJ
ap-1261	30	25	by	by	ADP
ap-1261	30	26	an	an	DET
ap-1261	30	27	inner	inner	ADJ
ap-1261	30	28	automorphism	automorphism	NOUN
ap-1261	30	29	of	of	ADP
ap-1261	30	30	order	order	NOUN
ap-1261	30	31	2	2	NUM
ap-1261	30	32	or	or	CCONJ
ap-1261	30	33	by	by	ADP
ap-1261	30	34	an	an	DET
ap-1261	30	35	outer	outer	ADJ
ap-1261	30	36	automorphism	automorphism	NOUN
ap-1261	30	37	of	of	ADP
ap-1261	30	38	order	order	NOUN
ap-1261	30	39	2	2	X
ap-1261	30	40	.	.	PUNCT
ap-1261	31	1	our	our	PRON
ap-1261	31	2	concrete	concrete	ADJ
ap-1261	31	3	results	result	NOUN
ap-1261	31	4	are	be	AUX
ap-1261	31	5	illustrated	illustrate	VERB
ap-1261	31	6	on	on	ADP
ap-1261	31	7	the	the	DET
ap-1261	31	8	simple	simple	ADJ
ap-1261	31	9	lie	lie	NOUN
ap-1261	31	10	algebra	algebra	PROPN
ap-1261	31	11	sl(3	sl(3	PROPN
ap-1261	31	12	,	,	PUNCT
ap-1261	31	13	c	c	NOUN
ap-1261	31	14	)	)	PUNCT
ap-1261	31	15	.	.	PUNCT
ap-1261	32	1	30	30	NUM
ap-1261	32	2	acta	acta	PROPN
ap-1261	32	3	polytechnica	polytechnica	PROPN
ap-1261	32	4	vol	vol	NOUN
ap-1261	32	5	.	.	PROPN
ap-1261	33	1	50	50	NUM
ap-1261	33	2	no	no	NOUN
ap-1261	33	3	.	.	PUNCT
ap-1261	34	1	5/2010	5/2010	NUM
ap-1261	34	2	2	2	NUM
ap-1261	34	3	representations	representation	NOUN
ap-1261	34	4	compatible	compatible	ADJ
ap-1261	34	5	with	with	ADP
ap-1261	34	6	grading	grade	VERB
ap-1261	34	7	2.1	2.1	NUM
ap-1261	34	8	graded	grade	VERB
ap-1261	34	9	contractions	contraction	NOUN
ap-1261	34	10	of	of	ADP
ap-1261	34	11	lie	lie	NOUN
ap-1261	34	12	algebras	algebra	VERB
ap-1261	34	13	a	a	DET
ap-1261	34	14	grading	grading	NOUN
ap-1261	34	15	of	of	ADP
ap-1261	34	16	a	a	DET
ap-1261	34	17	lie	lie	NOUN
ap-1261	34	18	algebra	algebra	NOUN
ap-1261	34	19	l	l	NOUN
ap-1261	34	20	is	be	AUX
ap-1261	34	21	a	a	DET
ap-1261	34	22	decomposition	decomposition	NOUN
ap-1261	34	23	γ	γ	NOUN
ap-1261	34	24	of	of	ADP
ap-1261	34	25	the	the	DET
ap-1261	34	26	vector	vector	NOUN
ap-1261	34	27	space	space	NOUN
ap-1261	34	28	l	l	NOUN
ap-1261	34	29	into	into	ADP
ap-1261	34	30	vector	vector	NOUN
ap-1261	34	31	subspaces	subspace	NOUN
ap-1261	34	32	lj	lj	ADV
ap-1261	34	33	,	,	PUNCT
ap-1261	34	34	j	j	PROPN
ap-1261	34	35	∈	∈	PROPN
ap-1261	34	36	j	j	PROPN
ap-1261	34	37	,	,	PUNCT
ap-1261	34	38	such	such	ADJ
ap-1261	34	39	that	that	SCONJ
ap-1261	34	40	l	l	NOUN
ap-1261	34	41	is	be	AUX
ap-1261	34	42	a	a	DET
ap-1261	34	43	direct	direct	ADJ
ap-1261	34	44	sum	sum	NOUN
ap-1261	34	45	of	of	ADP
ap-1261	34	46	these	these	DET
ap-1261	34	47	subspaces	subspace	NOUN
ap-1261	34	48	lj	lj	ADV
ap-1261	34	49	,	,	PUNCT
ap-1261	34	50	and	and	CCONJ
ap-1261	34	51	,	,	PUNCT
ap-1261	34	52	for	for	ADP
ap-1261	34	53	any	any	DET
ap-1261	34	54	pair	pair	NOUN
ap-1261	34	55	of	of	ADP
ap-1261	34	56	indices	index	NOUN
ap-1261	34	57	j	j	PROPN
ap-1261	34	58	,	,	PUNCT
ap-1261	34	59	k	k	PROPN
ap-1261	34	60	∈	∈	PROPN
ap-1261	34	61	j	j	PROPN
ap-1261	34	62	,	,	PUNCT
ap-1261	34	63	there	there	PRON
ap-1261	34	64	exists	exist	VERB
ap-1261	34	65	l	l	PROPN
ap-1261	34	66	∈	∈	PROPN
ap-1261	34	67	j	j	NOUN
ap-1261	34	68	such	such	ADJ
ap-1261	34	69	that	that	SCONJ
ap-1261	34	70	[	[	X
ap-1261	34	71	lj	lj	PROPN
ap-1261	34	72	,	,	PUNCT
ap-1261	34	73	lk	lk	PROPN
ap-1261	34	74	]	]	X
ap-1261	34	75	⊆	⊆	NUM
ap-1261	34	76	ll	ll	NOUN
ap-1261	34	77	.	.	PUNCT
ap-1261	35	1	we	we	PRON
ap-1261	35	2	denote	denote	VERB
ap-1261	35	3	the	the	DET
ap-1261	35	4	grading	grading	NOUN
ap-1261	35	5	by	by	ADP
ap-1261	35	6	γ	γ	NOUN
ap-1261	35	7	:	:	PUNCT
ap-1261	35	8	l	l	NOUN
ap-1261	35	9	=	=	SYM
ap-1261	35	10	⊕	⊕	PROPN
ap-1261	35	11	j∈j	j∈j	NOUN
ap-1261	35	12	lj	lj	PROPN
ap-1261	35	13	;	;	PUNCT
ap-1261	35	14	(	(	PUNCT
ap-1261	35	15	let	let	VERB
ap-1261	35	16	us	we	PRON
ap-1261	35	17	note	note	VERB
ap-1261	35	18	that	that	SCONJ
ap-1261	35	19	in	in	ADP
ap-1261	35	20	our	our	PRON
ap-1261	35	21	definition	definition	NOUN
ap-1261	35	22	of	of	ADP
ap-1261	35	23	grading	grade	VERB
ap-1261	35	24	we	we	PRON
ap-1261	35	25	do	do	AUX
ap-1261	35	26	not	not	PART
ap-1261	35	27	exclude	exclude	VERB
ap-1261	35	28	trivial	trivial	ADJ
ap-1261	35	29	subspaces	subspace	NOUN
ap-1261	35	30	li	li	NOUN
ap-1261	35	31	=	=	PUNCT
ap-1261	35	32	{	{	PUNCT
ap-1261	35	33	0	0	NUM
ap-1261	35	34	}	}	PUNCT
ap-1261	35	35	)	)	PUNCT
ap-1261	35	36	.	.	PUNCT
ap-1261	36	1	it	it	PRON
ap-1261	36	2	follows	follow	VERB
ap-1261	36	3	directly	directly	ADV
ap-1261	36	4	from	from	ADP
ap-1261	36	5	the	the	DET
ap-1261	36	6	definition	definition	NOUN
ap-1261	36	7	that	that	SCONJ
ap-1261	36	8	for	for	ADP
ap-1261	36	9	any	any	DET
ap-1261	36	10	grading	grade	VERB
ap-1261	36	11	γ	γ	X
ap-1261	36	12	:	:	PUNCT
ap-1261	36	13	⊕	⊕	PROPN
ap-1261	36	14	j∈j	j∈j	NOUN
ap-1261	36	15	lj	lj	PROPN
ap-1261	36	16	and	and	CCONJ
ap-1261	36	17	any	any	DET
ap-1261	36	18	automorphism	automorphism	NOUN
ap-1261	36	19	g	g	PROPN
ap-1261	36	20	∈	∈	PROPN
ap-1261	36	21	aut	aut	NOUN
ap-1261	36	22	l	l	NOUN
ap-1261	36	23	the	the	DET
ap-1261	36	24	decomposition	decomposition	NOUN
ap-1261	36	25	γ′	γ′	NOUN
ap-1261	36	26	:	:	PUNCT
ap-1261	36	27	⊕	⊕	PROPN
ap-1261	36	28	j∈j	j∈j	PROPN
ap-1261	36	29	g(lj	g(lj	PROPN
ap-1261	36	30	)	)	PUNCT
ap-1261	36	31	is	be	AUX
ap-1261	36	32	also	also	ADV
ap-1261	36	33	a	a	DET
ap-1261	36	34	grading	grading	NOUN
ap-1261	36	35	.	.	PUNCT
ap-1261	37	1	gradings	grading	NOUN
ap-1261	37	2	γ	γ	PROPN
ap-1261	37	3	and	and	CCONJ
ap-1261	37	4	γ′	γ′	PROPN
ap-1261	37	5	are	be	AUX
ap-1261	37	6	called	call	VERB
ap-1261	37	7	equivalent	equivalent	ADJ
ap-1261	37	8	.	.	PUNCT
ap-1261	38	1	now	now	ADV
ap-1261	38	2	we	we	PRON
ap-1261	38	3	describe	describe	VERB
ap-1261	38	4	a	a	DET
ap-1261	38	5	specific	specific	ADJ
ap-1261	38	6	type	type	NOUN
ap-1261	38	7	of	of	ADP
ap-1261	38	8	grading	grade	VERB
ap-1261	38	9	,	,	PUNCT
ap-1261	38	10	namely	namely	ADV
ap-1261	38	11	a	a	DET
ap-1261	38	12	group	group	NOUN
ap-1261	38	13	grading	grade	VERB
ap-1261	38	14	.	.	PUNCT
ap-1261	39	1	a	a	DET
ap-1261	39	2	grading	grade	VERB
ap-1261	39	3	γ	γ	NOUN
ap-1261	39	4	:	:	PUNCT
ap-1261	39	5	l	l	NOUN
ap-1261	39	6	=	=	SYM
ap-1261	39	7	⊕j∈j	⊕j∈j	X
ap-1261	39	8	lj	lj	ADV
ap-1261	39	9	is	be	AUX
ap-1261	39	10	called	call	VERB
ap-1261	39	11	a	a	DET
ap-1261	39	12	group	group	NOUN
ap-1261	39	13	grading	grade	VERB
ap-1261	39	14	if	if	SCONJ
ap-1261	39	15	the	the	DET
ap-1261	39	16	index	index	NOUN
ap-1261	39	17	set	set	VERB
ap-1261	39	18	j	j	PROPN
ap-1261	39	19	can	can	AUX
ap-1261	39	20	be	be	AUX
ap-1261	39	21	embedded	embed	VERB
ap-1261	39	22	into	into	ADP
ap-1261	39	23	a	a	DET
ap-1261	39	24	semigroup	semigroup	NOUN
ap-1261	39	25	g	g	NOUN
ap-1261	39	26	(	(	PUNCT
ap-1261	39	27	whose	whose	DET
ap-1261	39	28	binary	binary	ADJ
ap-1261	39	29	operation	operation	NOUN
ap-1261	39	30	is	be	AUX
ap-1261	39	31	denoted	denote	VERB
ap-1261	39	32	by	by	ADP
ap-1261	39	33	+	+	NOUN
ap-1261	39	34	)	)	PUNCT
ap-1261	39	35	,	,	PUNCT
ap-1261	39	36	and	and	CCONJ
ap-1261	39	37	,	,	PUNCT
ap-1261	39	38	for	for	ADP
ap-1261	39	39	any	any	DET
ap-1261	39	40	pair	pair	NOUN
ap-1261	39	41	of	of	ADP
ap-1261	39	42	indices	index	NOUN
ap-1261	39	43	j	j	PROPN
ap-1261	39	44	,	,	PUNCT
ap-1261	39	45	k	k	PROPN
ap-1261	39	46	∈	∈	PROPN
ap-1261	39	47	j	j	PROPN
ap-1261	39	48	,	,	PUNCT
ap-1261	39	49	it	it	PRON
ap-1261	39	50	holds	hold	VERB
ap-1261	39	51	that	that	SCONJ
ap-1261	39	52	[	[	X
ap-1261	39	53	lj	lj	PROPN
ap-1261	39	54	,	,	PUNCT
ap-1261	39	55	lk	lk	PROPN
ap-1261	39	56	]	]	X
ap-1261	39	57	⊆	⊆	NUM
ap-1261	39	58	lj+k	lj+k	NOUN
ap-1261	39	59	.	.	PUNCT
ap-1261	40	1	(	(	PUNCT
ap-1261	40	2	1	1	X
ap-1261	40	3	)	)	PUNCT
ap-1261	40	4	since	since	SCONJ
ap-1261	40	5	even	even	ADV
ap-1261	40	6	trivial	trivial	ADJ
ap-1261	40	7	subspaces	subspace	NOUN
ap-1261	40	8	are	be	AUX
ap-1261	40	9	generally	generally	ADV
ap-1261	40	10	allowed	allow	VERB
ap-1261	40	11	in	in	ADP
ap-1261	40	12	the	the	DET
ap-1261	40	13	decomposition	decomposition	NOUN
ap-1261	40	14	of	of	ADP
ap-1261	40	15	l	l	NOUN
ap-1261	40	16	,	,	PUNCT
ap-1261	40	17	the	the	DET
ap-1261	40	18	semigroup	semigroup	PROPN
ap-1261	40	19	g	g	PROPN
ap-1261	40	20	may	may	AUX
ap-1261	40	21	be	be	AUX
ap-1261	40	22	used	use	VERB
ap-1261	40	23	as	as	ADP
ap-1261	40	24	the	the	DET
ap-1261	40	25	index	index	NOUN
ap-1261	40	26	set	set	NOUN
ap-1261	40	27	of	of	ADP
ap-1261	40	28	the	the	DET
ap-1261	40	29	group	group	NOUN
ap-1261	40	30	grading	grading	NOUN
ap-1261	40	31	.	.	PUNCT
ap-1261	41	1	in	in	ADP
ap-1261	41	2	this	this	DET
ap-1261	41	3	case	case	NOUN
ap-1261	41	4	we	we	PRON
ap-1261	41	5	will	will	AUX
ap-1261	41	6	speak	speak	VERB
ap-1261	41	7	about	about	ADP
ap-1261	41	8	a	a	DET
ap-1261	41	9	g	g	NOUN
ap-1261	41	10	-	-	PUNCT
ap-1261	41	11	grading	grade	VERB
ap-1261	41	12	γ	γ	NOUN
ap-1261	41	13	.	.	PUNCT
ap-1261	42	1	we	we	PRON
ap-1261	42	2	will	will	AUX
ap-1261	42	3	focus	focus	VERB
ap-1261	42	4	in	in	ADP
ap-1261	42	5	this	this	DET
ap-1261	42	6	paper	paper	NOUN
ap-1261	42	7	on	on	ADP
ap-1261	42	8	group	group	NOUN
ap-1261	42	9	gradings	grading	NOUN
ap-1261	42	10	only	only	ADV
ap-1261	42	11	and	and	CCONJ
ap-1261	42	12	we	we	PRON
ap-1261	42	13	assume	assume	VERB
ap-1261	42	14	in	in	ADP
ap-1261	42	15	the	the	DET
ap-1261	42	16	sequel	sequel	NOUN
ap-1261	42	17	that	that	SCONJ
ap-1261	42	18	the	the	DET
ap-1261	42	19	indices	index	NOUN
ap-1261	42	20	of	of	ADP
ap-1261	42	21	the	the	DET
ap-1261	42	22	grading	grade	VERB
ap-1261	42	23	subspaces	subspace	NOUN
ap-1261	42	24	belong	belong	VERB
ap-1261	42	25	to	to	ADP
ap-1261	42	26	a	a	DET
ap-1261	42	27	group	group	NOUN
ap-1261	42	28	g	g	NOUN
ap-1261	42	29	,	,	PUNCT
ap-1261	42	30	i.e.	i.e.	X
ap-1261	42	31	γ	γ	X
ap-1261	42	32	is	be	AUX
ap-1261	42	33	a	a	DET
ap-1261	42	34	g	g	NOUN
ap-1261	42	35	-	-	PUNCT
ap-1261	42	36	grading	grading	NOUN
ap-1261	42	37	of	of	ADP
ap-1261	42	38	l.	l.	PROPN
ap-1261	42	39	a	a	DET
ap-1261	42	40	grading	grade	VERB
ap-1261	42	41	γ	γ	NOUN
ap-1261	42	42	:	:	PUNCT
ap-1261	42	43	l	l	NOUN
ap-1261	42	44	=	=	SYM
ap-1261	43	1	⊕i∈j	⊕i∈j	X
ap-1261	43	2	li	li	NOUN
ap-1261	43	3	of	of	ADP
ap-1261	43	4	a	a	DET
ap-1261	43	5	lie	lie	NOUN
ap-1261	43	6	algebra	algebra	NOUN
ap-1261	43	7	l	l	NOUN
ap-1261	43	8	is	be	AUX
ap-1261	43	9	a	a	DET
ap-1261	43	10	starting	starting	NOUN
ap-1261	43	11	point	point	NOUN
ap-1261	43	12	for	for	ADP
ap-1261	43	13	the	the	DET
ap-1261	43	14	study	study	NOUN
ap-1261	43	15	of	of	ADP
ap-1261	43	16	graded	grade	VERB
ap-1261	43	17	contractions	contraction	NOUN
ap-1261	43	18	of	of	ADP
ap-1261	43	19	the	the	DET
ap-1261	43	20	lie	lie	NOUN
ap-1261	43	21	algebra	algebra	NOUN
ap-1261	43	22	.	.	PUNCT
ap-1261	44	1	this	this	DET
ap-1261	44	2	method	method	NOUN
ap-1261	44	3	for	for	ADP
ap-1261	44	4	finding	find	VERB
ap-1261	44	5	contractions	contraction	NOUN
ap-1261	44	6	of	of	ADP
ap-1261	44	7	lie	lie	NOUN
ap-1261	44	8	algebras	algebra	NOUN
ap-1261	44	9	was	be	AUX
ap-1261	44	10	introduced	introduce	VERB
ap-1261	44	11	in	in	ADP
ap-1261	44	12	[	[	X
ap-1261	44	13	11	11	NUM
ap-1261	44	14	,	,	PUNCT
ap-1261	44	15	13	13	NUM
ap-1261	44	16	]	]	PUNCT
ap-1261	44	17	.	.	PUNCT
ap-1261	45	1	in	in	ADP
ap-1261	45	2	this	this	DET
ap-1261	45	3	type	type	NOUN
ap-1261	45	4	of	of	ADP
ap-1261	45	5	contraction	contraction	NOUN
ap-1261	45	6	,	,	PUNCT
ap-1261	45	7	we	we	PRON
ap-1261	45	8	define	define	VERB
ap-1261	45	9	new	new	ADJ
ap-1261	45	10	lie	lie	NOUN
ap-1261	45	11	brackets	bracket	NOUN
ap-1261	45	12	by	by	ADP
ap-1261	45	13	the	the	DET
ap-1261	45	14	prescription	prescription	NOUN
ap-1261	46	1	[	[	X
ap-1261	46	2	x	x	NOUN
ap-1261	46	3	,	,	PUNCT
ap-1261	46	4	y]new	y]new	ADJ
ap-1261	46	5	:	:	PUNCT
ap-1261	46	6	=	=	SYM
ap-1261	46	7	εj	εj	NOUN
ap-1261	46	8	,	,	PUNCT
ap-1261	46	9	k[x	k[x	PROPN
ap-1261	46	10	,	,	PUNCT
ap-1261	46	11	y	y	PROPN
ap-1261	46	12	]	]	X
ap-1261	46	13	,	,	PUNCT
ap-1261	46	14	where	where	SCONJ
ap-1261	46	15	x	x	PUNCT
ap-1261	46	16	∈	∈	PROPN
ap-1261	46	17	lj	lj	PROPN
ap-1261	46	18	,	,	PUNCT
ap-1261	46	19	y	y	PROPN
ap-1261	46	20	∈	∈	PROPN
ap-1261	46	21	lk	lk	PROPN
ap-1261	46	22	.	.	PROPN
ap-1261	46	23	(	(	PUNCT
ap-1261	46	24	2	2	X
ap-1261	46	25	)	)	PUNCT
ap-1261	46	26	the	the	DET
ap-1261	46	27	complex	complex	ADJ
ap-1261	46	28	or	or	CCONJ
ap-1261	46	29	real	real	ADJ
ap-1261	46	30	parameters	parameter	NOUN
ap-1261	46	31	εj	εj	VERB
ap-1261	46	32	,	,	PUNCT
ap-1261	46	33	k	k	PROPN
ap-1261	46	34	for	for	ADP
ap-1261	46	35	j	j	PROPN
ap-1261	46	36	,	,	PUNCT
ap-1261	46	37	k	k	PROPN
ap-1261	46	38	∈	∈	PROPN
ap-1261	46	39	g	g	PROPN
ap-1261	46	40	must	must	AUX
ap-1261	46	41	be	be	AUX
ap-1261	46	42	determined	determine	VERB
ap-1261	46	43	in	in	ADP
ap-1261	46	44	such	such	DET
ap-1261	46	45	a	a	DET
ap-1261	46	46	way	way	NOUN
ap-1261	46	47	that	that	PRON
ap-1261	46	48	the	the	DET
ap-1261	46	49	vector	vector	NOUN
ap-1261	46	50	space	space	NOUN
ap-1261	46	51	l	l	NOUN
ap-1261	46	52	with	with	ADP
ap-1261	46	53	the	the	DET
ap-1261	46	54	binary	binary	ADJ
ap-1261	46	55	operation	operation	NOUN
ap-1261	46	56	[	[	X
ap-1261	46	57	.	.	PROPN
ap-1261	46	58	,	,	PUNCT
ap-1261	46	59	.]new	.]new	PROPN
ap-1261	46	60	again	again	ADV
ap-1261	46	61	forms	form	VERB
ap-1261	46	62	a	a	DET
ap-1261	46	63	lie	lie	NOUN
ap-1261	46	64	algebra	algebra	NOUN
ap-1261	46	65	.	.	PUNCT
ap-1261	47	1	antisymmetry	antisymmetry	NOUN
ap-1261	47	2	of	of	ADP
ap-1261	47	3	lie	lie	NOUN
ap-1261	47	4	brackets	bracket	NOUN
ap-1261	47	5	demands	demand	NOUN
ap-1261	47	6	that	that	SCONJ
ap-1261	47	7	εj	εj	VERB
ap-1261	47	8	,	,	PUNCT
ap-1261	47	9	k	k	NOUN
ap-1261	47	10	=	=	SYM
ap-1261	47	11	εk	εk	PROPN
ap-1261	47	12	,	,	PUNCT
ap-1261	47	13	j	j	PROPN
ap-1261	47	14	.	.	PUNCT
ap-1261	48	1	if	if	SCONJ
ap-1261	48	2	,	,	PUNCT
ap-1261	48	3	moreover	moreover	ADV
ap-1261	48	4	,	,	PUNCT
ap-1261	48	5	the	the	DET
ap-1261	48	6	coefficients	coefficient	NOUN
ap-1261	48	7	εj	εj	PROPN
ap-1261	48	8	,	,	PUNCT
ap-1261	48	9	k	k	PROPN
ap-1261	48	10	fulfill	fulfill	VERB
ap-1261	48	11	the	the	DET
ap-1261	48	12	first	first	ADJ
ap-1261	48	13	basic	basic	ADJ
ap-1261	48	14	set	set	NOUN
ap-1261	48	15	of	of	ADP
ap-1261	48	16	contraction	contraction	NOUN
ap-1261	48	17	equations	equation	NOUN
ap-1261	48	18	[	[	X
ap-1261	48	19	14	14	NUM
ap-1261	48	20	]	]	X
ap-1261	48	21	:	:	PUNCT
ap-1261	48	22	εi	εi	VERB
ap-1261	48	23	,	,	PUNCT
ap-1261	48	24	jεi+j	jεi+j	PROPN
ap-1261	48	25	,	,	PUNCT
ap-1261	48	26	k	k	NOUN
ap-1261	48	27	=	=	SYM
ap-1261	48	28	εj	εj	PROPN
ap-1261	48	29	,	,	PUNCT
ap-1261	48	30	kεj+k	kεj+k	PROPN
ap-1261	48	31	,	,	PUNCT
ap-1261	48	32	i	i	NOUN
ap-1261	48	33	=	=	SYM
ap-1261	48	34	εk	εk	PROPN
ap-1261	48	35	,	,	PUNCT
ap-1261	48	36	iεk+i	iεk+i	PROPN
ap-1261	48	37	,	,	PUNCT
ap-1261	48	38	j	j	PROPN
ap-1261	48	39	for	for	ADP
ap-1261	48	40	all	all	DET
ap-1261	48	41	i	i	PROPN
ap-1261	48	42	,	,	PUNCT
ap-1261	48	43	j	j	PROPN
ap-1261	48	44	,	,	PUNCT
ap-1261	48	45	k	k	PROPN
ap-1261	48	46	∈	∈	PROPN
ap-1261	48	47	g	g	PROPN
ap-1261	48	48	,	,	PUNCT
ap-1261	48	49	(	(	PUNCT
ap-1261	48	50	3	3	X
ap-1261	48	51	)	)	PUNCT
ap-1261	48	52	then	then	ADV
ap-1261	48	53	the	the	DET
ap-1261	48	54	vector	vector	NOUN
ap-1261	48	55	space	space	NOUN
ap-1261	48	56	l	l	NOUN
ap-1261	48	57	with	with	ADP
ap-1261	48	58	new	new	ADJ
ap-1261	48	59	brackets	bracket	NOUN
ap-1261	48	60	[	[	X
ap-1261	48	61	x	x	NOUN
ap-1261	48	62	,	,	PUNCT
ap-1261	48	63	y]new	y]new	ADJ
ap-1261	48	64	satisfies	satisfy	VERB
ap-1261	48	65	the	the	DET
ap-1261	48	66	jacobi	jacobi	PROPN
ap-1261	48	67	identities	identity	NOUN
ap-1261	48	68	as	as	ADV
ap-1261	48	69	well	well	ADV
ap-1261	48	70	.	.	PUNCT
ap-1261	49	1	this	this	DET
ap-1261	49	2	new	new	ADJ
ap-1261	49	3	lie	lie	NOUN
ap-1261	49	4	algebra	algebra	NOUN
ap-1261	49	5	will	will	AUX
ap-1261	49	6	be	be	AUX
ap-1261	49	7	denoted	denote	VERB
ap-1261	49	8	by	by	ADP
ap-1261	49	9	lε	lε	PROPN
ap-1261	49	10	.	.	PUNCT
ap-1261	49	11	note	note	VERB
ap-1261	49	12	that	that	SCONJ
ap-1261	49	13	the	the	DET
ap-1261	49	14	equations	equation	NOUN
ap-1261	49	15	(	(	PUNCT
ap-1261	49	16	3	3	X
ap-1261	49	17	)	)	PUNCT
ap-1261	49	18	involve	involve	VERB
ap-1261	49	19	only	only	ADV
ap-1261	49	20	relevant	relevant	ADJ
ap-1261	49	21	parameters	parameter	NOUN
ap-1261	49	22	for	for	ADP
ap-1261	49	23	which	which	PRON
ap-1261	49	24	the	the	DET
ap-1261	49	25	corresponding	correspond	VERB
ap-1261	49	26	commutators	commutator	NOUN
ap-1261	49	27	[	[	X
ap-1261	49	28	lj	lj	PROPN
ap-1261	49	29	,	,	PUNCT
ap-1261	49	30	lk	lk	PROPN
ap-1261	49	31	]	]	X
ap-1261	49	32	do	do	AUX
ap-1261	49	33	not	not	PART
ap-1261	49	34	vanish	vanish	VERB
ap-1261	49	35	.	.	PUNCT
ap-1261	50	1	example	example	NOUN
ap-1261	50	2	1	1	NUM
ap-1261	50	3	z2	z2	NUM
ap-1261	50	4	-	-	PUNCT
ap-1261	50	5	grading	grading	NOUN
ap-1261	50	6	.	.	PUNCT
ap-1261	51	1	the	the	DET
ap-1261	51	2	most	most	ADV
ap-1261	51	3	notorious	notorious	ADJ
ap-1261	51	4	case	case	NOUN
ap-1261	51	5	of	of	ADP
ap-1261	51	6	group	group	NOUN
ap-1261	51	7	grading	grading	NOUN
ap-1261	51	8	is	be	AUX
ap-1261	51	9	z2	z2	NUM
ap-1261	51	10	-	-	PUNCT
ap-1261	51	11	grading.1	grading.1	PROPN
ap-1261	51	12	here	here	ADV
ap-1261	51	13	a	a	DET
ap-1261	51	14	lie	lie	NOUN
ap-1261	51	15	algebra	algebra	NOUN
ap-1261	51	16	l	l	NOUN
ap-1261	51	17	over	over	ADP
ap-1261	51	18	c	c	PROPN
ap-1261	51	19	is	be	AUX
ap-1261	51	20	decomposed	decompose	VERB
ap-1261	51	21	into	into	ADP
ap-1261	51	22	two	two	NUM
ap-1261	51	23	non	non	ADJ
ap-1261	51	24	-	-	ADJ
ap-1261	51	25	zero	zero	ADJ
ap-1261	51	26	grading	grading	NOUN
ap-1261	51	27	subspaces	subspace	NOUN
ap-1261	51	28	l0	l0	PROPN
ap-1261	51	29	and	and	CCONJ
ap-1261	51	30	l1	l1	PROPN
ap-1261	51	31	,	,	PUNCT
ap-1261	51	32	where	where	SCONJ
ap-1261	51	33	0	0	X
ap-1261	52	1	=	=	SYM
ap-1261	53	1	[	[	X
ap-1261	53	2	l0	l0	PROPN
ap-1261	53	3	,	,	PUNCT
ap-1261	53	4	l0	l0	PROPN
ap-1261	53	5	]	]	PUNCT
ap-1261	53	6	⊆	⊆	NUM
ap-1261	53	7	l0	l0	NOUN
ap-1261	53	8	,	,	PUNCT
ap-1261	53	9	0	0	NUM
ap-1261	53	10	=	=	PUNCT
ap-1261	54	1	[	[	X
ap-1261	54	2	l0	l0	PROPN
ap-1261	54	3	,	,	PUNCT
ap-1261	54	4	l1	l1	PROPN
ap-1261	54	5	]	]	PUNCT
ap-1261	54	6	⊆	⊆	NUM
ap-1261	54	7	l1	l1	PROPN
ap-1261	54	8	,	,	PUNCT
ap-1261	54	9	0	0	PUNCT
ap-1261	54	10	=	=	PUNCT
ap-1261	55	1	[	[	X
ap-1261	55	2	l1	l1	PROPN
ap-1261	55	3	,	,	PUNCT
ap-1261	55	4	l1	l1	PROPN
ap-1261	55	5	]	]	PUNCT
ap-1261	55	6	⊆	⊆	NUM
ap-1261	55	7	l0	l0	NOUN
ap-1261	55	8	.	.	PUNCT
ap-1261	56	1	(	(	PUNCT
ap-1261	56	2	4	4	X
ap-1261	56	3	)	)	PUNCT
ap-1261	56	4	here	here	ADV
ap-1261	56	5	we	we	PRON
ap-1261	56	6	have	have	AUX
ap-1261	56	7	applied	apply	VERB
ap-1261	56	8	the	the	DET
ap-1261	56	9	generic	generic	ADJ
ap-1261	56	10	condition	condition	NOUN
ap-1261	56	11	that	that	SCONJ
ap-1261	56	12	in	in	ADP
ap-1261	56	13	each	each	DET
ap-1261	56	14	class	class	NOUN
ap-1261	56	15	of	of	ADP
ap-1261	56	16	commutators	commutator	NOUN
ap-1261	56	17	there	there	PRON
ap-1261	56	18	exists	exist	VERB
ap-1261	56	19	at	at	ADP
ap-1261	56	20	least	least	ADV
ap-1261	56	21	one	one	NUM
ap-1261	56	22	nonvanishing	nonvanishe	VERB
ap-1261	56	23	commutator	commutator	NOUN
ap-1261	56	24	.	.	PUNCT
ap-1261	57	1	for	for	ADP
ap-1261	57	2	a	a	DET
ap-1261	57	3	z2	z2	NOUN
ap-1261	57	4	-	-	PUNCT
ap-1261	57	5	grading	grading	NOUN
ap-1261	57	6	of	of	ADP
ap-1261	57	7	a	a	DET
ap-1261	57	8	lie	lie	NOUN
ap-1261	57	9	algebra	algebra	PROPN
ap-1261	57	10	l	l	NOUN
ap-1261	57	11	,	,	PUNCT
ap-1261	57	12	the	the	DET
ap-1261	57	13	generic	generic	ADJ
ap-1261	57	14	system	system	NOUN
ap-1261	57	15	of	of	ADP
ap-1261	57	16	equations	equation	NOUN
ap-1261	57	17	(	(	PUNCT
ap-1261	57	18	3	3	X
ap-1261	57	19	)	)	PUNCT
ap-1261	57	20	has	have	VERB
ap-1261	57	21	a	a	DET
ap-1261	57	22	very	very	ADV
ap-1261	57	23	simple	simple	ADJ
ap-1261	57	24	form	form	NOUN
ap-1261	57	25	(	(	PUNCT
ap-1261	57	26	ε00	ε00	NOUN
ap-1261	57	27	−	−	PROPN
ap-1261	58	1	ε01)ε01	ε01)ε01	PROPN
ap-1261	58	2	=	=	SYM
ap-1261	58	3	0	0	PUNCT
ap-1261	59	1	=	=	SYM
ap-1261	59	2	(	(	PUNCT
ap-1261	59	3	ε00	ε00	NOUN
ap-1261	59	4	−	−	PROPN
ap-1261	59	5	ε01)ε11	ε01)ε11	PROPN
ap-1261	59	6	,	,	PUNCT
ap-1261	59	7	ε10	ε10	NOUN
ap-1261	59	8	=	=	PUNCT
ap-1261	59	9	ε01	ε01	NOUN
ap-1261	59	10	.	.	PUNCT
ap-1261	60	1	there	there	PRON
ap-1261	60	2	exist	exist	VERB
ap-1261	60	3	infinitely	infinitely	ADV
ap-1261	60	4	many	many	ADJ
ap-1261	60	5	solutions	solution	NOUN
ap-1261	60	6	ε	ε	PROPN
ap-1261	60	7	=	=	SYM
ap-1261	60	8	(	(	PUNCT
ap-1261	60	9	εjk	εjk	NOUN
ap-1261	60	10	)	)	PUNCT
ap-1261	60	11	of	of	ADP
ap-1261	60	12	this	this	DET
ap-1261	60	13	system	system	NOUN
ap-1261	60	14	.	.	PUNCT
ap-1261	61	1	however	however	ADV
ap-1261	61	2	for	for	ADP
ap-1261	61	3	many	many	ADJ
ap-1261	61	4	solutions	solution	NOUN
ap-1261	61	5	,	,	PUNCT
ap-1261	61	6	the	the	DET
ap-1261	61	7	contracted	contract	VERB
ap-1261	61	8	algebras	algebra	NOUN
ap-1261	61	9	lε	lε	AUX
ap-1261	61	10	are	be	AUX
ap-1261	61	11	isomorphic	isomorphic	ADJ
ap-1261	61	12	.	.	PUNCT
ap-1261	62	1	it	it	PRON
ap-1261	62	2	can	can	AUX
ap-1261	62	3	be	be	AUX
ap-1261	62	4	shown	show	VERB
ap-1261	62	5	that	that	SCONJ
ap-1261	62	6	only	only	ADV
ap-1261	62	7	four	four	NUM
ap-1261	62	8	solutions	solution	NOUN
ap-1261	62	9	(	(	PUNCT
ap-1261	62	10	εjk	εjk	NOUN
ap-1261	62	11	)	)	PUNCT
ap-1261	62	12	=	=	PUNCT
ap-1261	62	13	(	(	PUNCT
ap-1261	62	14	1	1	NUM
ap-1261	62	15	1	1	NUM
ap-1261	62	16	1	1	NUM
ap-1261	62	17	0	0	NUM
ap-1261	62	18	)	)	PUNCT
ap-1261	62	19	,	,	PUNCT
ap-1261	62	20	(	(	PUNCT
ap-1261	62	21	1	1	NUM
ap-1261	62	22	0	0	NUM
ap-1261	62	23	0	0	NUM
ap-1261	62	24	0	0	NUM
ap-1261	62	25	)	)	PUNCT
ap-1261	62	26	,	,	PUNCT
ap-1261	62	27	(	(	PUNCT
ap-1261	62	28	0	0	NUM
ap-1261	62	29	0	0	NUM
ap-1261	62	30	0	0	NUM
ap-1261	62	31	1	1	NUM
ap-1261	62	32	)	)	PUNCT
ap-1261	62	33	,	,	PUNCT
ap-1261	62	34	and	and	CCONJ
ap-1261	62	35	(	(	PUNCT
ap-1261	62	36	0	0	NUM
ap-1261	62	37	0	0	NUM
ap-1261	62	38	0	0	NUM
ap-1261	62	39	0	0	NUM
ap-1261	62	40	)	)	PUNCT
ap-1261	62	41	give	give	VERB
ap-1261	62	42	mutually	mutually	ADV
ap-1261	62	43	non	non	ADJ
ap-1261	62	44	-	-	ADJ
ap-1261	62	45	isomorphic	isomorphic	ADJ
ap-1261	62	46	lie	lie	NOUN
ap-1261	62	47	algebras	algebra	NOUN
ap-1261	62	48	lε	lε	X
ap-1261	62	49	over	over	ADP
ap-1261	62	50	c.	c.	PROPN
ap-1261	62	51	(	(	PUNCT
ap-1261	62	52	the	the	DET
ap-1261	62	53	original	original	ADJ
ap-1261	62	54	lie	lie	NOUN
ap-1261	62	55	algebra	algebra	NOUN
ap-1261	62	56	is	be	AUX
ap-1261	62	57	obtained	obtain	VERB
ap-1261	62	58	with	with	ADP
ap-1261	62	59	all	all	DET
ap-1261	62	60	parameters	parameter	NOUN
ap-1261	62	61	εij	εij	VERB
ap-1261	62	62	=	=	NOUN
ap-1261	62	63	1	1	NUM
ap-1261	62	64	.	.	PUNCT
ap-1261	62	65	)	)	PUNCT
ap-1261	63	1	the	the	DET
ap-1261	63	2	contracted	contract	VERB
ap-1261	63	3	algebra	algebra	NOUN
ap-1261	63	4	obtained	obtain	VERB
ap-1261	63	5	by	by	ADP
ap-1261	63	6	the	the	DET
ap-1261	63	7	first	first	ADJ
ap-1261	63	8	solution	solution	NOUN
ap-1261	63	9	is	be	AUX
ap-1261	63	10	the	the	DET
ap-1261	63	11	semidirect	semidirect	ADJ
ap-1261	63	12	sum	sum	NOUN
ap-1261	63	13	of	of	ADP
ap-1261	63	14	l0	l0	PROPN
ap-1261	63	15	with	with	ADP
ap-1261	63	16	a	a	DET
ap-1261	63	17	commutative	commutative	ADJ
ap-1261	63	18	algebra	algebra	NOUN
ap-1261	63	19	l1	l1	PROPN
ap-1261	63	20	and	and	CCONJ
ap-1261	63	21	corresponds	correspond	VERB
ap-1261	63	22	to	to	ADP
ap-1261	63	23	the	the	DET
ap-1261	63	24	inönü-wigner	inönü-wign	ADJ
ap-1261	63	25	contraction	contraction	NOUN
ap-1261	63	26	.	.	PUNCT
ap-1261	64	1	the	the	DET
ap-1261	64	2	second	second	ADJ
ap-1261	64	3	solution	solution	NOUN
ap-1261	64	4	is	be	AUX
ap-1261	64	5	the	the	DET
ap-1261	64	6	direct	direct	ADJ
ap-1261	64	7	sum	sum	NOUN
ap-1261	64	8	of	of	ADP
ap-1261	64	9	l0	l0	PROPN
ap-1261	64	10	and	and	CCONJ
ap-1261	64	11	the	the	DET
ap-1261	64	12	commutative	commutative	ADJ
ap-1261	64	13	algebra	algebra	PROPN
ap-1261	64	14	l1	l1	PROPN
ap-1261	64	15	.	.	PUNCT
ap-1261	65	1	the	the	DET
ap-1261	65	2	third	third	ADJ
ap-1261	65	3	solution	solution	NOUN
ap-1261	65	4	corresponds	correspond	VERB
ap-1261	65	5	to	to	ADP
ap-1261	65	6	the	the	DET
ap-1261	65	7	central	central	ADJ
ap-1261	65	8	extension	extension	NOUN
ap-1261	65	9	of	of	ADP
ap-1261	65	10	l1	l1	PROPN
ap-1261	65	11	(	(	PUNCT
ap-1261	65	12	considered	consider	VERB
ap-1261	65	13	as	as	ADP
ap-1261	65	14	a	a	DET
ap-1261	65	15	commutative	commutative	ADJ
ap-1261	65	16	algebra	algebra	NOUN
ap-1261	65	17	)	)	PUNCT
ap-1261	65	18	by	by	ADP
ap-1261	65	19	the	the	DET
ap-1261	65	20	commutative	commutative	ADJ
ap-1261	65	21	algebra	algebra	PROPN
ap-1261	65	22	l0	l0	PROPN
ap-1261	65	23	.	.	PUNCT
ap-1261	66	1	the	the	DET
ap-1261	66	2	fourth	fourth	ADJ
ap-1261	66	3	solution	solution	NOUN
ap-1261	66	4	is	be	AUX
ap-1261	66	5	an	an	DET
ap-1261	66	6	abelian	abelian	ADJ
ap-1261	66	7	lie	lie	NOUN
ap-1261	66	8	algebra	algebra	NOUN
ap-1261	66	9	.	.	PUNCT
ap-1261	67	1	1note	1note	NUM
ap-1261	67	2	that	that	PRON
ap-1261	67	3	special	special	ADJ
ap-1261	67	4	z2	z2	NOUN
ap-1261	67	5	-	-	PUNCT
ap-1261	67	6	graded	grade	VERB
ap-1261	67	7	contractions	contraction	NOUN
ap-1261	67	8	are	be	AUX
ap-1261	67	9	closely	closely	ADV
ap-1261	67	10	related	relate	VERB
ap-1261	67	11	to	to	ADP
ap-1261	67	12	inönü–wigner	inönü–wigner	NOUN
ap-1261	67	13	contractions	contraction	NOUN
ap-1261	67	14	[	[	X
ap-1261	67	15	12	12	NUM
ap-1261	67	16	]	]	PUNCT
ap-1261	67	17	.	.	PUNCT
ap-1261	68	1	31	31	NUM
ap-1261	68	2	acta	acta	PROPN
ap-1261	68	3	polytechnica	polytechnica	PROPN
ap-1261	68	4	vol	vol	NOUN
ap-1261	68	5	.	.	PROPN
ap-1261	69	1	50	50	NUM
ap-1261	69	2	no	no	NOUN
ap-1261	69	3	.	.	PUNCT
ap-1261	70	1	5/2010	5/2010	NUM
ap-1261	70	2	2.2	2.2	NUM
ap-1261	70	3	representations	representation	NOUN
ap-1261	70	4	of	of	ADP
ap-1261	70	5	graded	grade	VERB
ap-1261	70	6	contractions	contraction	NOUN
ap-1261	70	7	let	let	VERB
ap-1261	70	8	us	we	PRON
ap-1261	70	9	focus	focus	VERB
ap-1261	70	10	on	on	ADP
ap-1261	70	11	the	the	DET
ap-1261	70	12	question	question	NOUN
ap-1261	70	13	of	of	ADP
ap-1261	70	14	a	a	DET
ap-1261	70	15	representation	representation	NOUN
ap-1261	70	16	of	of	ADP
ap-1261	70	17	the	the	DET
ap-1261	70	18	contracted	contract	VERB
ap-1261	70	19	lie	lie	NOUN
ap-1261	70	20	algebra	algebra	NOUN
ap-1261	70	21	lε	lε	VERB
ap-1261	70	22	.	.	PUNCT
ap-1261	71	1	we	we	PRON
ap-1261	71	2	will	will	AUX
ap-1261	71	3	reformulate	reformulate	VERB
ap-1261	71	4	the	the	DET
ap-1261	71	5	method	method	NOUN
ap-1261	71	6	proposed	propose	VERB
ap-1261	71	7	in	in	ADP
ap-1261	71	8	[	[	X
ap-1261	71	9	13	13	NUM
ap-1261	71	10	]	]	PUNCT
ap-1261	71	11	,	,	PUNCT
ap-1261	71	12	which	which	PRON
ap-1261	71	13	enables	enable	VERB
ap-1261	71	14	us	we	PRON
ap-1261	71	15	to	to	PART
ap-1261	71	16	find	find	VERB
ap-1261	71	17	a	a	DET
ap-1261	71	18	representation	representation	NOUN
ap-1261	71	19	of	of	ADP
ap-1261	71	20	lε	lε	INTJ
ap-1261	71	21	by	by	ADP
ap-1261	71	22	modifying	modify	VERB
ap-1261	71	23	a	a	DET
ap-1261	71	24	given	give	VERB
ap-1261	71	25	representation	representation	NOUN
ap-1261	71	26	of	of	ADP
ap-1261	71	27	the	the	DET
ap-1261	71	28	original	original	ADJ
ap-1261	71	29	algebra	algebra	NOUN
ap-1261	71	30	l.	l.	NOUN
ap-1261	71	31	it	it	PRON
ap-1261	71	32	involves	involve	VERB
ap-1261	71	33	a	a	DET
ap-1261	71	34	simultaneous	simultaneous	ADJ
ap-1261	71	35	grading	grading	NOUN
ap-1261	71	36	of	of	ADP
ap-1261	71	37	the	the	DET
ap-1261	71	38	lie	lie	NOUN
ap-1261	71	39	algebra	algebra	PROPN
ap-1261	71	40	l	l	NOUN
ap-1261	71	41	and	and	CCONJ
ap-1261	71	42	the	the	DET
ap-1261	71	43	representation	representation	NOUN
ap-1261	71	44	space	space	NOUN
ap-1261	71	45	v	v	NOUN
ap-1261	71	46	.	.	PUNCT
ap-1261	72	1	definition	definition	NOUN
ap-1261	72	2	2.1	2.1	NUM
ap-1261	72	3	let	let	VERB
ap-1261	72	4	r	r	NOUN
ap-1261	72	5	:	:	PUNCT
ap-1261	72	6	l	l	NOUN
ap-1261	72	7	�	�	PROPN
ap-1261	72	8	→	→	SYM
ap-1261	72	9	endv	endv	PROPN
ap-1261	72	10	be	be	AUX
ap-1261	72	11	a	a	DET
ap-1261	72	12	representation	representation	NOUN
ap-1261	72	13	of	of	ADP
ap-1261	72	14	lie	lie	NOUN
ap-1261	72	15	algebra	algebra	NOUN
ap-1261	72	16	l	l	NOUN
ap-1261	72	17	and	and	CCONJ
ap-1261	72	18	let	let	VERB
ap-1261	72	19	γ	γ	NOUN
ap-1261	72	20	:	:	PUNCT
ap-1261	72	21	l	l	NOUN
ap-1261	72	22	=	=	PUNCT
ap-1261	72	23	⊕i∈gli	⊕i∈gli	NOUN
ap-1261	72	24	be	be	AUX
ap-1261	72	25	its	its	PRON
ap-1261	72	26	g	g	NOUN
ap-1261	72	27	-	-	PUNCT
ap-1261	72	28	grading	grade	VERB
ap-1261	72	29	.	.	PUNCT
ap-1261	73	1	we	we	PRON
ap-1261	73	2	say	say	VERB
ap-1261	73	3	that	that	SCONJ
ap-1261	73	4	the	the	DET
ap-1261	73	5	representation	representation	NOUN
ap-1261	73	6	r	r	NOUN
ap-1261	73	7	is	be	AUX
ap-1261	73	8	compatible	compatible	ADJ
ap-1261	73	9	with	with	ADP
ap-1261	73	10	the	the	DET
ap-1261	73	11	g	g	NOUN
ap-1261	73	12	-	-	PUNCT
ap-1261	73	13	grading	grade	VERB
ap-1261	73	14	,	,	PUNCT
ap-1261	73	15	if	if	SCONJ
ap-1261	73	16	there	there	PRON
ap-1261	73	17	exists	exist	VERB
ap-1261	73	18	a	a	DET
ap-1261	73	19	decomposition	decomposition	NOUN
ap-1261	73	20	of	of	ADP
ap-1261	73	21	the	the	DET
ap-1261	73	22	vector	vector	NOUN
ap-1261	73	23	space	space	NOUN
ap-1261	73	24	v	v	NOUN
ap-1261	73	25	into	into	ADP
ap-1261	73	26	a	a	DET
ap-1261	73	27	direct	direct	ADJ
ap-1261	73	28	sum	sum	NOUN
ap-1261	73	29	v	v	ADP
ap-1261	73	30	=	=	SYM
ap-1261	73	31	⊕i∈gvi	⊕i∈gvi	INTJ
ap-1261	73	32	such	such	ADJ
ap-1261	73	33	that	that	DET
ap-1261	73	34	r(xi)vj	r(xi)vj	NOUN
ap-1261	73	35	⊂	⊂	PUNCT
ap-1261	73	36	vi+j	vi+j	PROPN
ap-1261	73	37	for	for	ADP
ap-1261	73	38	each	each	DET
ap-1261	73	39	i	i	PROPN
ap-1261	73	40	,	,	PUNCT
ap-1261	73	41	j	j	PROPN
ap-1261	73	42	∈	∈	PROPN
ap-1261	73	43	g	g	PROPN
ap-1261	73	44	and	and	CCONJ
ap-1261	73	45	any	any	DET
ap-1261	73	46	xi	xi	ADP
ap-1261	73	47	∈	∈	PROPN
ap-1261	73	48	li	li	PROPN
ap-1261	73	49	.	.	PUNCT
ap-1261	74	1	(	(	PUNCT
ap-1261	74	2	5	5	X
ap-1261	74	3	)	)	PUNCT
ap-1261	74	4	remark	remark	NOUN
ap-1261	74	5	2.2	2.2	NUM
ap-1261	74	6	let	let	VERB
ap-1261	74	7	r	r	PRON
ap-1261	74	8	be	be	AUX
ap-1261	74	9	a	a	DET
ap-1261	74	10	representation	representation	NOUN
ap-1261	74	11	of	of	ADP
ap-1261	74	12	l	l	NOUN
ap-1261	74	13	compatible	compatible	ADJ
ap-1261	74	14	with	with	ADP
ap-1261	74	15	the	the	DET
ap-1261	74	16	grading	grade	VERB
ap-1261	74	17	l	l	NOUN
ap-1261	75	1	=	=	PUNCT
ap-1261	75	2	⊕i∈gli	⊕i∈gli	NOUN
ap-1261	75	3	and	and	CCONJ
ap-1261	75	4	h	h	NOUN
ap-1261	75	5	∈	∈	PROPN
ap-1261	75	6	aut	aut	PROPN
ap-1261	75	7	l	l	NOUN
ap-1261	75	8	be	be	AUX
ap-1261	75	9	any	any	DET
ap-1261	75	10	automorphism	automorphism	NOUN
ap-1261	75	11	of	of	ADP
ap-1261	75	12	l.	l.	PROPN
ap-1261	75	13	then	then	ADV
ap-1261	75	14	r	r	VERB
ap-1261	75	15	◦	◦	NOUN
ap-1261	75	16	h−1	h−1	PROPN
ap-1261	75	17	is	be	AUX
ap-1261	75	18	a	a	DET
ap-1261	75	19	representation	representation	NOUN
ap-1261	75	20	of	of	ADP
ap-1261	75	21	l	l	NOUN
ap-1261	75	22	compatible	compatible	ADJ
ap-1261	75	23	with	with	ADP
ap-1261	75	24	the	the	DET
ap-1261	75	25	equivalent	equivalent	ADJ
ap-1261	75	26	grading	grade	VERB
ap-1261	75	27	l	l	NOUN
ap-1261	75	28	=	=	SYM
ap-1261	75	29	⊕i∈gh(li	⊕i∈gh(li	NOUN
ap-1261	75	30	)	)	PUNCT
ap-1261	75	31	,	,	PUNCT
ap-1261	75	32	since	since	SCONJ
ap-1261	75	33	(	(	PUNCT
ap-1261	75	34	r	r	NOUN
ap-1261	75	35	◦	◦	NOUN
ap-1261	75	36	h−1)h(xi)vj	h−1)h(xi)vj	NOUN
ap-1261	75	37	=	=	SYM
ap-1261	75	38	r(xi)vj	r(xi)vj	NOUN
ap-1261	75	39	⊂	⊂	PROPN
ap-1261	75	40	vi+j	vi+j	PROPN
ap-1261	75	41	.	.	PUNCT
ap-1261	76	1	suppose	suppose	VERB
ap-1261	76	2	we	we	PRON
ap-1261	76	3	are	be	AUX
ap-1261	76	4	given	give	VERB
ap-1261	76	5	a	a	DET
ap-1261	76	6	representation	representation	NOUN
ap-1261	76	7	r	r	NOUN
ap-1261	76	8	of	of	ADP
ap-1261	76	9	l	l	NOUN
ap-1261	76	10	compatible	compatible	ADJ
ap-1261	76	11	with	with	ADP
ap-1261	76	12	the	the	DET
ap-1261	76	13	g	g	NOUN
ap-1261	76	14	-	-	PUNCT
ap-1261	76	15	grading	grade	VERB
ap-1261	76	16	.	.	PUNCT
ap-1261	77	1	we	we	PRON
ap-1261	77	2	are	be	AUX
ap-1261	77	3	looking	look	VERB
ap-1261	77	4	for	for	ADP
ap-1261	77	5	a	a	DET
ap-1261	77	6	representation	representation	NOUN
ap-1261	77	7	rε	rε	X
ap-1261	77	8	of	of	ADP
ap-1261	77	9	a	a	DET
ap-1261	77	10	contracted	contract	VERB
ap-1261	77	11	lie	lie	NOUN
ap-1261	77	12	algebra	algebra	NOUN
ap-1261	77	13	lε	lε	AUX
ap-1261	77	14	.	.	PUNCT
ap-1261	78	1	according	accord	VERB
ap-1261	78	2	to	to	ADP
ap-1261	78	3	[	[	X
ap-1261	78	4	13	13	NUM
ap-1261	78	5	]	]	PUNCT
ap-1261	78	6	we	we	PRON
ap-1261	78	7	define	define	VERB
ap-1261	78	8	rε(xi)vj	rε(xi)vj	NOUN
ap-1261	78	9	:	:	PUNCT
ap-1261	78	10	=	=	SYM
ap-1261	78	11	ψi	ψi	PROPN
ap-1261	78	12	,	,	PUNCT
ap-1261	78	13	j	j	PROPN
ap-1261	78	14	r(xi)vj	r(xi)vj	NOUN
ap-1261	78	15	(	(	PUNCT
ap-1261	78	16	for	for	ADP
ap-1261	78	17	each	each	DET
ap-1261	78	18	i	i	PROPN
ap-1261	78	19	,	,	PUNCT
ap-1261	78	20	j	j	PROPN
ap-1261	78	21	∈	∈	PROPN
ap-1261	78	22	g	g	PROPN
ap-1261	78	23	,	,	PUNCT
ap-1261	78	24	any	any	DET
ap-1261	78	25	xi	xi	PROPN
ap-1261	78	26	∈	∈	PROPN
ap-1261	78	27	li	li	PROPN
ap-1261	78	28	and	and	CCONJ
ap-1261	78	29	any	any	DET
ap-1261	78	30	vj	vj	PROPN
ap-1261	78	31	∈	∈	PROPN
ap-1261	78	32	vj	vj	PROPN
ap-1261	78	33	)	)	PUNCT
ap-1261	78	34	,	,	PUNCT
ap-1261	78	35	(	(	PUNCT
ap-1261	78	36	6	6	NUM
ap-1261	78	37	)	)	PUNCT
ap-1261	78	38	where	where	SCONJ
ap-1261	78	39	ψi	ψi	NOUN
ap-1261	78	40	,	,	PUNCT
ap-1261	78	41	j	j	PROPN
ap-1261	78	42	are	be	AUX
ap-1261	78	43	unknown	unknown	ADJ
ap-1261	78	44	parameters	parameter	NOUN
ap-1261	78	45	.	.	PUNCT
ap-1261	79	1	the	the	DET
ap-1261	79	2	requirement	requirement	NOUN
ap-1261	79	3	that	that	SCONJ
ap-1261	79	4	rε	rε	PROPN
ap-1261	79	5	is	be	AUX
ap-1261	79	6	a	a	DET
ap-1261	79	7	representation	representation	NOUN
ap-1261	79	8	of	of	ADP
ap-1261	79	9	lε	lε	PART
ap-1261	79	10	formally	formally	ADV
ap-1261	79	11	means	mean	VERB
ap-1261	79	12	rε	rε	X
ap-1261	79	13	(	(	PUNCT
ap-1261	79	14	[	[	X
ap-1261	79	15	xi	xi	X
ap-1261	79	16	,	,	PUNCT
ap-1261	79	17	xj	xj	PROPN
ap-1261	79	18	]	]	PUNCT
ap-1261	79	19	new	new	ADJ
ap-1261	79	20	)	)	PUNCT
ap-1261	79	21	vk	vk	NOUN
ap-1261	79	22	=	=	PUNCT
ap-1261	80	1	[	[	X
ap-1261	80	2	rε(xi	rε(xi	NOUN
ap-1261	80	3	)	)	PUNCT
ap-1261	80	4	,	,	PUNCT
ap-1261	80	5	rε(xj)]vk	rε(xj)]vk	X
ap-1261	80	6	=	=	SYM
ap-1261	80	7	(	(	PUNCT
ap-1261	80	8	rε(xi)rε(xj)−	rε(xi)rε(xj)−	PROPN
ap-1261	80	9	rε(xj)rε(xi	rε(xj)rε(xi	NOUN
ap-1261	80	10	)	)	PUNCT
ap-1261	80	11	)	)	PUNCT
ap-1261	81	1	vk	vk	VERB
ap-1261	81	2	for	for	ADP
ap-1261	81	3	any	any	DET
ap-1261	81	4	xi	xi	ADP
ap-1261	81	5	∈	∈	PROPN
ap-1261	81	6	li	li	PROPN
ap-1261	81	7	,	,	PUNCT
ap-1261	81	8	xj	xj	PROPN
ap-1261	81	9	∈	∈	PROPN
ap-1261	81	10	lj	lj	ADV
ap-1261	81	11	,	,	PUNCT
ap-1261	81	12	and	and	CCONJ
ap-1261	81	13	vk	vk	ADP
ap-1261	81	14	∈	∈	PROPN
ap-1261	81	15	vk	vk	NOUN
ap-1261	81	16	.	.	PUNCT
ap-1261	82	1	using	use	VERB
ap-1261	82	2	equations	equation	NOUN
ap-1261	82	3	(	(	PUNCT
ap-1261	82	4	2	2	NUM
ap-1261	82	5	)	)	PUNCT
ap-1261	82	6	and	and	CCONJ
ap-1261	82	7	(	(	PUNCT
ap-1261	82	8	6	6	NUM
ap-1261	82	9	)	)	PUNCT
ap-1261	82	10	and	and	CCONJ
ap-1261	82	11	relation	relation	NOUN
ap-1261	82	12	(	(	PUNCT
ap-1261	82	13	5	5	NUM
ap-1261	82	14	)	)	PUNCT
ap-1261	82	15	we	we	PRON
ap-1261	82	16	obtain	obtain	VERB
ap-1261	82	17	ψj	ψj	ADP
ap-1261	82	18	,	,	PUNCT
ap-1261	82	19	kψi	kψi	PROPN
ap-1261	82	20	,	,	PUNCT
ap-1261	82	21	j+kr(xi)r(xj)−	j+kr(xi)r(xj)−	PROPN
ap-1261	82	22	ψi	ψi	NOUN
ap-1261	82	23	,	,	PUNCT
ap-1261	82	24	kψj	kψj	PROPN
ap-1261	82	25	,	,	PUNCT
ap-1261	82	26	i+kr(xj)r(xi	i+kr(xj)r(xi	X
ap-1261	82	27	)	)	PUNCT
ap-1261	82	28	=	=	SYM
ap-1261	83	1	εi	εi	VERB
ap-1261	83	2	,	,	PUNCT
ap-1261	83	3	jψi+j	jψi+j	PROPN
ap-1261	83	4	,	,	PUNCT
ap-1261	83	5	kr([xi	kr([xi	PROPN
ap-1261	83	6	,	,	PUNCT
ap-1261	83	7	xj	xj	PROPN
ap-1261	83	8	]	]	X
ap-1261	83	9	)	)	PUNCT
ap-1261	83	10	since	since	SCONJ
ap-1261	83	11	r	r	NOUN
ap-1261	83	12	is	be	AUX
ap-1261	83	13	a	a	DET
ap-1261	83	14	representation	representation	NOUN
ap-1261	83	15	of	of	ADP
ap-1261	83	16	l	l	NOUN
ap-1261	83	17	,	,	PUNCT
ap-1261	83	18	we	we	PRON
ap-1261	83	19	know	know	VERB
ap-1261	83	20	that	that	DET
ap-1261	83	21	r(xi)r(xj)−	r(xi)r(xj)−	NOUN
ap-1261	84	1	r(xj)r(xi	r(xj)r(xi	ADJ
ap-1261	84	2	)	)	PUNCT
ap-1261	85	1	=	=	SYM
ap-1261	85	2	r([xi	r([xi	NOUN
ap-1261	85	3	,	,	PUNCT
ap-1261	85	4	xj	xj	PROPN
ap-1261	85	5	]	]	PUNCT
ap-1261	85	6	)	)	PUNCT
ap-1261	85	7	.	.	PUNCT
ap-1261	86	1	therefore	therefore	ADV
ap-1261	86	2	,	,	PUNCT
ap-1261	86	3	the	the	DET
ap-1261	86	4	choice	choice	NOUN
ap-1261	86	5	of	of	ADP
ap-1261	86	6	parameters	parameter	NOUN
ap-1261	86	7	ψi	ψi	ADP
ap-1261	86	8	,	,	PUNCT
ap-1261	86	9	j	j	PROPN
ap-1261	86	10	satisfying	satisfy	VERB
ap-1261	86	11	the	the	DET
ap-1261	86	12	second	second	ADJ
ap-1261	86	13	basic	basic	ADJ
ap-1261	86	14	set	set	NOUN
ap-1261	86	15	of	of	ADP
ap-1261	86	16	contraction	contraction	NOUN
ap-1261	86	17	equations	equation	NOUN
ap-1261	86	18	[	[	X
ap-1261	86	19	14	14	NUM
ap-1261	86	20	]	]	PUNCT
ap-1261	86	21	ψj	ψj	ADP
ap-1261	86	22	,	,	PUNCT
ap-1261	86	23	kψi	kψi	PROPN
ap-1261	86	24	,	,	PUNCT
ap-1261	86	25	j+k	j+k	ADJ
ap-1261	86	26	=	=	SYM
ap-1261	86	27	ψi	ψi	NOUN
ap-1261	86	28	,	,	PUNCT
ap-1261	86	29	kψj	kψj	PROPN
ap-1261	86	30	,	,	PUNCT
ap-1261	86	31	i+k	i+k	PUNCT
ap-1261	86	32	=	=	SYM
ap-1261	86	33	εi	εi	NOUN
ap-1261	86	34	,	,	PUNCT
ap-1261	86	35	jψi+j	jψi+j	PROPN
ap-1261	86	36	,	,	PUNCT
ap-1261	86	37	k	k	X
ap-1261	86	38	(	(	PUNCT
ap-1261	86	39	7	7	NUM
ap-1261	86	40	)	)	PUNCT
ap-1261	86	41	implies	imply	VERB
ap-1261	86	42	that	that	SCONJ
ap-1261	86	43	rε	rε	PRON
ap-1261	86	44	defined	define	VERB
ap-1261	86	45	by	by	ADP
ap-1261	86	46	(	(	PUNCT
ap-1261	86	47	6	6	NUM
ap-1261	86	48	)	)	PUNCT
ap-1261	86	49	is	be	AUX
ap-1261	86	50	a	a	DET
ap-1261	86	51	representation	representation	NOUN
ap-1261	86	52	of	of	ADP
ap-1261	86	53	the	the	DET
ap-1261	86	54	contracted	contract	VERB
ap-1261	86	55	lie	lie	NOUN
ap-1261	86	56	algebra	algebra	NOUN
ap-1261	87	1	lε	lε	PROPN
ap-1261	87	2	.	.	PUNCT
ap-1261	87	3	solutions	solution	NOUN
ap-1261	87	4	of	of	ADP
ap-1261	87	5	(	(	PUNCT
ap-1261	87	6	7	7	X
ap-1261	87	7	)	)	PUNCT
ap-1261	87	8	determine	determine	VERB
ap-1261	87	9	the	the	DET
ap-1261	87	10	contractions	contraction	NOUN
ap-1261	87	11	of	of	ADP
ap-1261	87	12	the	the	DET
ap-1261	87	13	chosen	choose	VERB
ap-1261	87	14	representations	representation	NOUN
ap-1261	87	15	.	.	PUNCT
ap-1261	88	1	let	let	VERB
ap-1261	88	2	us	we	PRON
ap-1261	88	3	stress	stress	VERB
ap-1261	88	4	that	that	SCONJ
ap-1261	88	5	,	,	PUNCT
ap-1261	88	6	if	if	SCONJ
ap-1261	88	7	r([xi	r([xi	PROPN
ap-1261	88	8	,	,	PUNCT
ap-1261	88	9	xj	xj	PROPN
ap-1261	88	10	]	]	X
ap-1261	88	11	=	=	SYM
ap-1261	88	12	0	0	NUM
ap-1261	88	13	for	for	SCONJ
ap-1261	88	14	all	all	PRON
ap-1261	88	15	xi	xi	ADP
ap-1261	88	16	∈	∈	PROPN
ap-1261	88	17	li	li	PROPN
ap-1261	88	18	,	,	PUNCT
ap-1261	88	19	xj	xj	PROPN
ap-1261	88	20	∈	∈	PROPN
ap-1261	88	21	lj	lj	PROPN
ap-1261	88	22	,	,	PUNCT
ap-1261	88	23	conditions	condition	NOUN
ap-1261	88	24	(	(	PUNCT
ap-1261	88	25	7	7	X
ap-1261	88	26	)	)	PUNCT
ap-1261	88	27	are	be	AUX
ap-1261	88	28	not	not	PART
ap-1261	88	29	necessary	necessary	ADJ
ap-1261	88	30	.	.	PUNCT
ap-1261	89	1	comparing	compare	VERB
ap-1261	89	2	(	(	PUNCT
ap-1261	89	3	7	7	NUM
ap-1261	89	4	)	)	PUNCT
ap-1261	89	5	and	and	CCONJ
ap-1261	89	6	(	(	PUNCT
ap-1261	89	7	3	3	X
ap-1261	89	8	)	)	PUNCT
ap-1261	89	9	we	we	PRON
ap-1261	89	10	see	see	VERB
ap-1261	89	11	that	that	SCONJ
ap-1261	89	12	the	the	DET
ap-1261	89	13	system	system	NOUN
ap-1261	89	14	of	of	ADP
ap-1261	89	15	quadratic	quadratic	ADJ
ap-1261	89	16	equations	equation	NOUN
ap-1261	89	17	for	for	ADP
ap-1261	89	18	parameters	parameter	NOUN
ap-1261	89	19	ψi	ψi	ADP
ap-1261	89	20	,	,	PUNCT
ap-1261	89	21	j	j	PROPN
ap-1261	89	22	has	have	VERB
ap-1261	89	23	at	at	ADV
ap-1261	89	24	least	least	ADV
ap-1261	89	25	one	one	NUM
ap-1261	89	26	solution	solution	NOUN
ap-1261	89	27	,	,	PUNCT
ap-1261	89	28	namely	namely	ADV
ap-1261	89	29	ψi	ψi	NOUN
ap-1261	89	30	,	,	PUNCT
ap-1261	89	31	j	j	PROPN
ap-1261	90	1	=	=	SYM
ap-1261	90	2	εi	εi	PROPN
ap-1261	90	3	,	,	PUNCT
ap-1261	90	4	j	j	PROPN
ap-1261	90	5	for	for	ADP
ap-1261	90	6	each	each	DET
ap-1261	90	7	pair	pair	NOUN
ap-1261	91	1	i	i	PRON
ap-1261	91	2	,	,	PUNCT
ap-1261	91	3	j	j	PROPN
ap-1261	91	4	(	(	PUNCT
ap-1261	91	5	adjoint	adjoint	PROPN
ap-1261	91	6	representation	representation	NOUN
ap-1261	91	7	of	of	ADP
ap-1261	91	8	lε	lε	PROPN
ap-1261	91	9	)	)	PUNCT
ap-1261	91	10	.	.	PUNCT
ap-1261	92	1	therefore	therefore	ADV
ap-1261	92	2	the	the	DET
ap-1261	92	3	mapping	mapping	NOUN
ap-1261	92	4	rε	rε	X
ap-1261	92	5	:	:	PUNCT
ap-1261	92	6	lε	lε	PROPN
ap-1261	92	7	�	�	PROPN
ap-1261	92	8	→	→	SYM
ap-1261	92	9	endv	endv	PROPN
ap-1261	92	10	defined	define	VERB
ap-1261	92	11	by	by	ADP
ap-1261	92	12	(	(	PUNCT
ap-1261	92	13	6	6	NUM
ap-1261	92	14	)	)	PUNCT
ap-1261	92	15	is	be	AUX
ap-1261	92	16	a	a	DET
ap-1261	92	17	representation	representation	NOUN
ap-1261	92	18	of	of	ADP
ap-1261	92	19	the	the	DET
ap-1261	92	20	graded	grade	VERB
ap-1261	92	21	lie	lie	NOUN
ap-1261	92	22	algebra	algebra	NOUN
ap-1261	92	23	lε	lε	AUX
ap-1261	92	24	.	.	PUNCT
ap-1261	93	1	usually	usually	ADV
ap-1261	93	2	,	,	PUNCT
ap-1261	93	3	there	there	PRON
ap-1261	93	4	also	also	ADV
ap-1261	93	5	exist	exist	VERB
ap-1261	93	6	other	other	ADJ
ap-1261	93	7	solutions	solution	NOUN
ap-1261	93	8	of	of	ADP
ap-1261	93	9	the	the	DET
ap-1261	93	10	system	system	NOUN
ap-1261	93	11	(	(	PUNCT
ap-1261	93	12	7	7	NUM
ap-1261	93	13	)	)	PUNCT
ap-1261	93	14	,	,	PUNCT
ap-1261	93	15	and	and	CCONJ
ap-1261	93	16	therefore	therefore	ADV
ap-1261	93	17	more	more	ADJ
ap-1261	93	18	representations	representation	NOUN
ap-1261	93	19	of	of	ADP
ap-1261	93	20	the	the	DET
ap-1261	93	21	same	same	ADJ
ap-1261	93	22	contracted	contract	VERB
ap-1261	93	23	algebra	algebra	NOUN
ap-1261	94	1	lε	lε	PROPN
ap-1261	94	2	.	.	PROPN
ap-1261	94	3	example	example	NOUN
ap-1261	94	4	2	2	NUM
ap-1261	94	5	z2	z2	NUM
ap-1261	94	6	-	-	PUNCT
ap-1261	94	7	graded	grade	VERB
ap-1261	94	8	representation	representation	NOUN
ap-1261	94	9	.	.	PUNCT
ap-1261	95	1	consider	consider	VERB
ap-1261	95	2	a	a	DET
ap-1261	95	3	z2	z2	NOUN
ap-1261	95	4	-	-	PUNCT
ap-1261	95	5	grading	grading	NOUN
ap-1261	95	6	of	of	ADP
ap-1261	95	7	a	a	DET
ap-1261	95	8	lie	lie	NOUN
ap-1261	95	9	algebra	algebra	NOUN
ap-1261	95	10	l	l	NOUN
ap-1261	95	11	and	and	CCONJ
ap-1261	95	12	its	its	PRON
ap-1261	95	13	representation	representation	NOUN
ap-1261	95	14	r	r	NOUN
ap-1261	95	15	which	which	PRON
ap-1261	95	16	is	be	AUX
ap-1261	95	17	compatible	compatible	ADJ
ap-1261	95	18	with	with	ADP
ap-1261	95	19	the	the	DET
ap-1261	95	20	grading	grading	NOUN
ap-1261	95	21	.	.	PUNCT
ap-1261	96	1	for	for	ADP
ap-1261	96	2	the	the	DET
ap-1261	96	3	corresponding	corresponding	ADJ
ap-1261	96	4	decomposition	decomposition	NOUN
ap-1261	96	5	of	of	ADP
ap-1261	96	6	the	the	DET
ap-1261	96	7	vector	vector	NOUN
ap-1261	96	8	space	space	NOUN
ap-1261	96	9	v	v	NOUN
ap-1261	96	10	=	=	SYM
ap-1261	96	11	v0⊕	v0⊕	X
ap-1261	96	12	v1	v1	NOUN
ap-1261	96	13	we	we	PRON
ap-1261	96	14	may	may	AUX
ap-1261	96	15	construct	construct	VERB
ap-1261	96	16	a	a	DET
ap-1261	96	17	basis	basis	NOUN
ap-1261	96	18	b	b	NOUN
ap-1261	96	19	of	of	ADP
ap-1261	96	20	v	v	NUM
ap-1261	96	21	composed	compose	VERB
ap-1261	96	22	of	of	ADP
ap-1261	96	23	the	the	DET
ap-1261	96	24	basis	basis	NOUN
ap-1261	96	25	of	of	ADP
ap-1261	96	26	v0	v0	NOUN
ap-1261	96	27	and	and	CCONJ
ap-1261	96	28	the	the	DET
ap-1261	96	29	basis	basis	NOUN
ap-1261	96	30	of	of	ADP
ap-1261	96	31	v1	v1	NOUN
ap-1261	96	32	.	.	PUNCT
ap-1261	97	1	in	in	ADP
ap-1261	97	2	such	such	DET
ap-1261	97	3	a	a	DET
ap-1261	97	4	basis	basis	NOUN
ap-1261	97	5	b	b	NOUN
ap-1261	97	6	,	,	PUNCT
ap-1261	97	7	the	the	DET
ap-1261	97	8	grading	grade	VERB
ap-1261	97	9	relations	relation	NOUN
ap-1261	97	10	(	(	PUNCT
ap-1261	97	11	4	4	X
ap-1261	97	12	)	)	PUNCT
ap-1261	97	13	acquire	acquire	VERB
ap-1261	97	14	the	the	DET
ap-1261	97	15	block	block	NOUN
ap-1261	97	16	form	form	NOUN
ap-1261	97	17	explicitly	explicitly	ADV
ap-1261	97	18	r(x0	r(x0	VERB
ap-1261	97	19	)	)	PUNCT
ap-1261	97	20	=	=	PRON
ap-1261	97	21	(	(	PUNCT
ap-1261	97	22	a(x0	a(x0	ADV
ap-1261	97	23	)	)	PUNCT
ap-1261	97	24	0	0	NUM
ap-1261	97	25	0	0	NUM
ap-1261	97	26	b(x0	b(x0	NOUN
ap-1261	97	27	)	)	PUNCT
ap-1261	97	28	)	)	PUNCT
ap-1261	97	29	and	and	CCONJ
ap-1261	97	30	r(x1	r(x1	ADJ
ap-1261	97	31	)	)	PUNCT
ap-1261	97	32	=	=	SYM
ap-1261	98	1	(	(	PUNCT
ap-1261	98	2	0	0	NUM
ap-1261	98	3	c(x1	c(x1	NOUN
ap-1261	98	4	)	)	PUNCT
ap-1261	98	5	d(x1	d(x1	NOUN
ap-1261	98	6	)	)	PUNCT
ap-1261	98	7	0	0	NUM
ap-1261	98	8	)	)	PUNCT
ap-1261	98	9	.	.	PUNCT
ap-1261	99	1	in	in	ADP
ap-1261	99	2	the	the	DET
ap-1261	99	3	sequel	sequel	NOUN
ap-1261	99	4	,	,	PUNCT
ap-1261	99	5	we	we	PRON
ap-1261	99	6	will	will	AUX
ap-1261	99	7	illustrate	illustrate	VERB
ap-1261	99	8	all	all	DET
ap-1261	99	9	notions	notion	NOUN
ap-1261	99	10	on	on	ADP
ap-1261	99	11	the	the	DET
ap-1261	99	12	lie	lie	NOUN
ap-1261	99	13	algebra	algebra	NOUN
ap-1261	99	14	lε	lε	ADP
ap-1261	99	15	obtained	obtain	VERB
ap-1261	99	16	by	by	ADP
ap-1261	99	17	contraction	contraction	NOUN
ap-1261	99	18	from	from	ADP
ap-1261	99	19	a	a	DET
ap-1261	99	20	z2	z2	NOUN
ap-1261	99	21	-	-	PUNCT
ap-1261	99	22	grading	grading	NOUN
ap-1261	99	23	of	of	ADP
ap-1261	99	24	a	a	DET
ap-1261	99	25	lie	lie	NOUN
ap-1261	99	26	algebra	algebra	NOUN
ap-1261	99	27	l	l	NOUN
ap-1261	99	28	by	by	ADP
ap-1261	99	29	the	the	DET
ap-1261	99	30	first	first	ADJ
ap-1261	99	31	solution	solution	NOUN
ap-1261	99	32	(	(	PUNCT
ap-1261	99	33	εjk	εjk	NOUN
ap-1261	99	34	)	)	PUNCT
ap-1261	99	35	=	=	PUNCT
ap-1261	100	1	(	(	PUNCT
ap-1261	100	2	1	1	NUM
ap-1261	100	3	1	1	NUM
ap-1261	100	4	1	1	NUM
ap-1261	100	5	0	0	NUM
ap-1261	100	6	)	)	PUNCT
ap-1261	100	7	given	give	VERB
ap-1261	100	8	in	in	ADP
ap-1261	100	9	example	example	NOUN
ap-1261	100	10	1	1	NUM
ap-1261	100	11	.	.	X
ap-1261	101	1	for	for	ADP
ap-1261	101	2	this	this	DET
ap-1261	101	3	lie	lie	NOUN
ap-1261	101	4	algebra	algebra	NOUN
ap-1261	101	5	lε	lε	ADP
ap-1261	101	6	the	the	DET
ap-1261	101	7	commutation	commutation	NOUN
ap-1261	101	8	relations	relation	NOUN
ap-1261	101	9	have	have	VERB
ap-1261	101	10	the	the	DET
ap-1261	101	11	form	form	NOUN
ap-1261	101	12	[	[	X
ap-1261	101	13	x	x	NOUN
ap-1261	101	14	,	,	PUNCT
ap-1261	101	15	y]new	y]new	ADJ
ap-1261	102	1	=	=	X
ap-1261	103	1	[	[	X
ap-1261	103	2	x	x	X
ap-1261	103	3	,	,	PUNCT
ap-1261	103	4	y	y	PROPN
ap-1261	103	5	]	]	X
ap-1261	103	6	,	,	PUNCT
ap-1261	103	7	if	if	SCONJ
ap-1261	103	8	x	x	X
ap-1261	103	9	,	,	PUNCT
ap-1261	103	10	y	y	PROPN
ap-1261	103	11	∈	∈	PROPN
ap-1261	103	12	l0	l0	PROPN
ap-1261	103	13	or	or	CCONJ
ap-1261	103	14	if	if	SCONJ
ap-1261	103	15	x	x	SYM
ap-1261	103	16	∈	∈	PROPN
ap-1261	103	17	l0	l0	PROPN
ap-1261	103	18	,	,	PUNCT
ap-1261	103	19	y	y	PROPN
ap-1261	103	20	∈	∈	PROPN
ap-1261	103	21	l1	l1	PROPN
ap-1261	103	22	and	and	CCONJ
ap-1261	103	23	[	[	X
ap-1261	103	24	x	x	X
ap-1261	103	25	,	,	PUNCT
ap-1261	103	26	y]new	y]new	ADJ
ap-1261	103	27	=	=	NOUN
ap-1261	103	28	0	0	NUM
ap-1261	103	29	,	,	PUNCT
ap-1261	103	30	if	if	SCONJ
ap-1261	103	31	x	x	NOUN
ap-1261	103	32	,	,	PUNCT
ap-1261	103	33	y	y	PROPN
ap-1261	103	34	∈	∈	PROPN
ap-1261	103	35	l1	l1	PROPN
ap-1261	103	36	.	.	PUNCT
ap-1261	104	1	in	in	ADP
ap-1261	104	2	this	this	DET
ap-1261	104	3	case	case	NOUN
ap-1261	104	4	the	the	DET
ap-1261	104	5	system	system	NOUN
ap-1261	104	6	of	of	ADP
ap-1261	104	7	equations	equation	NOUN
ap-1261	104	8	(	(	PUNCT
ap-1261	104	9	7	7	X
ap-1261	104	10	)	)	PUNCT
ap-1261	104	11	is	be	AUX
ap-1261	104	12	ψ00ψ00	ψ00ψ00	NOUN
ap-1261	104	13	=	=	SYM
ap-1261	104	14	ψ00	ψ00	PROPN
ap-1261	104	15	,	,	PUNCT
ap-1261	104	16	ψ10ψ01	ψ10ψ01	NOUN
ap-1261	104	17	=	=	PUNCT
ap-1261	104	18	ψ00ψ10	ψ00ψ10	NOUN
ap-1261	104	19	=	=	SYM
ap-1261	104	20	ψ10	ψ10	NOUN
ap-1261	104	21	,	,	PUNCT
ap-1261	104	22	32	32	NUM
ap-1261	104	23	acta	acta	PROPN
ap-1261	104	24	polytechnica	polytechnica	PROPN
ap-1261	104	25	vol	vol	NOUN
ap-1261	104	26	.	.	PROPN
ap-1261	105	1	50	50	NUM
ap-1261	105	2	no	no	NOUN
ap-1261	105	3	.	.	PUNCT
ap-1261	106	1	5/2010	5/2010	NUM
ap-1261	106	2	ψ01ψ01	ψ01ψ01	NOUN
ap-1261	106	3	=	=	SYM
ap-1261	106	4	ψ01	ψ01	NOUN
ap-1261	106	5	,	,	PUNCT
ap-1261	106	6	ψ11ψ00	ψ11ψ00	NOUN
ap-1261	106	7	=	=	SYM
ap-1261	106	8	ψ01ψ11	ψ01ψ11	NOUN
ap-1261	106	9	=	=	SYM
ap-1261	106	10	ψ11	ψ11	NOUN
ap-1261	106	11	,	,	PUNCT
ap-1261	106	12	ψ10ψ11	ψ10ψ11	NOUN
ap-1261	106	13	=	=	NOUN
ap-1261	106	14	0	0	NUM
ap-1261	106	15	.	.	PUNCT
ap-1261	107	1	all	all	DET
ap-1261	107	2	solutions	solution	NOUN
ap-1261	107	3	(	(	PUNCT
ap-1261	107	4	up	up	ADP
ap-1261	107	5	to	to	ADP
ap-1261	107	6	equivalence	equivalence	NOUN
ap-1261	107	7	of	of	ADP
ap-1261	107	8	representations	representation	NOUN
ap-1261	107	9	)	)	PUNCT
ap-1261	107	10	of	of	ADP
ap-1261	107	11	this	this	DET
ap-1261	107	12	system	system	NOUN
ap-1261	107	13	are	be	AUX
ap-1261	107	14	(	(	PUNCT
ap-1261	107	15	ψjk	ψjk	NOUN
ap-1261	107	16	)	)	PUNCT
ap-1261	107	17	=	=	PUNCT
ap-1261	108	1	(	(	PUNCT
ap-1261	108	2	1	1	NUM
ap-1261	108	3	1	1	NUM
ap-1261	108	4	1	1	NUM
ap-1261	108	5	0	0	NUM
ap-1261	108	6	)	)	PUNCT
ap-1261	108	7	,	,	PUNCT
ap-1261	108	8	(	(	PUNCT
ap-1261	108	9	1	1	NUM
ap-1261	108	10	1	1	NUM
ap-1261	108	11	0	0	NUM
ap-1261	108	12	1	1	NUM
ap-1261	108	13	)	)	PUNCT
ap-1261	108	14	,	,	PUNCT
ap-1261	108	15	(	(	PUNCT
ap-1261	108	16	1	1	NUM
ap-1261	108	17	1	1	NUM
ap-1261	108	18	0	0	NUM
ap-1261	108	19	0	0	NUM
ap-1261	108	20	)	)	PUNCT
ap-1261	108	21	,	,	PUNCT
ap-1261	108	22	(	(	PUNCT
ap-1261	108	23	1	1	NUM
ap-1261	108	24	0	0	NUM
ap-1261	108	25	0	0	NUM
ap-1261	108	26	0	0	NUM
ap-1261	108	27	)	)	PUNCT
ap-1261	108	28	,	,	PUNCT
ap-1261	108	29	(	(	PUNCT
ap-1261	108	30	0	0	NUM
ap-1261	108	31	1	1	NUM
ap-1261	108	32	0	0	NUM
ap-1261	108	33	0	0	NUM
ap-1261	108	34	)	)	PUNCT
ap-1261	108	35	and	and	CCONJ
ap-1261	108	36	(	(	PUNCT
ap-1261	108	37	0	0	NUM
ap-1261	108	38	0	0	NUM
ap-1261	108	39	0	0	NUM
ap-1261	108	40	0	0	NUM
ap-1261	108	41	)	)	PUNCT
ap-1261	108	42	the	the	DET
ap-1261	108	43	representations	representation	NOUN
ap-1261	108	44	rε	rε	PRON
ap-1261	108	45	of	of	ADP
ap-1261	108	46	the	the	DET
ap-1261	108	47	contracted	contract	VERB
ap-1261	108	48	lie	lie	NOUN
ap-1261	108	49	algebra	algebra	NOUN
ap-1261	108	50	lε	lε	INTJ
ap-1261	108	51	in	in	ADP
ap-1261	108	52	the	the	DET
ap-1261	108	53	chosen	choose	VERB
ap-1261	108	54	basis	basis	NOUN
ap-1261	108	55	b	b	PROPN
ap-1261	108	56	of	of	ADP
ap-1261	108	57	the	the	DET
ap-1261	108	58	vector	vector	NOUN
ap-1261	108	59	space	space	NOUN
ap-1261	108	60	v	v	NOUN
ap-1261	108	61	have	have	VERB
ap-1261	108	62	the	the	DET
ap-1261	108	63	block	block	NOUN
ap-1261	108	64	form	form	NOUN
ap-1261	108	65	rε(x0	rε(x0	NOUN
ap-1261	108	66	)	)	PUNCT
ap-1261	108	67	=	=	SYM
ap-1261	108	68	(	(	PUNCT
ap-1261	108	69	ψ00a(x0	ψ00a(x0	PROPN
ap-1261	108	70	)	)	PUNCT
ap-1261	109	1	0	0	NUM
ap-1261	109	2	0	0	NUM
ap-1261	109	3	ψ01b(x0	ψ01b(x0	NOUN
ap-1261	109	4	)	)	PUNCT
ap-1261	109	5	)	)	PUNCT
ap-1261	109	6	and	and	CCONJ
ap-1261	109	7	rε(x1	rε(x1	X
ap-1261	109	8	)	)	PUNCT
ap-1261	109	9	=	=	SYM
ap-1261	109	10	(	(	PUNCT
ap-1261	109	11	0	0	NUM
ap-1261	109	12	ψ11c(x1	ψ11c(x1	NOUN
ap-1261	109	13	)	)	PUNCT
ap-1261	109	14	ψ10d(x1	ψ10d(x1	NOUN
ap-1261	109	15	)	)	PUNCT
ap-1261	109	16	0	0	NUM
ap-1261	109	17	)	)	PUNCT
ap-1261	109	18	,	,	PUNCT
ap-1261	109	19	where	where	SCONJ
ap-1261	109	20	for	for	ADP
ap-1261	109	21	parameters	parameter	NOUN
ap-1261	109	22	(	(	PUNCT
ap-1261	109	23	ψij	ψij	NOUN
ap-1261	109	24	)	)	PUNCT
ap-1261	109	25	one	one	NOUN
ap-1261	109	26	may	may	AUX
ap-1261	109	27	choose	choose	VERB
ap-1261	109	28	one	one	NUM
ap-1261	109	29	of	of	ADP
ap-1261	109	30	the	the	DET
ap-1261	109	31	six	six	NUM
ap-1261	109	32	solutions	solution	NOUN
ap-1261	109	33	.	.	PUNCT
ap-1261	110	1	let	let	VERB
ap-1261	110	2	us	we	PRON
ap-1261	110	3	mention	mention	VERB
ap-1261	110	4	that	that	SCONJ
ap-1261	110	5	only	only	ADV
ap-1261	110	6	the	the	DET
ap-1261	110	7	first	first	ADJ
ap-1261	110	8	two	two	NUM
ap-1261	110	9	solutions	solution	NOUN
ap-1261	110	10	are	be	AUX
ap-1261	110	11	interesting	interesting	ADJ
ap-1261	110	12	since	since	SCONJ
ap-1261	110	13	the	the	DET
ap-1261	110	14	elements	element	NOUN
ap-1261	110	15	of	of	ADP
ap-1261	110	16	subalgebra	subalgebra	PROPN
ap-1261	110	17	l1	l1	PROPN
ap-1261	110	18	are	be	AUX
ap-1261	110	19	represented	represent	VERB
ap-1261	110	20	by	by	ADP
ap-1261	110	21	zero	zero	NUM
ap-1261	110	22	operators	operator	NOUN
ap-1261	110	23	in	in	ADP
ap-1261	110	24	the	the	DET
ap-1261	110	25	remaining	remain	VERB
ap-1261	110	26	solutions	solution	NOUN
ap-1261	110	27	.	.	PUNCT
ap-1261	111	1	2.3	2.3	NUM
ap-1261	111	2	group	group	NOUN
ap-1261	111	3	gradings	grading	NOUN
ap-1261	111	4	and	and	CCONJ
ap-1261	111	5	automorphisms	automorphism	VERB
ap-1261	111	6	the	the	DET
ap-1261	111	7	simplest	simple	ADJ
ap-1261	111	8	way	way	NOUN
ap-1261	111	9	to	to	PART
ap-1261	111	10	find	find	VERB
ap-1261	111	11	a	a	DET
ap-1261	111	12	group	group	NOUN
ap-1261	111	13	grading	grading	NOUN
ap-1261	111	14	of	of	ADP
ap-1261	111	15	a	a	DET
ap-1261	111	16	lie	lie	NOUN
ap-1261	111	17	algebra	algebra	NOUN
ap-1261	111	18	is	be	AUX
ap-1261	111	19	to	to	PART
ap-1261	111	20	decompose	decompose	VERB
ap-1261	111	21	the	the	DET
ap-1261	111	22	vector	vector	NOUN
ap-1261	111	23	space	space	NOUN
ap-1261	111	24	l	l	NOUN
ap-1261	111	25	into	into	ADP
ap-1261	111	26	eigensubspaces	eigensubspace	NOUN
ap-1261	111	27	of	of	ADP
ap-1261	111	28	a	a	DET
ap-1261	111	29	diagonalizable	diagonalizable	ADJ
ap-1261	111	30	automorphism	automorphism	NOUN
ap-1261	111	31	g	g	PROPN
ap-1261	111	32	∈	∈	PROPN
ap-1261	111	33	aut	aut	X
ap-1261	111	34	l	l	X
ap-1261	112	1	[	[	X
ap-1261	112	2	6	6	NUM
ap-1261	112	3	]	]	PUNCT
ap-1261	112	4	.	.	PUNCT
ap-1261	113	1	for	for	ADP
ap-1261	113	2	any	any	DET
ap-1261	113	3	pair	pair	NOUN
ap-1261	113	4	of	of	ADP
ap-1261	113	5	its	its	PRON
ap-1261	113	6	eigenvectors	eigenvector	NOUN
ap-1261	113	7	xλ	xλ	VERB
ap-1261	113	8	and	and	CCONJ
ap-1261	113	9	xμ	xμ	PROPN
ap-1261	113	10	corresponding	correspond	VERB
ap-1261	113	11	to	to	PART
ap-1261	113	12	eigenvalues	eigenvalues	VERB
ap-1261	113	13	λ	λ	PROPN
ap-1261	113	14	and	and	CCONJ
ap-1261	113	15	μ	μ	NUM
ap-1261	113	16	,	,	PUNCT
ap-1261	113	17	respectively	respectively	ADV
ap-1261	113	18	,	,	PUNCT
ap-1261	113	19	we	we	PRON
ap-1261	113	20	have	have	AUX
ap-1261	113	21	g([xλ	g([xλ	NOUN
ap-1261	113	22	,	,	PUNCT
ap-1261	113	23	xμ	xμ	NOUN
ap-1261	113	24	]	]	X
ap-1261	113	25	)	)	PUNCT
ap-1261	113	26	=	=	PUNCT
ap-1261	114	1	[	[	X
ap-1261	114	2	g(xλ	g(xλ	NOUN
ap-1261	114	3	)	)	PUNCT
ap-1261	114	4	,	,	PUNCT
ap-1261	114	5	g(xμ	g(xμ	ADV
ap-1261	114	6	)	)	PUNCT
ap-1261	114	7	]	]	PUNCT
ap-1261	115	1	=	=	SYM
ap-1261	115	2	λμ[xλ	λμ[xλ	PROPN
ap-1261	115	3	,	,	PUNCT
ap-1261	115	4	xμ	xμ	X
ap-1261	115	5	]	]	PUNCT
ap-1261	115	6	.	.	PUNCT
ap-1261	116	1	thus	thus	ADV
ap-1261	116	2	the	the	DET
ap-1261	116	3	commutator	commutator	NOUN
ap-1261	116	4	[	[	X
ap-1261	116	5	xλ	xλ	NOUN
ap-1261	116	6	,	,	PUNCT
ap-1261	116	7	xμ	xμ	PRON
ap-1261	116	8	]	]	X
ap-1261	116	9	is	be	AUX
ap-1261	116	10	either	either	PRON
ap-1261	116	11	zero	zero	NUM
ap-1261	116	12	or	or	CCONJ
ap-1261	116	13	an	an	DET
ap-1261	116	14	eigenvector	eigenvector	NOUN
ap-1261	116	15	corresponding	correspond	VERB
ap-1261	116	16	to	to	ADP
ap-1261	116	17	the	the	DET
ap-1261	116	18	eigenvalue	eigenvalue	PROPN
ap-1261	116	19	λμ	λμ	X
ap-1261	116	20	.	.	PUNCT
ap-1261	117	1	let	let	VERB
ap-1261	117	2	us	we	PRON
ap-1261	117	3	denote	denote	VERB
ap-1261	117	4	by	by	ADP
ap-1261	117	5	σ(g	σ(g	NOUN
ap-1261	117	6	)	)	PUNCT
ap-1261	117	7	the	the	DET
ap-1261	117	8	spectrum	spectrum	NOUN
ap-1261	117	9	of	of	ADP
ap-1261	117	10	automorphism	automorphism	NOUN
ap-1261	117	11	g	g	NOUN
ap-1261	117	12	and	and	CCONJ
ap-1261	117	13	by	by	ADP
ap-1261	117	14	lλ	lλ	INTJ
ap-1261	117	15	the	the	DET
ap-1261	117	16	eigensubspace	eigensubspace	NOUN
ap-1261	117	17	corresponding	correspond	VERB
ap-1261	117	18	to	to	ADP
ap-1261	117	19	λ	λ	PROPN
ap-1261	117	20	∈	∈	NOUN
ap-1261	117	21	σ(g	σ(g	NOUN
ap-1261	117	22	)	)	PUNCT
ap-1261	117	23	.	.	PUNCT
ap-1261	118	1	the	the	DET
ap-1261	118	2	decomposition	decomposition	NOUN
ap-1261	118	3	γ	γ	X
ap-1261	118	4	:	:	PUNCT
ap-1261	118	5	l	l	NOUN
ap-1261	118	6	=	=	PUNCT
ap-1261	118	7	⊕	⊕	PROPN
ap-1261	118	8	λ∈σ(g	λ∈σ(g	NOUN
ap-1261	118	9	)	)	PUNCT
ap-1261	118	10	lλ	lλ	CCONJ
ap-1261	118	11	(	(	PUNCT
ap-1261	118	12	8)	8)	NUM
ap-1261	118	13	is	be	AUX
ap-1261	118	14	a	a	DET
ap-1261	118	15	group	group	NOUN
ap-1261	118	16	grading	grading	NOUN
ap-1261	118	17	,	,	PUNCT
ap-1261	118	18	where	where	SCONJ
ap-1261	118	19	the	the	DET
ap-1261	118	20	multiplicative	multiplicative	ADJ
ap-1261	118	21	semigroup	semigroup	NOUN
ap-1261	118	22	generated	generate	VERB
ap-1261	118	23	by	by	ADP
ap-1261	118	24	the	the	DET
ap-1261	118	25	spectrum	spectrum	NOUN
ap-1261	118	26	of	of	ADP
ap-1261	118	27	g	g	NOUN
ap-1261	118	28	can	can	AUX
ap-1261	118	29	be	be	AUX
ap-1261	118	30	taken	take	VERB
ap-1261	118	31	as	as	ADP
ap-1261	118	32	a	a	DET
ap-1261	118	33	semigroup	semigroup	NOUN
ap-1261	118	34	g.	g.	NOUN
ap-1261	118	35	remark	remark	VERB
ap-1261	118	36	2.3	2.3	NUM
ap-1261	118	37	if	if	SCONJ
ap-1261	118	38	h	h	NOUN
ap-1261	118	39	∈	∈	PROPN
ap-1261	118	40	aut	aut	PROPN
ap-1261	118	41	l	l	PROPN
ap-1261	118	42	,	,	PUNCT
ap-1261	118	43	then	then	ADV
ap-1261	118	44	the	the	DET
ap-1261	118	45	decomposition	decomposition	NOUN
ap-1261	118	46	of	of	ADP
ap-1261	118	47	l	l	NOUN
ap-1261	118	48	into	into	ADP
ap-1261	118	49	eigensubspaces	eigensubspace	NOUN
ap-1261	118	50	of	of	ADP
ap-1261	118	51	the	the	DET
ap-1261	118	52	automorphism	automorphism	NOUN
ap-1261	118	53	hgh−1	hgh−1	PRON
ap-1261	118	54	is	be	AUX
ap-1261	118	55	l	l	NOUN
ap-1261	118	56	=	=	PUNCT
ap-1261	118	57	⊕	⊕	PROPN
ap-1261	118	58	λ∈σ(g	λ∈σ(g	NOUN
ap-1261	118	59	)	)	PUNCT
ap-1261	118	60	h(lλ	h(lλ	NOUN
ap-1261	118	61	)	)	PUNCT
ap-1261	118	62	,	,	PUNCT
ap-1261	118	63	i.e.	i.e.	X
ap-1261	118	64	the	the	DET
ap-1261	118	65	gradings	grading	NOUN
ap-1261	118	66	given	give	VERB
ap-1261	118	67	by	by	ADP
ap-1261	118	68	conjugated	conjugated	ADJ
ap-1261	118	69	automorphisms	automorphisms	PROPN
ap-1261	118	70	g	g	PROPN
ap-1261	118	71	and	and	CCONJ
ap-1261	118	72	hgh−1	hgh−1	PROPN
ap-1261	118	73	are	be	AUX
ap-1261	118	74	equivalent	equivalent	ADJ
ap-1261	118	75	.	.	PUNCT
ap-1261	119	1	therefore	therefore	ADV
ap-1261	119	2	,	,	PUNCT
ap-1261	119	3	the	the	DET
ap-1261	119	4	automorphisms	automorphisms	PROPN
ap-1261	119	5	g	g	PROPN
ap-1261	119	6	and	and	CCONJ
ap-1261	119	7	hgh−1	hgh−1	PROPN
ap-1261	119	8	are	be	AUX
ap-1261	119	9	called	call	VERB
ap-1261	119	10	equivalent	equivalent	ADJ
ap-1261	119	11	as	as	ADV
ap-1261	119	12	well	well	ADV
ap-1261	119	13	.	.	PUNCT
ap-1261	120	1	note	note	VERB
ap-1261	120	2	however	however	ADV
ap-1261	120	3	that	that	SCONJ
ap-1261	120	4	different	different	ADJ
ap-1261	120	5	inequivalent	inequivalent	NOUN
ap-1261	120	6	automorphisms	automorphism	NOUN
ap-1261	120	7	may	may	AUX
ap-1261	120	8	even	even	ADV
ap-1261	120	9	give	give	VERB
ap-1261	120	10	the	the	DET
ap-1261	120	11	same	same	ADJ
ap-1261	120	12	grading	grading	NOUN
ap-1261	120	13	.	.	PUNCT
ap-1261	121	1	similarly	similarly	ADV
ap-1261	121	2	,	,	PUNCT
ap-1261	121	3	if	if	SCONJ
ap-1261	121	4	g1	g1	NOUN
ap-1261	121	5	,	,	PUNCT
ap-1261	121	6	g2	g2	PROPN
ap-1261	121	7	,	,	PUNCT
ap-1261	121	8	.	.	PUNCT
ap-1261	121	9	.	.	PUNCT
ap-1261	122	1	.	.	PUNCT
ap-1261	123	1	,	,	PUNCT
ap-1261	123	2	gr	gr	NOUN
ap-1261	123	3	are	be	AUX
ap-1261	123	4	mutually	mutually	ADV
ap-1261	123	5	commuting	commute	VERB
ap-1261	123	6	automorphisms	automorphism	NOUN
ap-1261	123	7	of	of	ADP
ap-1261	123	8	l	l	NOUN
ap-1261	123	9	,	,	PUNCT
ap-1261	123	10	then	then	ADV
ap-1261	123	11	the	the	DET
ap-1261	123	12	decomposition	decomposition	NOUN
ap-1261	123	13	of	of	ADP
ap-1261	123	14	l	l	NOUN
ap-1261	123	15	into	into	ADP
ap-1261	123	16	common	common	ADJ
ap-1261	123	17	eigensubspaces	eigensubspace	NOUN
ap-1261	123	18	of	of	ADP
ap-1261	123	19	all	all	DET
ap-1261	123	20	these	these	DET
ap-1261	123	21	automorphisms	automorphism	NOUN
ap-1261	123	22	is	be	AUX
ap-1261	123	23	a	a	DET
ap-1261	123	24	group	group	NOUN
ap-1261	123	25	grading	grading	NOUN
ap-1261	123	26	of	of	ADP
ap-1261	123	27	l.	l.	PROPN
ap-1261	123	28	the	the	DET
ap-1261	123	29	semigroup	semigroup	PROPN
ap-1261	123	30	suitable	suitable	ADJ
ap-1261	123	31	for	for	ADP
ap-1261	123	32	indexing	index	VERB
ap-1261	123	33	this	this	DET
ap-1261	123	34	grading	grade	VERB
ap-1261	123	35	isg1×g2×.	isg1×g2×.	PROPN
ap-1261	123	36	.	.	PUNCT
ap-1261	124	1	.×gr	.×gr	PROPN
ap-1261	124	2	,	,	PUNCT
ap-1261	124	3	where	where	SCONJ
ap-1261	124	4	eachgi	eachgi	NOUN
ap-1261	124	5	is	be	AUX
ap-1261	124	6	the	the	DET
ap-1261	124	7	semigroup	semigroup	NOUN
ap-1261	124	8	generated	generate	VERB
ap-1261	124	9	by	by	ADP
ap-1261	124	10	the	the	DET
ap-1261	124	11	spectrum	spectrum	NOUN
ap-1261	124	12	of	of	ADP
ap-1261	124	13	the	the	DET
ap-1261	124	14	automorphism	automorphism	NOUN
ap-1261	124	15	gi	gi	NOUN
ap-1261	124	16	.	.	PUNCT
ap-1261	125	1	furthermore	furthermore	ADV
ap-1261	125	2	,	,	PUNCT
ap-1261	125	3	for	for	ADP
ap-1261	125	4	lie	lie	NOUN
ap-1261	125	5	algebras	algebra	VERB
ap-1261	125	6	over	over	ADP
ap-1261	125	7	the	the	DET
ap-1261	125	8	complex	complex	ADJ
ap-1261	125	9	field	field	NOUN
ap-1261	125	10	c	c	NOUN
ap-1261	125	11	,	,	PUNCT
ap-1261	125	12	any	any	DET
ap-1261	125	13	group	group	NOUN
ap-1261	125	14	grading	grading	NOUN
ap-1261	125	15	can	can	AUX
ap-1261	125	16	be	be	AUX
ap-1261	125	17	obtained	obtain	VERB
ap-1261	125	18	by	by	ADP
ap-1261	125	19	this	this	DET
ap-1261	125	20	procedure	procedure	NOUN
ap-1261	125	21	.	.	PUNCT
ap-1261	126	1	let	let	VERB
ap-1261	126	2	us	we	PRON
ap-1261	126	3	emphasize	emphasize	VERB
ap-1261	126	4	that	that	SCONJ
ap-1261	126	5	this	this	PRON
ap-1261	126	6	is	be	AUX
ap-1261	126	7	not	not	PART
ap-1261	126	8	the	the	DET
ap-1261	126	9	case	case	NOUN
ap-1261	126	10	for	for	ADP
ap-1261	126	11	real	real	ADJ
ap-1261	126	12	lie	lie	NOUN
ap-1261	126	13	algebras	algebra	VERB
ap-1261	126	14	.	.	PUNCT
ap-1261	127	1	in	in	ADP
ap-1261	127	2	the	the	DET
ap-1261	127	3	following	following	NOUN
ap-1261	127	4	,	,	PUNCT
ap-1261	127	5	in	in	ADP
ap-1261	127	6	order	order	NOUN
ap-1261	127	7	to	to	PART
ap-1261	127	8	study	study	VERB
ap-1261	127	9	the	the	DET
ap-1261	127	10	compatibility	compatibility	NOUN
ap-1261	127	11	problem	problem	NOUN
ap-1261	127	12	,	,	PUNCT
ap-1261	127	13	we	we	PRON
ap-1261	127	14	shall	shall	AUX
ap-1261	127	15	consider	consider	VERB
ap-1261	127	16	the	the	DET
ap-1261	127	17	simplest	simple	ADJ
ap-1261	127	18	case	case	NOUN
ap-1261	127	19	of	of	ADP
ap-1261	127	20	group	group	NOUN
ap-1261	127	21	grading	grading	NOUN
ap-1261	127	22	determined	determine	VERB
ap-1261	127	23	by	by	ADP
ap-1261	127	24	one	one	NUM
ap-1261	127	25	automorphism	automorphism	NOUN
ap-1261	127	26	.	.	PUNCT
ap-1261	128	1	2.4	2.4	NUM
ap-1261	128	2	group	group	NOUN
ap-1261	128	3	grading	grading	NOUN
ap-1261	128	4	determined	determine	VERB
ap-1261	128	5	by	by	ADP
ap-1261	128	6	one	one	NUM
ap-1261	128	7	automorphism	automorphism	NOUN
ap-1261	128	8	let	let	VERB
ap-1261	128	9	γ	γ	NOUN
ap-1261	128	10	be	be	AUX
ap-1261	128	11	a	a	DET
ap-1261	128	12	grading	grading	NOUN
ap-1261	128	13	of	of	ADP
ap-1261	128	14	the	the	DET
ap-1261	128	15	form	form	NOUN
ap-1261	128	16	(	(	PUNCT
ap-1261	128	17	8)	8)	NUM
ap-1261	128	18	,	,	PUNCT
ap-1261	128	19	i.e.	i.e.	X
ap-1261	128	20	obtained	obtain	VERB
ap-1261	128	21	by	by	ADP
ap-1261	128	22	decomposition	decomposition	NOUN
ap-1261	128	23	of	of	ADP
ap-1261	128	24	l	l	NOUN
ap-1261	128	25	into	into	ADP
ap-1261	128	26	eigensubspaces	eigensubspace	NOUN
ap-1261	128	27	of	of	ADP
ap-1261	128	28	a	a	DET
ap-1261	128	29	single	single	ADJ
ap-1261	128	30	automorphism	automorphism	NOUN
ap-1261	128	31	g.	g.	NOUN
ap-1261	128	32	we	we	PRON
ap-1261	128	33	may	may	AUX
ap-1261	128	34	assume	assume	VERB
ap-1261	128	35	that	that	SCONJ
ap-1261	128	36	g	g	PROPN
ap-1261	128	37	has	have	VERB
ap-1261	128	38	a	a	DET
ap-1261	128	39	finite	finite	ADJ
ap-1261	128	40	order	order	NOUN
ap-1261	128	41	,	,	PUNCT
ap-1261	128	42	say	say	VERB
ap-1261	128	43	gk	gk	NOUN
ap-1261	128	44	=	=	PROPN
ap-1261	128	45	i	i	PROPN
ap-1261	128	46	d.	d.	PROPN
ap-1261	128	47	for	for	ADP
ap-1261	128	48	its	its	PRON
ap-1261	128	49	spectrum	spectrum	NOUN
ap-1261	128	50	we	we	PRON
ap-1261	128	51	have	have	VERB
ap-1261	128	52	σ(g	σ(g	NOUN
ap-1261	128	53	)	)	PUNCT
ap-1261	128	54	⊂	⊂	PRON
ap-1261	128	55	{	{	PUNCT
ap-1261	128	56	ei	ei	X
ap-1261	128	57	2π	2π	NOUN
ap-1261	129	1	k	k	PROPN
ap-1261	129	2	|	|	ADV
ap-1261	129	3	�	�	PROPN
ap-1261	129	4	=	=	SYM
ap-1261	129	5	0	0	NUM
ap-1261	129	6	,	,	PUNCT
ap-1261	129	7	1	1	NUM
ap-1261	129	8	,	,	PUNCT
ap-1261	129	9	2	2	NUM
ap-1261	129	10	,	,	PUNCT
ap-1261	129	11	.	.	PUNCT
ap-1261	129	12	.	.	PUNCT
ap-1261	130	1	.	.	PUNCT
ap-1261	131	1	,	,	PUNCT
ap-1261	132	1	k	k	PROPN
ap-1261	132	2	−	−	NOUN
ap-1261	132	3	1	1	NUM
ap-1261	132	4	}	}	PUNCT
ap-1261	132	5	=	=	PRON
ap-1261	132	6	:	:	PUNCT
ap-1261	132	7	g.	g.	PROPN
ap-1261	132	8	(	(	PUNCT
ap-1261	132	9	9	9	X
ap-1261	132	10	)	)	PUNCT
ap-1261	132	11	this	this	PRON
ap-1261	132	12	means	mean	VERB
ap-1261	132	13	that	that	SCONJ
ap-1261	132	14	γ	γ	PROPN
ap-1261	132	15	is	be	AUX
ap-1261	132	16	a	a	DET
ap-1261	132	17	g	g	NOUN
ap-1261	132	18	-	-	PUNCT
ap-1261	132	19	grading	grade	VERB
ap-1261	132	20	.	.	PUNCT
ap-1261	133	1	let	let	VERB
ap-1261	133	2	us	we	PRON
ap-1261	133	3	consider	consider	VERB
ap-1261	133	4	an	an	DET
ap-1261	133	5	irreducible	irreducible	ADJ
ap-1261	133	6	d	d	ADJ
ap-1261	133	7	-	-	ADJ
ap-1261	133	8	dimensional	dimensional	ADJ
ap-1261	133	9	representation	representation	NOUN
ap-1261	133	10	r	r	NOUN
ap-1261	133	11	of	of	ADP
ap-1261	133	12	the	the	DET
ap-1261	133	13	lie	lie	NOUN
ap-1261	133	14	algebra	algebra	NOUN
ap-1261	133	15	l.	l.	NOUN
ap-1261	133	16	our	our	PRON
ap-1261	133	17	aim	aim	NOUN
ap-1261	133	18	is	be	AUX
ap-1261	133	19	to	to	PART
ap-1261	133	20	discuss	discuss	VERB
ap-1261	133	21	the	the	DET
ap-1261	133	22	question	question	NOUN
ap-1261	133	23	of	of	ADP
ap-1261	133	24	compatibility	compatibility	NOUN
ap-1261	133	25	of	of	ADP
ap-1261	133	26	r	r	NOUN
ap-1261	133	27	with	with	ADP
ap-1261	133	28	g	g	NOUN
ap-1261	133	29	-	-	PUNCT
ap-1261	133	30	grading	grade	VERB
ap-1261	133	31	.	.	PUNCT
ap-1261	134	1	let	let	VERB
ap-1261	134	2	rg	rg	PRON
ap-1261	134	3	be	be	AUX
ap-1261	134	4	a	a	DET
ap-1261	134	5	non	non	ADJ
ap-1261	134	6	-	-	ADJ
ap-1261	134	7	singular	singular	ADJ
ap-1261	134	8	matrix	matrix	NOUN
ap-1261	134	9	in	in	ADP
ap-1261	134	10	c	c	NOUN
ap-1261	134	11	d×d	d×d	PROPN
ap-1261	134	12	such	such	ADJ
ap-1261	134	13	that	that	PRON
ap-1261	134	14	r(g(x	r(g(x	NOUN
ap-1261	134	15	)	)	PUNCT
ap-1261	134	16	)	)	PUNCT
ap-1261	135	1	=	=	PUNCT
ap-1261	136	1	rgr(x)r−1	rgr(x)r−1	PRON
ap-1261	136	2	g	g	NOUN
ap-1261	136	3	for	for	ADP
ap-1261	136	4	all	all	PRON
ap-1261	136	5	x	x	SYM
ap-1261	136	6	∈	∈	PROPN
ap-1261	136	7	l	l	NOUN
ap-1261	136	8	.	.	PUNCT
ap-1261	137	1	(	(	PUNCT
ap-1261	137	2	10	10	NUM
ap-1261	137	3	)	)	PUNCT
ap-1261	137	4	33	33	NUM
ap-1261	137	5	acta	acta	PROPN
ap-1261	137	6	polytechnica	polytechnica	PROPN
ap-1261	137	7	vol	vol	NOUN
ap-1261	137	8	.	.	PROPN
ap-1261	138	1	50	50	NUM
ap-1261	138	2	no	no	NOUN
ap-1261	138	3	.	.	PUNCT
ap-1261	139	1	5/2010	5/2010	NUM
ap-1261	139	2	as	as	ADP
ap-1261	139	3	gk	gk	PROPN
ap-1261	139	4	=	=	PROPN
ap-1261	139	5	i	i	PROPN
ap-1261	139	6	d	d	PROPN
ap-1261	139	7	,	,	PUNCT
ap-1261	139	8	the	the	DET
ap-1261	139	9	previous	previous	ADJ
ap-1261	139	10	equality	equality	NOUN
ap-1261	139	11	gives	give	VERB
ap-1261	139	12	r(x	r(x	PROPN
ap-1261	139	13	)	)	PUNCT
ap-1261	139	14	=	=	SYM
ap-1261	139	15	r(gk(x	r(gk(x	PROPN
ap-1261	139	16	)	)	PUNCT
ap-1261	139	17	)	)	PUNCT
ap-1261	140	1	=	=	PRON
ap-1261	140	2	rk	rk	NOUN
ap-1261	140	3	gr(x)r−k	gr(x)r−k	VERB
ap-1261	140	4	g	g	NOUN
ap-1261	140	5	or	or	CCONJ
ap-1261	140	6	[	[	X
ap-1261	140	7	rk	rk	NOUN
ap-1261	140	8	g	g	NOUN
ap-1261	140	9	,	,	PUNCT
ap-1261	140	10	r(x	r(x	PROPN
ap-1261	140	11	)	)	PUNCT
ap-1261	140	12	]	]	PUNCT
ap-1261	141	1	=	=	PUNCT
ap-1261	141	2	0	0	PUNCT
ap-1261	141	3	for	for	ADP
ap-1261	141	4	all	all	PRON
ap-1261	141	5	x	x	SYM
ap-1261	141	6	∈	∈	ADJ
ap-1261	141	7	l	l	NOUN
ap-1261	141	8	.	.	PUNCT
ap-1261	142	1	since	since	SCONJ
ap-1261	142	2	the	the	DET
ap-1261	142	3	representation	representation	NOUN
ap-1261	142	4	r	r	NOUN
ap-1261	142	5	is	be	AUX
ap-1261	142	6	irreducible	irreducible	ADJ
ap-1261	142	7	,	,	PUNCT
ap-1261	142	8	by	by	ADP
ap-1261	142	9	schur	schur	PROPN
ap-1261	142	10	’s	’s	PART
ap-1261	142	11	lemma	lemma	PROPN
ap-1261	142	12	rk	rk	PROPN
ap-1261	142	13	g	g	PROPN
ap-1261	142	14	=	=	PUNCT
ap-1261	142	15	α	α	PROPN
ap-1261	142	16	i	i	PROPN
ap-1261	142	17	d	d	PROPN
ap-1261	142	18	for	for	ADP
ap-1261	142	19	some	some	DET
ap-1261	142	20	α	α	PROPN
ap-1261	142	21	∈	∈	PROPN
ap-1261	142	22	c.	c.	NOUN
ap-1261	142	23	of	of	ADP
ap-1261	142	24	course	course	NOUN
ap-1261	142	25	,	,	PUNCT
ap-1261	142	26	any	any	DET
ap-1261	142	27	nonzero	nonzero	ADJ
ap-1261	142	28	multiple	multiple	NOUN
ap-1261	142	29	of	of	ADP
ap-1261	142	30	rg	rg	PROPN
ap-1261	142	31	also	also	ADV
ap-1261	142	32	satisfies	satisfy	VERB
ap-1261	142	33	the	the	DET
ap-1261	142	34	relation	relation	NOUN
ap-1261	142	35	(	(	PUNCT
ap-1261	142	36	10	10	NUM
ap-1261	142	37	)	)	PUNCT
ap-1261	142	38	.	.	PUNCT
ap-1261	143	1	therefore	therefore	ADV
ap-1261	143	2	without	without	ADP
ap-1261	143	3	loss	loss	NOUN
ap-1261	143	4	of	of	ADP
ap-1261	143	5	generality	generality	NOUN
ap-1261	143	6	,	,	PUNCT
ap-1261	143	7	we	we	PRON
ap-1261	143	8	may	may	AUX
ap-1261	143	9	assume	assume	VERB
ap-1261	143	10	that	that	SCONJ
ap-1261	143	11	rk	rk	VERB
ap-1261	143	12	g	g	NOUN
ap-1261	143	13	=	=	PUNCT
ap-1261	143	14	i	i	PROPN
ap-1261	143	15	d	d	PROPN
ap-1261	143	16	,	,	PUNCT
ap-1261	143	17	where	where	SCONJ
ap-1261	143	18	k	k	PROPN
ap-1261	143	19	is	be	AUX
ap-1261	143	20	the	the	DET
ap-1261	143	21	order	order	NOUN
ap-1261	143	22	of	of	ADP
ap-1261	143	23	automorphism	automorphism	NOUN
ap-1261	143	24	g.	g.	NOUN
ap-1261	143	25	(	(	PUNCT
ap-1261	143	26	11	11	NUM
ap-1261	143	27	)	)	PUNCT
ap-1261	143	28	this	this	DET
ap-1261	143	29	normalization	normalization	NOUN
ap-1261	143	30	guarantees	guarantee	VERB
ap-1261	143	31	that	that	SCONJ
ap-1261	143	32	the	the	DET
ap-1261	143	33	spectrum	spectrum	NOUN
ap-1261	143	34	of	of	ADP
ap-1261	143	35	matrix	matrix	NOUN
ap-1261	143	36	rg	rg	PROPN
ap-1261	143	37	and	and	CCONJ
ap-1261	143	38	the	the	DET
ap-1261	143	39	spectrum	spectrum	NOUN
ap-1261	143	40	of	of	ADP
ap-1261	143	41	automorphism	automorphism	NOUN
ap-1261	143	42	g	g	PROPN
ap-1261	143	43	belong	belong	VERB
ap-1261	143	44	to	to	ADP
ap-1261	143	45	the	the	DET
ap-1261	143	46	same	same	ADJ
ap-1261	143	47	group	group	NOUN
ap-1261	143	48	g.	g.	PROPN
ap-1261	143	49	in	in	ADP
ap-1261	143	50	particular	particular	ADJ
ap-1261	143	51	,	,	PUNCT
ap-1261	143	52	since	since	SCONJ
ap-1261	143	53	rk	rk	PROPN
ap-1261	143	54	g	g	PROPN
ap-1261	143	55	is	be	AUX
ap-1261	143	56	the	the	DET
ap-1261	143	57	identity	identity	NOUN
ap-1261	143	58	,	,	PUNCT
ap-1261	143	59	matrix	matrix	NOUN
ap-1261	143	60	rg	rg	NOUN
ap-1261	143	61	is	be	AUX
ap-1261	143	62	diagonalizable	diagonalizable	ADJ
ap-1261	143	63	.	.	PUNCT
ap-1261	144	1	let	let	VERB
ap-1261	144	2	v	v	NOUN
ap-1261	144	3	=	=	SYM
ap-1261	144	4	⊕λ∈gvλ	⊕λ∈gvλ	PROPN
ap-1261	144	5	denote	denote	VERB
ap-1261	144	6	the	the	DET
ap-1261	144	7	decomposition	decomposition	NOUN
ap-1261	144	8	of	of	ADP
ap-1261	144	9	column	column	NOUN
ap-1261	144	10	space	space	NOUN
ap-1261	144	11	cd	cd	PROPN
ap-1261	144	12	into	into	ADP
ap-1261	144	13	eigensubspaces	eigensubspace	NOUN
ap-1261	144	14	of	of	ADP
ap-1261	144	15	matrix	matrix	NOUN
ap-1261	144	16	rg	rg	NOUN
ap-1261	144	17	,	,	PUNCT
ap-1261	144	18	i.e.	i.e.	X
ap-1261	144	19	rgvλ	rgvλ	NOUN
ap-1261	144	20	=	=	PUNCT
ap-1261	144	21	λvλ	λvλ	NOUN
ap-1261	144	22	for	for	ADP
ap-1261	144	23	all	all	DET
ap-1261	144	24	vλ	vλ	ADP
ap-1261	144	25	∈	∈	NOUN
ap-1261	144	26	vλ	vλ	INTJ
ap-1261	144	27	.	.	PUNCT
ap-1261	145	1	we	we	PRON
ap-1261	145	2	will	will	AUX
ap-1261	145	3	show	show	VERB
ap-1261	145	4	that	that	SCONJ
ap-1261	145	5	this	this	DET
ap-1261	145	6	decomposition	decomposition	NOUN
ap-1261	145	7	is	be	AUX
ap-1261	145	8	exactly	exactly	ADV
ap-1261	145	9	the	the	DET
ap-1261	145	10	decomposition	decomposition	NOUN
ap-1261	145	11	required	require	VERB
ap-1261	145	12	in	in	ADP
ap-1261	145	13	definition	definition	NOUN
ap-1261	145	14	2.1	2.1	NUM
ap-1261	145	15	.	.	PUNCT
ap-1261	146	1	let	let	VERB
ap-1261	146	2	us	we	PRON
ap-1261	146	3	consider	consider	VERB
ap-1261	146	4	some	some	DET
ap-1261	146	5	μ	μ	NUM
ap-1261	146	6	∈	∈	PROPN
ap-1261	146	7	σ(g	σ(g	NOUN
ap-1261	146	8	)	)	PUNCT
ap-1261	146	9	so	so	SCONJ
ap-1261	146	10	that	that	SCONJ
ap-1261	146	11	g(xμ	g(xμ	ADV
ap-1261	146	12	)	)	PUNCT
ap-1261	146	13	=	=	PUNCT
ap-1261	146	14	μxμ	μxμ	VERB
ap-1261	146	15	for	for	ADP
ap-1261	146	16	all	all	PRON
ap-1261	146	17	xμ	xμ	PROPN
ap-1261	146	18	∈	∈	PROPN
ap-1261	146	19	lμ	lμ	PROPN
ap-1261	146	20	.	.	PUNCT
ap-1261	147	1	relation	relation	NOUN
ap-1261	147	2	(	(	PUNCT
ap-1261	147	3	10	10	NUM
ap-1261	147	4	)	)	PUNCT
ap-1261	147	5	for	for	ADP
ap-1261	147	6	x	x	SYM
ap-1261	147	7	=	=	PUNCT
ap-1261	147	8	xμ	xμ	PROPN
ap-1261	147	9	leads	lead	VERB
ap-1261	147	10	to	to	ADP
ap-1261	147	11	the	the	DET
ap-1261	147	12	matrix	matrix	NOUN
ap-1261	147	13	relation	relation	NOUN
ap-1261	147	14	r(g(xμ))rg	r(g(xμ))rg	PROPN
ap-1261	147	15	=	=	PUNCT
ap-1261	147	16	r(μxμ)rg	r(μxμ)rg	PROPN
ap-1261	147	17	=	=	SYM
ap-1261	147	18	μ	μ	NOUN
ap-1261	147	19	r(xμ)rg	r(xμ)rg	NOUN
ap-1261	147	20	=	=	SYM
ap-1261	147	21	rgr(xμ	rgr(xμ	X
ap-1261	147	22	)	)	PUNCT
ap-1261	147	23	which	which	PRON
ap-1261	147	24	acts	act	VERB
ap-1261	147	25	on	on	ADP
ap-1261	147	26	a	a	DET
ap-1261	147	27	column	column	NOUN
ap-1261	147	28	vector	vector	NOUN
ap-1261	147	29	vλ	vλ	INTJ
ap-1261	147	30	∈	∈	PROPN
ap-1261	147	31	vλ	vλ	INTJ
ap-1261	147	32	as	as	ADP
ap-1261	147	33	μλ	μλ	NOUN
ap-1261	147	34	r(xμ)vλ	r(xμ)vλ	NOUN
ap-1261	147	35	=	=	SYM
ap-1261	147	36	rgr(xμ)vλ	rgr(xμ)vλ	PROPN
ap-1261	147	37	.	.	PUNCT
ap-1261	148	1	the	the	DET
ap-1261	148	2	last	last	ADJ
ap-1261	148	3	equality	equality	NOUN
ap-1261	148	4	means	mean	VERB
ap-1261	148	5	that	that	SCONJ
ap-1261	148	6	the	the	DET
ap-1261	148	7	column	column	NOUN
ap-1261	148	8	r(xμ)vλ	r(xμ)vλ	NOUN
ap-1261	148	9	is	be	AUX
ap-1261	148	10	either	either	CCONJ
ap-1261	148	11	zero	zero	NUM
ap-1261	148	12	or	or	CCONJ
ap-1261	148	13	it	it	PRON
ap-1261	148	14	is	be	AUX
ap-1261	148	15	an	an	DET
ap-1261	148	16	eigenvector	eigenvector	NOUN
ap-1261	148	17	of	of	ADP
ap-1261	148	18	matrix	matrix	NOUN
ap-1261	148	19	rg	rg	NOUN
ap-1261	148	20	corresponding	correspond	VERB
ap-1261	148	21	to	to	ADP
ap-1261	148	22	eigenvalue	eigenvalue	PROPN
ap-1261	148	23	μ	μ	PROPN
ap-1261	148	24	λ	λ	PROPN
ap-1261	148	25	.	.	PUNCT
ap-1261	148	26	therefore	therefore	ADV
ap-1261	148	27	r(xμ)vλ	r(xμ)vλ	PROPN
ap-1261	148	28	⊂	⊂	PROPN
ap-1261	148	29	vμλ	vμλ	PROPN
ap-1261	148	30	for	for	ADP
ap-1261	148	31	any	any	DET
ap-1261	148	32	λ	λ	PROPN
ap-1261	148	33	,	,	PUNCT
ap-1261	148	34	μ	μ	PROPN
ap-1261	148	35	∈	∈	PROPN
ap-1261	148	36	g	g	NOUN
ap-1261	148	37	and	and	CCONJ
ap-1261	148	38	any	any	DET
ap-1261	148	39	xμ	xμ	NOUN
ap-1261	149	1	∈	∈	PROPN
ap-1261	150	1	lμ	lμ	ADP
ap-1261	150	2	.	.	PUNCT
ap-1261	151	1	this	this	PRON
ap-1261	151	2	is	be	AUX
ap-1261	151	3	relation	relation	NOUN
ap-1261	151	4	(	(	PUNCT
ap-1261	151	5	5	5	NUM
ap-1261	151	6	)	)	PUNCT
ap-1261	151	7	written	write	VERB
ap-1261	151	8	in	in	ADP
ap-1261	151	9	the	the	DET
ap-1261	151	10	multiplicative	multiplicative	ADJ
ap-1261	151	11	form	form	NOUN
ap-1261	151	12	.	.	PUNCT
ap-1261	152	1	of	of	ADP
ap-1261	152	2	course	course	NOUN
ap-1261	152	3	,	,	PUNCT
ap-1261	152	4	our	our	PRON
ap-1261	152	5	multiplicative	multiplicative	ADJ
ap-1261	152	6	group	group	NOUN
ap-1261	152	7	g	g	PROPN
ap-1261	152	8	defined	define	VERB
ap-1261	152	9	in	in	ADP
ap-1261	152	10	(	(	PUNCT
ap-1261	152	11	9	9	NUM
ap-1261	152	12	)	)	PUNCT
ap-1261	152	13	is	be	AUX
ap-1261	152	14	isomorphic	isomorphic	ADJ
ap-1261	152	15	to	to	ADP
ap-1261	152	16	the	the	DET
ap-1261	152	17	additive	additive	ADJ
ap-1261	152	18	group	group	NOUN
ap-1261	152	19	zk	zk	PROPN
ap-1261	152	20	.	.	PUNCT
ap-1261	153	1	we	we	PRON
ap-1261	153	2	have	have	AUX
ap-1261	153	3	seen	see	VERB
ap-1261	153	4	that	that	DET
ap-1261	153	5	matrix	matrix	NOUN
ap-1261	153	6	rg	rg	NOUN
ap-1261	153	7	with	with	ADP
ap-1261	153	8	the	the	DET
ap-1261	153	9	properties	property	NOUN
ap-1261	153	10	(	(	PUNCT
ap-1261	153	11	10	10	NUM
ap-1261	153	12	)	)	PUNCT
ap-1261	153	13	and	and	CCONJ
ap-1261	153	14	(	(	PUNCT
ap-1261	153	15	11	11	NUM
ap-1261	153	16	)	)	PUNCT
ap-1261	153	17	guarantees	guarantee	VERB
ap-1261	153	18	the	the	DET
ap-1261	153	19	compatibility	compatibility	NOUN
ap-1261	153	20	of	of	ADP
ap-1261	153	21	grading	grade	VERB
ap-1261	153	22	of	of	ADP
ap-1261	153	23	l	l	NOUN
ap-1261	153	24	with	with	ADP
ap-1261	153	25	the	the	DET
ap-1261	153	26	representation	representation	NOUN
ap-1261	153	27	of	of	ADP
ap-1261	153	28	the	the	DET
ap-1261	153	29	lie	lie	NOUN
ap-1261	153	30	algebra	algebra	PROPN
ap-1261	153	31	l.	l.	NOUN
ap-1261	153	32	such	such	ADJ
ap-1261	153	33	matrix	matrix	NOUN
ap-1261	153	34	rg	rg	X
ap-1261	153	35	will	will	AUX
ap-1261	153	36	be	be	AUX
ap-1261	153	37	called	call	VERB
ap-1261	153	38	the	the	DET
ap-1261	153	39	simulation	simulation	NOUN
ap-1261	153	40	matrix	matrix	NOUN
ap-1261	153	41	of	of	ADP
ap-1261	153	42	automorphism	automorphism	NOUN
ap-1261	153	43	g.	g.	NOUN
ap-1261	153	44	matrix	matrix	NOUN
ap-1261	153	45	rg	rg	PROPN
ap-1261	153	46	depends	depend	VERB
ap-1261	153	47	on	on	ADP
ap-1261	153	48	the	the	DET
ap-1261	153	49	chosen	choose	VERB
ap-1261	153	50	automorphism	automorphism	NOUN
ap-1261	153	51	g	g	PROPN
ap-1261	153	52	and	and	CCONJ
ap-1261	153	53	on	on	ADP
ap-1261	153	54	the	the	DET
ap-1261	153	55	chosen	choose	VERB
ap-1261	153	56	representation	representation	NOUN
ap-1261	153	57	r.	r.	NOUN
ap-1261	153	58	the	the	DET
ap-1261	153	59	idea	idea	NOUN
ap-1261	153	60	for	for	ADP
ap-1261	153	61	finding	find	VERB
ap-1261	153	62	the	the	DET
ap-1261	153	63	simulation	simulation	NOUN
ap-1261	153	64	matrix	matrix	NOUN
ap-1261	153	65	is	be	AUX
ap-1261	153	66	more	more	ADV
ap-1261	153	67	straightforward	straightforward	ADJ
ap-1261	153	68	if	if	SCONJ
ap-1261	153	69	g	g	PROPN
ap-1261	153	70	∈	∈	PROPN
ap-1261	153	71	aut	aut	PROPN
ap-1261	153	72	l	l	NOUN
ap-1261	153	73	is	be	AUX
ap-1261	153	74	an	an	DET
ap-1261	153	75	inner	inner	ADJ
ap-1261	153	76	automorphism	automorphism	NOUN
ap-1261	153	77	.	.	PUNCT
ap-1261	154	1	in	in	ADP
ap-1261	154	2	this	this	DET
ap-1261	154	3	case	case	NOUN
ap-1261	154	4	it	it	PRON
ap-1261	154	5	is	be	AUX
ap-1261	154	6	natural	natural	ADJ
ap-1261	154	7	to	to	PART
ap-1261	154	8	search	search	VERB
ap-1261	154	9	for	for	ADP
ap-1261	154	10	rg	rg	PRON
ap-1261	154	11	among	among	ADP
ap-1261	154	12	matrices	matrix	NOUN
ap-1261	154	13	in	in	ADP
ap-1261	154	14	the	the	DET
ap-1261	154	15	representation	representation	NOUN
ap-1261	154	16	of	of	ADP
ap-1261	154	17	the	the	DET
ap-1261	154	18	corresponding	corresponding	ADJ
ap-1261	154	19	lie	lie	NOUN
ap-1261	154	20	group	group	NOUN
ap-1261	154	21	.	.	PUNCT
ap-1261	155	1	this	this	DET
ap-1261	155	2	idea	idea	NOUN
ap-1261	155	3	was	be	AUX
ap-1261	155	4	already	already	ADV
ap-1261	155	5	presented	present	VERB
ap-1261	155	6	in	in	ADP
ap-1261	155	7	[	[	X
ap-1261	155	8	11	11	NUM
ap-1261	155	9	]	]	PUNCT
ap-1261	155	10	and	and	CCONJ
ap-1261	155	11	[	[	X
ap-1261	155	12	15	15	NUM
ap-1261	155	13	]	]	X
ap-1261	155	14	,	,	PUNCT
ap-1261	155	15	where	where	SCONJ
ap-1261	155	16	rg	rg	PROPN
ap-1261	155	17	was	be	AUX
ap-1261	155	18	a	a	DET
ap-1261	155	19	representation	representation	NOUN
ap-1261	155	20	of	of	ADP
ap-1261	155	21	an	an	DET
ap-1261	155	22	element	element	NOUN
ap-1261	155	23	of	of	ADP
ap-1261	155	24	finite	finite	ADJ
ap-1261	155	25	order	order	NOUN
ap-1261	156	1	[	[	X
ap-1261	156	2	9	9	NUM
ap-1261	156	3	]	]	PUNCT
ap-1261	156	4	.	.	PUNCT
ap-1261	157	1	nevertheless	nevertheless	ADV
ap-1261	157	2	,	,	PUNCT
ap-1261	157	3	we	we	PRON
ap-1261	157	4	show	show	VERB
ap-1261	157	5	that	that	SCONJ
ap-1261	157	6	it	it	PRON
ap-1261	157	7	is	be	AUX
ap-1261	157	8	also	also	ADV
ap-1261	157	9	possible	possible	ADJ
ap-1261	157	10	to	to	PART
ap-1261	157	11	find	find	VERB
ap-1261	157	12	the	the	DET
ap-1261	157	13	simulation	simulation	NOUN
ap-1261	157	14	matrix	matrix	NOUN
ap-1261	157	15	rg	rg	X
ap-1261	157	16	even	even	ADV
ap-1261	157	17	for	for	ADP
ap-1261	157	18	an	an	DET
ap-1261	157	19	outer	outer	ADJ
ap-1261	157	20	automorphism	automorphism	NOUN
ap-1261	157	21	g.	g.	NOUN
ap-1261	157	22	in	in	ADP
ap-1261	157	23	the	the	DET
ap-1261	157	24	sequel	sequel	NOUN
ap-1261	157	25	,	,	PUNCT
ap-1261	157	26	we	we	PRON
ap-1261	157	27	will	will	AUX
ap-1261	157	28	concentrate	concentrate	VERB
ap-1261	157	29	on	on	ADP
ap-1261	157	30	the	the	DET
ap-1261	157	31	lie	lie	NOUN
ap-1261	157	32	algebras	algebras	PROPN
ap-1261	157	33	sl(n	sl(n	PROPN
ap-1261	157	34	,	,	PUNCT
ap-1261	157	35	c	c	NOUN
ap-1261	157	36	)	)	PUNCT
ap-1261	157	37	.	.	PUNCT
ap-1261	158	1	the	the	DET
ap-1261	158	2	reason	reason	NOUN
ap-1261	158	3	is	be	AUX
ap-1261	158	4	that	that	SCONJ
ap-1261	158	5	these	these	DET
ap-1261	158	6	algebras	algebra	NOUN
ap-1261	158	7	(	(	PUNCT
ap-1261	158	8	with	with	ADP
ap-1261	158	9	the	the	DET
ap-1261	158	10	exception	exception	NOUN
ap-1261	158	11	of	of	ADP
ap-1261	158	12	o(8	o(8	PROPN
ap-1261	158	13	,	,	PUNCT
ap-1261	158	14	c	c	NOUN
ap-1261	158	15	)	)	PUNCT
ap-1261	158	16	)	)	PUNCT
ap-1261	158	17	are	be	AUX
ap-1261	158	18	the	the	DET
ap-1261	158	19	only	only	ADJ
ap-1261	158	20	simple	simple	ADJ
ap-1261	158	21	classical	classical	ADJ
ap-1261	158	22	lie	lie	NOUN
ap-1261	158	23	algebras	algebra	NOUN
ap-1261	158	24	over	over	ADP
ap-1261	158	25	c	c	PROPN
ap-1261	158	26	for	for	ADP
ap-1261	158	27	which	which	PRON
ap-1261	158	28	the	the	DET
ap-1261	158	29	group	group	NOUN
ap-1261	158	30	of	of	ADP
ap-1261	158	31	automorphisms	automorphisms	PROPN
ap-1261	158	32	contains	contain	VERB
ap-1261	158	33	an	an	DET
ap-1261	158	34	outer	outer	ADJ
ap-1261	158	35	automorphism	automorphism	NOUN
ap-1261	158	36	as	as	ADP
ap-1261	158	37	well	well	ADV
ap-1261	158	38	[	[	X
ap-1261	158	39	7	7	NUM
ap-1261	158	40	]	]	PUNCT
ap-1261	158	41	.	.	PUNCT
ap-1261	159	1	3	3	NUM
ap-1261	159	2	representations	representation	NOUN
ap-1261	159	3	of	of	ADP
ap-1261	159	4	sl(n	sl(n	ADJ
ap-1261	159	5	,	,	PUNCT
ap-1261	159	6	c	c	NOUN
ap-1261	159	7	)	)	PUNCT
ap-1261	159	8	compatible	compatible	ADJ
ap-1261	159	9	with	with	ADP
ap-1261	159	10	z2	z2	NOUN
ap-1261	159	11	-	-	PUNCT
ap-1261	159	12	grading	grading	NOUN
ap-1261	159	13	we	we	PRON
ap-1261	159	14	will	will	AUX
ap-1261	159	15	identify	identify	VERB
ap-1261	159	16	the	the	DET
ap-1261	159	17	lie	lie	NOUN
ap-1261	159	18	algebra	algebra	PROPN
ap-1261	159	19	sl(n	sl(n	NOUN
ap-1261	159	20	,	,	PUNCT
ap-1261	159	21	c	c	NOUN
ap-1261	159	22	)	)	PUNCT
ap-1261	159	23	with	with	ADP
ap-1261	159	24	{	{	PUNCT
ap-1261	159	25	x	x	SYM
ap-1261	159	26	∈	∈	PROPN
ap-1261	159	27	cn×n	cn×n	NOUN
ap-1261	159	28	|	|	NOUN
ap-1261	159	29	trx	trx	NOUN
ap-1261	159	30	=	=	SYM
ap-1261	159	31	0	0	NUM
ap-1261	159	32	}	}	PUNCT
ap-1261	159	33	.	.	PUNCT
ap-1261	160	1	any	any	DET
ap-1261	160	2	z2	z2	NOUN
ap-1261	160	3	-	-	PUNCT
ap-1261	160	4	grading	grading	NOUN
ap-1261	160	5	of	of	ADP
ap-1261	160	6	it	it	PRON
ap-1261	160	7	is	be	AUX
ap-1261	160	8	uniquely	uniquely	ADV
ap-1261	160	9	related	relate	VERB
ap-1261	160	10	to	to	ADP
ap-1261	160	11	an	an	DET
ap-1261	160	12	automorphism	automorphism	NOUN
ap-1261	160	13	of	of	ADP
ap-1261	160	14	order	order	NOUN
ap-1261	160	15	2	2	X
ap-1261	160	16	.	.	PUNCT
ap-1261	161	1	let	let	VERB
ap-1261	161	2	us	we	PRON
ap-1261	161	3	therefore	therefore	ADV
ap-1261	161	4	recall	recall	VERB
ap-1261	161	5	the	the	DET
ap-1261	161	6	structure	structure	NOUN
ap-1261	161	7	of	of	ADP
ap-1261	161	8	aut	aut	PROPN
ap-1261	161	9	sl(n	sl(n	PUNCT
ap-1261	161	10	,	,	PUNCT
ap-1261	161	11	c	c	NOUN
ap-1261	161	12	)	)	PUNCT
ap-1261	161	13	as	as	SCONJ
ap-1261	161	14	described	describe	VERB
ap-1261	161	15	in	in	ADP
ap-1261	161	16	[	[	X
ap-1261	161	17	7	7	NUM
ap-1261	161	18	]	]	SYM
ap-1261	161	19	:	:	PUNCT
ap-1261	161	20	1	1	X
ap-1261	161	21	.	.	X
ap-1261	161	22	for	for	ADP
ap-1261	161	23	any	any	DET
ap-1261	161	24	inner	inner	ADJ
ap-1261	161	25	automorphism	automorphism	NOUN
ap-1261	161	26	g	g	NOUN
ap-1261	161	27	there	there	PRON
ap-1261	161	28	exists	exist	VERB
ap-1261	161	29	a	a	DET
ap-1261	161	30	matrix	matrix	NOUN
ap-1261	161	31	a	a	DET
ap-1261	161	32	∈	∈	PROPN
ap-1261	161	33	sl(n	sl(n	NOUN
ap-1261	161	34	,	,	PUNCT
ap-1261	161	35	c	c	NOUN
ap-1261	161	36	)	)	PUNCT
ap-1261	161	37	:	:	PUNCT
ap-1261	162	1	=	=	X
ap-1261	162	2	{	{	PUNCT
ap-1261	162	3	a	a	DET
ap-1261	162	4	∈	∈	NOUN
ap-1261	162	5	c	c	NOUN
ap-1261	162	6	n×n	n×n	PROPN
ap-1261	162	7	|	|	ADV
ap-1261	162	8	deta	deta	NOUN
ap-1261	162	9	=	=	NOUN
ap-1261	162	10	1	1	NUM
ap-1261	162	11	}	}	PUNCT
ap-1261	162	12	such	such	ADJ
ap-1261	162	13	that	that	SCONJ
ap-1261	162	14	g(x	g(x	NOUN
ap-1261	162	15	)	)	PUNCT
ap-1261	162	16	=	=	SYM
ap-1261	162	17	adax	adax	NOUN
ap-1261	162	18	=	=	SYM
ap-1261	162	19	axa−1	axa−1	PROPN
ap-1261	162	20	for	for	ADP
ap-1261	162	21	any	any	DET
ap-1261	162	22	x	x	SYM
ap-1261	162	23	∈	∈	PROPN
ap-1261	162	24	sl(n	sl(n	NOUN
ap-1261	162	25	,	,	PUNCT
ap-1261	162	26	c	c	NOUN
ap-1261	162	27	)	)	PUNCT
ap-1261	162	28	;	;	PUNCT
ap-1261	162	29	2	2	X
ap-1261	162	30	.	.	X
ap-1261	162	31	the	the	DET
ap-1261	162	32	mapping	mapping	NOUN
ap-1261	162	33	given	give	VERB
ap-1261	162	34	by	by	ADP
ap-1261	162	35	the	the	DET
ap-1261	162	36	prescription	prescription	NOUN
ap-1261	162	37	outix	outix	NOUN
ap-1261	162	38	:	:	PUNCT
ap-1261	162	39	=	=	SYM
ap-1261	162	40	−xt	−xt	X
ap-1261	162	41	for	for	ADP
ap-1261	162	42	any	any	DET
ap-1261	162	43	x	x	SYM
ap-1261	162	44	∈	∈	PROPN
ap-1261	162	45	sl(n	sl(n	NOUN
ap-1261	162	46	,	,	PUNCT
ap-1261	162	47	c	c	NOUN
ap-1261	162	48	)	)	PUNCT
ap-1261	162	49	is	be	AUX
ap-1261	162	50	an	an	DET
ap-1261	162	51	outer	outer	ADJ
ap-1261	162	52	automorphism	automorphism	NOUN
ap-1261	162	53	of	of	ADP
ap-1261	162	54	order	order	NOUN
ap-1261	162	55	2	2	NUM
ap-1261	162	56	;	;	PUNCT
ap-1261	162	57	3	3	NUM
ap-1261	162	58	.	.	X
ap-1261	162	59	any	any	DET
ap-1261	162	60	outer	outer	ADJ
ap-1261	162	61	automorphism	automorphism	NOUN
ap-1261	162	62	g	g	NOUN
ap-1261	162	63	is	be	AUX
ap-1261	162	64	a	a	DET
ap-1261	162	65	composition	composition	NOUN
ap-1261	162	66	of	of	ADP
ap-1261	162	67	an	an	DET
ap-1261	162	68	inner	inner	ADJ
ap-1261	162	69	automorphism	automorphism	NOUN
ap-1261	162	70	and	and	CCONJ
ap-1261	162	71	the	the	DET
ap-1261	162	72	automorphism	automorphism	NOUN
ap-1261	162	73	outi	outi	NOUN
ap-1261	162	74	.	.	PUNCT
ap-1261	163	1	4	4	X
ap-1261	163	2	.	.	X
ap-1261	163	3	to	to	ADP
ap-1261	163	4	any	any	DET
ap-1261	163	5	outer	outer	ADJ
ap-1261	163	6	automorphism	automorphism	NOUN
ap-1261	163	7	outa	outa	ADJ
ap-1261	163	8	of	of	ADP
ap-1261	163	9	order	order	NOUN
ap-1261	163	10	two	two	NUM
ap-1261	163	11	there	there	ADV
ap-1261	163	12	exists	exist	VERB
ap-1261	163	13	an	an	DET
ap-1261	163	14	inner	inner	ADJ
ap-1261	163	15	automorphism	automorphism	NOUN
ap-1261	163	16	adp	adp	PROPN
ap-1261	163	17	such	such	ADJ
ap-1261	163	18	that	that	SCONJ
ap-1261	163	19	ad−1p	ad−1p	NOUN
ap-1261	163	20	outaadp	outaadp	NOUN
ap-1261	163	21	=	=	SYM
ap-1261	163	22	outp	outp	PROPN
ap-1261	164	1	t	t	X
ap-1261	164	2	ap	ap	PROPN
ap-1261	165	1	=	=	PROPN
ap-1261	165	2	outi	outi	PROPN
ap-1261	165	3	,	,	PUNCT
ap-1261	165	4	i.e.	i.e.	X
ap-1261	165	5	outa	outa	ADJ
ap-1261	165	6	and	and	CCONJ
ap-1261	165	7	outi	outi	NOUN
ap-1261	165	8	are	be	AUX
ap-1261	165	9	equivalent	equivalent	ADJ
ap-1261	165	10	(	(	PUNCT
ap-1261	165	11	see	see	VERB
ap-1261	165	12	[	[	X
ap-1261	165	13	6	6	NUM
ap-1261	165	14	]	]	PUNCT
ap-1261	165	15	,	,	PUNCT
ap-1261	165	16	lemma	lemma	PROPN
ap-1261	165	17	a.1	a.1	PROPN
ap-1261	165	18	)	)	PUNCT
ap-1261	165	19	.	.	PUNCT
ap-1261	166	1	34	34	NUM
ap-1261	166	2	acta	acta	PROPN
ap-1261	166	3	polytechnica	polytechnica	PROPN
ap-1261	166	4	vol	vol	NOUN
ap-1261	166	5	.	.	PROPN
ap-1261	167	1	50	50	NUM
ap-1261	167	2	no	no	NOUN
ap-1261	167	3	.	.	PUNCT
ap-1261	168	1	5/2010	5/2010	NUM
ap-1261	168	2	the	the	DET
ap-1261	168	3	next	next	ADJ
ap-1261	168	4	ingredient	ingredient	NOUN
ap-1261	168	5	for	for	ADP
ap-1261	168	6	the	the	DET
ap-1261	168	7	construction	construction	NOUN
ap-1261	168	8	of	of	ADP
ap-1261	168	9	simulation	simulation	NOUN
ap-1261	168	10	matrices	matrix	NOUN
ap-1261	168	11	of	of	ADP
ap-1261	168	12	automorphisms	automorphisms	PROPN
ap-1261	168	13	is	be	AUX
ap-1261	168	14	the	the	DET
ap-1261	168	15	knowledge	knowledge	NOUN
ap-1261	168	16	of	of	ADP
ap-1261	168	17	finitedimensional	finitedimensional	ADJ
ap-1261	168	18	irreducible	irreducible	ADJ
ap-1261	168	19	representations	representation	NOUN
ap-1261	168	20	of	of	ADP
ap-1261	168	21	sl(n	sl(n	ADJ
ap-1261	168	22	,	,	PUNCT
ap-1261	168	23	c	c	NOUN
ap-1261	168	24	)	)	PUNCT
ap-1261	168	25	.	.	PUNCT
ap-1261	169	1	these	these	DET
ap-1261	169	2	representations	representation	NOUN
ap-1261	169	3	are	be	AUX
ap-1261	169	4	well	well	ADV
ap-1261	169	5	described	describe	VERB
ap-1261	169	6	by	by	ADP
ap-1261	169	7	gel’fand	gel’fand	NOUN
ap-1261	169	8	-	-	PUNCT
ap-1261	169	9	tseitlin	tseitlin	NOUN
ap-1261	169	10	formalism	formalism	NOUN
ap-1261	169	11	[	[	X
ap-1261	169	12	4	4	NUM
ap-1261	169	13	,	,	PUNCT
ap-1261	169	14	10	10	NUM
ap-1261	169	15	,	,	PUNCT
ap-1261	169	16	2	2	NUM
ap-1261	169	17	]	]	PUNCT
ap-1261	169	18	.	.	PUNCT
ap-1261	170	1	any	any	DET
ap-1261	170	2	irreducible	irreducible	ADJ
ap-1261	170	3	representation	representation	NOUN
ap-1261	170	4	r	r	NOUN
ap-1261	170	5	of	of	ADP
ap-1261	170	6	sl(n	sl(n	ADJ
ap-1261	170	7	,	,	PUNCT
ap-1261	170	8	c	c	X
ap-1261	170	9	)	)	PUNCT
ap-1261	170	10	is	be	AUX
ap-1261	170	11	in	in	ADP
ap-1261	170	12	one	one	NUM
ap-1261	170	13	-	-	PUNCT
ap-1261	170	14	to	to	ADP
ap-1261	170	15	-	-	PUNCT
ap-1261	170	16	one	one	NUM
ap-1261	170	17	correspondence	correspondence	NOUN
ap-1261	170	18	with	with	ADP
ap-1261	170	19	an	an	DET
ap-1261	170	20	n	n	CCONJ
ap-1261	170	21	-	-	PUNCT
ap-1261	170	22	tuple	tuple	NOUN
ap-1261	170	23	(	(	PUNCT
ap-1261	170	24	m1,n	m1,n	PROPN
ap-1261	170	25	,	,	PUNCT
ap-1261	170	26	m2,n	m2,n	PROPN
ap-1261	170	27	,	,	PUNCT
ap-1261	170	28	.	.	PUNCT
ap-1261	170	29	.	.	PUNCT
ap-1261	171	1	.	.	PUNCT
ap-1261	172	1	,	,	PUNCT
ap-1261	172	2	mn	mn	PROPN
ap-1261	172	3	,	,	PUNCT
ap-1261	172	4	n	n	CCONJ
ap-1261	172	5	)	)	PUNCT
ap-1261	172	6	of	of	ADP
ap-1261	172	7	non	non	ADJ
ap-1261	172	8	-	-	ADJ
ap-1261	172	9	negative	negative	ADJ
ap-1261	172	10	integer	integer	NOUN
ap-1261	172	11	parameters	parameter	NOUN
ap-1261	172	12	m1,n	m1,n	PROPN
ap-1261	172	13	≥	≥	NUM
ap-1261	172	14	m2,n	m2,n	PROPN
ap-1261	172	15	≥	≥	NOUN
ap-1261	172	16	.	.	PUNCT
ap-1261	172	17	.	.	PUNCT
ap-1261	173	1	.	.	PUNCT
ap-1261	174	1	≥	≥	PROPN
ap-1261	174	2	mn	mn	PROPN
ap-1261	174	3	,	,	PUNCT
ap-1261	174	4	n	n	NOUN
ap-1261	174	5	=	=	SYM
ap-1261	174	6	0	0	NUM
ap-1261	174	7	.	.	PUNCT
ap-1261	175	1	the	the	DET
ap-1261	175	2	dimension	dimension	NOUN
ap-1261	175	3	of	of	ADP
ap-1261	175	4	the	the	DET
ap-1261	175	5	representation	representation	NOUN
ap-1261	175	6	space	space	NOUN
ap-1261	175	7	of	of	ADP
ap-1261	175	8	r	r	NOUN
ap-1261	175	9	=	=	SYM
ap-1261	175	10	r(m1,n	r(m1,n	PROPN
ap-1261	175	11	,	,	PUNCT
ap-1261	175	12	m2,n	m2,n	PROPN
ap-1261	175	13	,	,	PUNCT
ap-1261	175	14	.	.	PUNCT
ap-1261	175	15	.	.	PUNCT
ap-1261	175	16	.	.	PUNCT
ap-1261	176	1	,	,	PUNCT
ap-1261	176	2	mn	mn	PROPN
ap-1261	176	3	,	,	PUNCT
ap-1261	176	4	n	n	CCONJ
ap-1261	176	5	)	)	PUNCT
ap-1261	176	6	is	be	AUX
ap-1261	176	7	given	give	VERB
ap-1261	176	8	by	by	ADP
ap-1261	176	9	the	the	DET
ap-1261	176	10	number	number	NOUN
ap-1261	176	11	of	of	ADP
ap-1261	176	12	triangular	triangular	NOUN
ap-1261	176	13	patterns	pattern	NOUN
ap-1261	176	14	m	m	NOUN
ap-1261	176	15	=	=	SYM
ap-1261	176	16	⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝	⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝	X
ap-1261	176	17	m1,n	m1,n	PROPN
ap-1261	176	18	m2,n	m2,n	PROPN
ap-1261	176	19	m3,n	m3,n	PROPN
ap-1261	176	20	.	.	PUNCT
ap-1261	176	21	.	.	PUNCT
ap-1261	176	22	.	.	PUNCT
ap-1261	177	1	mn	mn	PROPN
ap-1261	177	2	,	,	PUNCT
ap-1261	177	3	n	n	PRON
ap-1261	177	4	m1,n−1	m1,n−1	ADJ
ap-1261	177	5	m2,n−1	m2,n−1	ADJ
ap-1261	177	6	m3,n−1	m3,n−1	NOUN
ap-1261	177	7	.	.	PUNCT
ap-1261	177	8	.	.	PUNCT
ap-1261	177	9	.	.	PUNCT
ap-1261	178	1	mn−1,n−1	mn−1,n−1	ADJ
ap-1261	178	2	m1,n−2	m1,n−2	ADJ
ap-1261	178	3	m2,n−2	m2,n−2	NOUN
ap-1261	178	4	.	.	PUNCT
ap-1261	178	5	.	.	PUNCT
ap-1261	178	6	.	.	PUNCT
ap-1261	179	1	mn−2,n−2	mn−2,n−2	PROPN
ap-1261	179	2	...	...	PUNCT
ap-1261	179	3	...	...	PUNCT
ap-1261	179	4	...	...	PUNCT
ap-1261	180	1	m1,2	m1,2	ADJ
ap-1261	180	2	m2,2	m2,2	PROPN
ap-1261	180	3	m1,1	m1,1	PROPN
ap-1261	180	4	⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠	⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠	PROPN
ap-1261	180	5	in	in	ADP
ap-1261	180	6	which	which	PRON
ap-1261	180	7	the	the	DET
ap-1261	180	8	numbers	number	NOUN
ap-1261	180	9	mi	mi	PROPN
ap-1261	180	10	,	,	PUNCT
ap-1261	180	11	j	j	PROPN
ap-1261	180	12	∈	∈	PROPN
ap-1261	180	13	z	z	PROPN
ap-1261	180	14	satisfy	satisfy	PROPN
ap-1261	180	15	mi	mi	PROPN
ap-1261	180	16	,	,	PUNCT
ap-1261	180	17	j+1	j+1	PROPN
ap-1261	180	18	≥	≥	NUM
ap-1261	180	19	mi	mi	PROPN
ap-1261	180	20	,	,	PUNCT
ap-1261	180	21	j	j	PROPN
ap-1261	180	22	≥	≥	X
ap-1261	180	23	mi+1,j+1	mi+1,j+1	X
ap-1261	180	24	for	for	ADP
ap-1261	180	25	all	all	DET
ap-1261	180	26	1	1	NUM
ap-1261	180	27	≤	≤	NUM
ap-1261	180	28	i	i	PRON
ap-1261	180	29	≤	≤	NUM
ap-1261	180	30	j	j	PROPN
ap-1261	180	31	≤	≤	ADV
ap-1261	180	32	n	n	CCONJ
ap-1261	180	33	−	−	PROPN
ap-1261	180	34	1	1	NUM
ap-1261	180	35	.	.	PUNCT
ap-1261	180	36	to	to	ADP
ap-1261	180	37	any	any	DET
ap-1261	180	38	such	such	ADJ
ap-1261	180	39	pattern	pattern	NOUN
ap-1261	180	40	m	m	PRON
ap-1261	180	41	,	,	PUNCT
ap-1261	180	42	we	we	PRON
ap-1261	180	43	assign	assign	VERB
ap-1261	180	44	the	the	DET
ap-1261	180	45	basis	basis	NOUN
ap-1261	180	46	vector	vector	NOUN
ap-1261	180	47	ξ(m	ξ(m	NOUN
ap-1261	180	48	)	)	PUNCT
ap-1261	180	49	.	.	PUNCT
ap-1261	181	1	the	the	DET
ap-1261	181	2	representation	representation	NOUN
ap-1261	181	3	r	r	NOUN
ap-1261	181	4	is	be	AUX
ap-1261	181	5	fully	fully	ADV
ap-1261	181	6	determined	determine	VERB
ap-1261	181	7	by	by	ADP
ap-1261	181	8	the	the	DET
ap-1261	181	9	action	action	NOUN
ap-1261	181	10	r(ek	r(ek	NUM
ap-1261	181	11	)	)	PUNCT
ap-1261	181	12	on	on	ADP
ap-1261	181	13	all	all	DET
ap-1261	181	14	basis	basis	NOUN
ap-1261	181	15	vectors	vector	NOUN
ap-1261	181	16	ξ(m	ξ(m	NOUN
ap-1261	181	17	)	)	PUNCT
ap-1261	181	18	for	for	ADP
ap-1261	181	19	any	any	DET
ap-1261	181	20	k	k	X
ap-1261	181	21	,	,	PUNCT
ap-1261	181	22	�	�	PROPN
ap-1261	181	23	=	=	SYM
ap-1261	181	24	1	1	NUM
ap-1261	181	25	,	,	PUNCT
ap-1261	181	26	2	2	NUM
ap-1261	181	27	,	,	PUNCT
ap-1261	181	28	.	.	PUNCT
ap-1261	181	29	.	.	PUNCT
ap-1261	182	1	.	.	PUNCT
ap-1261	183	1	,	,	PUNCT
ap-1261	183	2	n.	n.	INTJ
ap-1261	183	3	(	(	PUNCT
ap-1261	183	4	we	we	PRON
ap-1261	183	5	have	have	AUX
ap-1261	183	6	adopted	adopt	VERB
ap-1261	183	7	the	the	DET
ap-1261	183	8	notation	notation	NOUN
ap-1261	183	9	ek	ek	NOUN
ap-1261	183	10	for	for	ADP
ap-1261	183	11	n	n	NUM
ap-1261	183	12	×	×	NOUN
ap-1261	183	13	n	n	PRON
ap-1261	183	14	matrices	matrix	NOUN
ap-1261	183	15	with	with	ADP
ap-1261	183	16	elements	element	NOUN
ap-1261	183	17	(	(	PUNCT
ap-1261	183	18	ek	ek	NOUN
ap-1261	183	19	)	)	PUNCT
ap-1261	183	20	ij	ij	NOUN
ap-1261	184	1	=	=	PROPN
ap-1261	184	2	δikδ	δikδ	PROPN
ap-1261	184	3	j	j	PROPN
ap-1261	184	4	.	.	PUNCT
ap-1261	184	5	)	)	PUNCT
ap-1261	185	1	this	this	DET
ap-1261	185	2	action	action	NOUN
ap-1261	185	3	can	can	AUX
ap-1261	185	4	be	be	AUX
ap-1261	185	5	found	find	VERB
ap-1261	185	6	e.g.	e.g.	ADV
ap-1261	185	7	in	in	ADP
ap-1261	185	8	[	[	X
ap-1261	185	9	4	4	NUM
ap-1261	185	10	]	]	PUNCT
ap-1261	185	11	,	,	PUNCT
ap-1261	185	12	but	but	CCONJ
ap-1261	185	13	for	for	ADP
ap-1261	185	14	the	the	DET
ap-1261	185	15	reader	reader	NOUN
ap-1261	185	16	’s	’s	PART
ap-1261	185	17	convenience	convenience	VERB
ap-1261	185	18	the	the	DET
ap-1261	185	19	representation	representation	NOUN
ap-1261	185	20	of	of	ADP
ap-1261	185	21	gl(n	gl(n	PROPN
ap-1261	185	22	,	,	PUNCT
ap-1261	185	23	c	c	X
ap-1261	185	24	)	)	PUNCT
ap-1261	185	25	is	be	AUX
ap-1261	185	26	described	describe	VERB
ap-1261	185	27	in	in	ADP
ap-1261	185	28	the	the	DET
ap-1261	185	29	appendix	appendix	NOUN
ap-1261	185	30	.	.	PUNCT
ap-1261	186	1	3.1	3.1	NUM
ap-1261	186	2	inner	inner	ADJ
ap-1261	186	3	automorphisms	automorphism	NOUN
ap-1261	186	4	of	of	ADP
ap-1261	186	5	order	order	NOUN
ap-1261	186	6	two	two	NUM
ap-1261	186	7	any	any	DET
ap-1261	186	8	inner	inner	ADJ
ap-1261	186	9	automorphism	automorphism	NOUN
ap-1261	186	10	g	g	NOUN
ap-1261	186	11	of	of	ADP
ap-1261	186	12	order	order	NOUN
ap-1261	186	13	two	two	NUM
ap-1261	186	14	is	be	AUX
ap-1261	186	15	associated	associate	VERB
ap-1261	186	16	by	by	ADP
ap-1261	186	17	the	the	DET
ap-1261	186	18	equality	equality	NOUN
ap-1261	186	19	g	g	PROPN
ap-1261	186	20	=	=	PROPN
ap-1261	186	21	ada	ada	PROPN
ap-1261	186	22	with	with	ADP
ap-1261	186	23	a	a	DET
ap-1261	186	24	group	group	NOUN
ap-1261	186	25	element	element	NOUN
ap-1261	186	26	a	a	DET
ap-1261	186	27	∈	∈	PROPN
ap-1261	186	28	sl(n	sl(n	NOUN
ap-1261	186	29	,	,	PUNCT
ap-1261	186	30	c	c	NOUN
ap-1261	186	31	)	)	PUNCT
ap-1261	186	32	such	such	ADJ
ap-1261	186	33	that	that	SCONJ
ap-1261	186	34	a	a	PRON
ap-1261	186	35	does	do	AUX
ap-1261	186	36	not	not	PART
ap-1261	186	37	belong	belong	VERB
ap-1261	186	38	to	to	ADP
ap-1261	186	39	the	the	DET
ap-1261	186	40	center	center	NOUN
ap-1261	186	41	z[sl(n	z[sl(n	PROPN
ap-1261	186	42	,	,	PUNCT
ap-1261	186	43	c	c	NOUN
ap-1261	186	44	)	)	PUNCT
ap-1261	186	45	]	]	PUNCT
ap-1261	186	46	and	and	CCONJ
ap-1261	186	47	a2	a2	PROPN
ap-1261	186	48	belongs	belong	VERB
ap-1261	186	49	to	to	ADP
ap-1261	186	50	the	the	DET
ap-1261	186	51	center	center	NOUN
ap-1261	186	52	.	.	PUNCT
ap-1261	187	1	if	if	SCONJ
ap-1261	187	2	we	we	PRON
ap-1261	187	3	denote	denote	VERB
ap-1261	187	4	ω	ω	NOUN
ap-1261	187	5	=	=	PUNCT
ap-1261	187	6	e	e	X
ap-1261	187	7	iπ	iπ	NOUN
ap-1261	187	8	n	n	ADV
ap-1261	187	9	,	,	PUNCT
ap-1261	187	10	then	then	ADV
ap-1261	187	11	the	the	DET
ap-1261	187	12	center	center	NOUN
ap-1261	187	13	can	can	AUX
ap-1261	187	14	be	be	AUX
ap-1261	187	15	written	write	VERB
ap-1261	187	16	explicitly	explicitly	ADV
ap-1261	187	17	z[sl(n	z[sl(n	ADJ
ap-1261	187	18	,	,	PUNCT
ap-1261	187	19	c	c	NOUN
ap-1261	187	20	)	)	PUNCT
ap-1261	187	21	]	]	PUNCT
ap-1261	188	1	=	=	PUNCT
ap-1261	188	2	{	{	PUNCT
ap-1261	188	3	ω2	ω2	ADJ
ap-1261	188	4	in	in	ADP
ap-1261	188	5	|	|	ADV
ap-1261	188	6	�	�	PROPN
ap-1261	188	7	=	=	SYM
ap-1261	188	8	0	0	NUM
ap-1261	188	9	,	,	PUNCT
ap-1261	188	10	1	1	NUM
ap-1261	188	11	,	,	PUNCT
ap-1261	188	12	.	.	PUNCT
ap-1261	188	13	.	.	PUNCT
ap-1261	188	14	.	.	PUNCT
ap-1261	189	1	,	,	PUNCT
ap-1261	189	2	n−1	n−1	PROPN
ap-1261	189	3	}	}	PUNCT
ap-1261	189	4	.	.	PUNCT
ap-1261	190	1	a	a	DET
ap-1261	190	2	simple	simple	ADJ
ap-1261	190	3	calculation	calculation	NOUN
ap-1261	190	4	shows	show	VERB
ap-1261	190	5	that	that	SCONJ
ap-1261	190	6	any	any	DET
ap-1261	190	7	such	such	ADJ
ap-1261	190	8	element	element	NOUN
ap-1261	190	9	a	a	DET
ap-1261	190	10	∈	∈	PROPN
ap-1261	190	11	sl(n	sl(n	NOUN
ap-1261	190	12	,	,	PUNCT
ap-1261	190	13	c	c	X
ap-1261	190	14	)	)	PUNCT
ap-1261	190	15	is	be	AUX
ap-1261	190	16	up	up	ADP
ap-1261	190	17	to	to	PART
ap-1261	190	18	equivalence	equivalence	NOUN
ap-1261	190	19	one	one	NUM
ap-1261	190	20	of	of	ADP
ap-1261	190	21	the	the	DET
ap-1261	190	22	matrices	matrix	NOUN
ap-1261	190	23	an	an	PRON
ap-1261	190	24	,	,	PUNCT
ap-1261	190	25	s	s	PART
ap-1261	190	26	:	:	PUNCT
ap-1261	190	27	=	=	SYM
ap-1261	190	28	ωη(s	ωη(s	X
ap-1261	190	29	)	)	PUNCT
ap-1261	190	30	(	(	PUNCT
ap-1261	190	31	in−s	in−s	ADJ
ap-1261	190	32	0	0	NUM
ap-1261	190	33	0	0	NUM
ap-1261	190	34	−is	−is	NOUN
ap-1261	190	35	)	)	PUNCT
ap-1261	190	36	where	where	SCONJ
ap-1261	190	37	s	s	VERB
ap-1261	190	38	=	=	NOUN
ap-1261	190	39	1	1	NUM
ap-1261	190	40	,	,	PUNCT
ap-1261	190	41	.	.	PUNCT
ap-1261	190	42	.	.	PUNCT
ap-1261	190	43	.	.	PUNCT
ap-1261	191	1	,	,	PUNCT
ap-1261	191	2	�	�	PROPN
ap-1261	191	3	n	n	CCONJ
ap-1261	191	4	2	2	NUM
ap-1261	191	5	�	�	PROPN
ap-1261	191	6	and	and	CCONJ
ap-1261	191	7	η(s	η(s	PROPN
ap-1261	191	8	)	)	PUNCT
ap-1261	192	1	=	=	PRON
ap-1261	192	2	{	{	PUNCT
ap-1261	192	3	0	0	NUM
ap-1261	192	4	if	if	SCONJ
ap-1261	192	5	s	s	VERB
ap-1261	192	6	is	be	AUX
ap-1261	192	7	even	even	ADV
ap-1261	192	8	1	1	NUM
ap-1261	192	9	if	if	SCONJ
ap-1261	192	10	s	s	VERB
ap-1261	192	11	is	be	AUX
ap-1261	192	12	odd	odd	ADJ
ap-1261	192	13	(	(	PUNCT
ap-1261	192	14	note	note	VERB
ap-1261	192	15	that	that	SCONJ
ap-1261	192	16	an,0	an,0	NOUN
ap-1261	192	17	=	=	PUNCT
ap-1261	192	18	in	in	ADP
ap-1261	192	19	belongs	belong	VERB
ap-1261	192	20	to	to	ADP
ap-1261	192	21	z[sl(n	z[sl(n	PROPN
ap-1261	192	22	,	,	PUNCT
ap-1261	192	23	c	c	NOUN
ap-1261	192	24	)	)	PUNCT
ap-1261	192	25	]	]	PUNCT
ap-1261	192	26	.	.	PUNCT
ap-1261	192	27	)	)	PUNCT
ap-1261	193	1	these	these	DET
ap-1261	193	2	matrices	matrix	NOUN
ap-1261	193	3	may	may	AUX
ap-1261	193	4	be	be	AUX
ap-1261	193	5	rewritten	rewrite	VERB
ap-1261	193	6	by	by	ADP
ap-1261	193	7	using	use	VERB
ap-1261	193	8	elements	element	NOUN
ap-1261	193	9	of	of	ADP
ap-1261	193	10	the	the	DET
ap-1261	193	11	lie	lie	NOUN
ap-1261	193	12	algebra	algebra	PROPN
ap-1261	193	13	sl(n	sl(n	NOUN
ap-1261	193	14	,	,	PUNCT
ap-1261	193	15	c	c	NOUN
ap-1261	193	16	)	)	PUNCT
ap-1261	193	17	as	as	SCONJ
ap-1261	193	18	follows	follow	VERB
ap-1261	193	19	:	:	PUNCT
ap-1261	193	20	an	an	DET
ap-1261	193	21	,	,	PUNCT
ap-1261	193	22	s	s	NOUN
ap-1261	193	23	=	=	NOUN
ap-1261	193	24	exp(xn	exp(xn	X
ap-1261	193	25	,	,	PUNCT
ap-1261	193	26	s	s	PART
ap-1261	193	27	)	)	PUNCT
ap-1261	193	28	with	with	ADP
ap-1261	193	29	xn	xn	PROPN
ap-1261	193	30	,	,	PUNCT
ap-1261	193	31	s	s	PART
ap-1261	193	32	=	=	PUNCT
ap-1261	193	33	iπ	iπ	NOUN
ap-1261	193	34	⎛⎜⎝	⎛⎜⎝	PROPN
ap-1261	193	35	η(s	η(s	PROPN
ap-1261	193	36	)	)	PUNCT
ap-1261	193	37	n	n	CCONJ
ap-1261	193	38	in−s	in−s	ADJ
ap-1261	193	39	0	0	NUM
ap-1261	193	40	0	0	NUM
ap-1261	193	41	η(s	η(	NOUN
ap-1261	193	42	)	)	PUNCT
ap-1261	193	43	n	n	PART
ap-1261	193	44	is	be	AUX
ap-1261	193	45	+	+	ADP
ap-1261	193	46	ms	ms	NOUN
ap-1261	193	47	⎞⎟⎠	⎞⎟⎠	PROPN
ap-1261	193	48	,	,	PUNCT
ap-1261	193	49	where	where	SCONJ
ap-1261	193	50	ms	ms	PROPN
ap-1261	193	51	=	=	PROPN
ap-1261	193	52	diag(−1	diag(−1	PROPN
ap-1261	193	53	,	,	PUNCT
ap-1261	193	54	1	1	NUM
ap-1261	193	55	,	,	PUNCT
ap-1261	193	56	−1	−1	NOUN
ap-1261	193	57	,	,	PUNCT
ap-1261	193	58	.	.	PUNCT
ap-1261	193	59	.	.	PUNCT
ap-1261	194	1	.	.	PUNCT
ap-1261	195	1	,	,	PUNCT
ap-1261	195	2	(	(	PUNCT
ap-1261	195	3	−1)s	−1)s	X
ap-1261	195	4	)	)	PUNCT
ap-1261	195	5	∈	∈	PROPN
ap-1261	195	6	c	c	X
ap-1261	195	7	s×s	s×s	PROPN
ap-1261	195	8	.	.	PUNCT
ap-1261	196	1	one	one	PRON
ap-1261	196	2	can	can	AUX
ap-1261	196	3	use	use	VERB
ap-1261	196	4	the	the	DET
ap-1261	196	5	notation	notation	NOUN
ap-1261	196	6	of	of	ADP
ap-1261	196	7	ekk	ekk	PROPN
ap-1261	196	8	and	and	CCONJ
ap-1261	196	9	write	write	VERB
ap-1261	196	10	xn	xn	PROPN
ap-1261	196	11	,	,	PUNCT
ap-1261	196	12	s	s	PART
ap-1261	196	13	=	=	VERB
ap-1261	196	14	iπ	iπ	INTJ
ap-1261	196	15	(	(	PUNCT
ap-1261	196	16	η(s	η(s	PROPN
ap-1261	196	17	)	)	PUNCT
ap-1261	196	18	n	n	NUM
ap-1261	196	19	n∑	n∑	NOUN
ap-1261	196	20	k=1	k=1	PROPN
ap-1261	197	1	ekk	ekk	PROPN
ap-1261	198	1	+	+	CCONJ
ap-1261	198	2	n∑	n∑	PROPN
ap-1261	198	3	k	k	X
ap-1261	199	1	=	=	NOUN
ap-1261	199	2	n−s+1	n−s+1	PROPN
ap-1261	199	3	(	(	PUNCT
ap-1261	199	4	−1)n−s+1−kekk	−1)n−s+1−kekk	NOUN
ap-1261	199	5	)	)	PUNCT
ap-1261	199	6	.	.	PUNCT
ap-1261	200	1	(	(	PUNCT
ap-1261	200	2	12	12	NUM
ap-1261	200	3	)	)	PUNCT
ap-1261	200	4	if	if	SCONJ
ap-1261	200	5	r	r	NOUN
ap-1261	200	6	is	be	AUX
ap-1261	200	7	any	any	DET
ap-1261	200	8	representation	representation	NOUN
ap-1261	200	9	of	of	ADP
ap-1261	200	10	the	the	DET
ap-1261	200	11	lie	lie	NOUN
ap-1261	200	12	algebra	algebra	PROPN
ap-1261	200	13	sl(n	sl(n	NOUN
ap-1261	200	14	,	,	PUNCT
ap-1261	200	15	c	c	NOUN
ap-1261	200	16	)	)	PUNCT
ap-1261	200	17	,	,	PUNCT
ap-1261	200	18	then	then	ADV
ap-1261	200	19	ran	run	VERB
ap-1261	200	20	,	,	PUNCT
ap-1261	200	21	s	s	PART
ap-1261	200	22	:	:	PUNCT
ap-1261	200	23	=	=	SYM
ap-1261	200	24	exp(r(xn	exp(r(xn	X
ap-1261	200	25	,	,	PUNCT
ap-1261	200	26	s	s	NOUN
ap-1261	200	27	)	)	PUNCT
ap-1261	200	28	)	)	PUNCT
ap-1261	200	29	satisfies	satisfie	NOUN
ap-1261	200	30	ran	run	VERB
ap-1261	200	31	,	,	PUNCT
ap-1261	200	32	sr(x	sr(x	NOUN
ap-1261	200	33	)	)	PUNCT
ap-1261	200	34	(	(	PUNCT
ap-1261	200	35	ran	run	VERB
ap-1261	200	36	,	,	PUNCT
ap-1261	200	37	s	s	PART
ap-1261	200	38	)	)	PUNCT
ap-1261	200	39	−1	−1	NOUN
ap-1261	200	40	=	=	SYM
ap-1261	200	41	r(an	r(an	PROPN
ap-1261	200	42	,	,	PUNCT
ap-1261	200	43	sxa−1	sxa−1	PROPN
ap-1261	200	44	n	n	CCONJ
ap-1261	200	45	,	,	PUNCT
ap-1261	200	46	s	s	PART
ap-1261	200	47	)	)	PUNCT
ap-1261	200	48	=	=	SYM
ap-1261	201	1	r(adan	r(adan	PROPN
ap-1261	201	2	,	,	PUNCT
ap-1261	201	3	sx	sx	PROPN
ap-1261	201	4	)	)	PUNCT
ap-1261	201	5	and	and	CCONJ
ap-1261	201	6	(	(	PUNCT
ap-1261	201	7	ran	run	VERB
ap-1261	201	8	,	,	PUNCT
ap-1261	201	9	s	s	PART
ap-1261	201	10	)	)	PUNCT
ap-1261	201	11	2	2	NUM
ap-1261	201	12	=	=	SYM
ap-1261	201	13	i	i	PROPN
ap-1261	201	14	d	d	PROPN
ap-1261	201	15	.	.	PUNCT
ap-1261	202	1	therefore	therefore	ADV
ap-1261	202	2	,	,	PUNCT
ap-1261	202	3	matrix	matrix	NOUN
ap-1261	202	4	ran	run	VERB
ap-1261	202	5	,	,	PUNCT
ap-1261	202	6	s	s	PART
ap-1261	202	7	is	be	AUX
ap-1261	202	8	the	the	DET
ap-1261	202	9	simulation	simulation	NOUN
ap-1261	202	10	matrix	matrix	NOUN
ap-1261	202	11	of	of	ADP
ap-1261	202	12	the	the	DET
ap-1261	202	13	inner	inner	ADJ
ap-1261	202	14	automorphism	automorphism	NOUN
ap-1261	202	15	g	g	PROPN
ap-1261	202	16	=	=	SYM
ap-1261	202	17	adan	adan	PROPN
ap-1261	202	18	,	,	PUNCT
ap-1261	202	19	s	s	PART
ap-1261	202	20	.	.	PUNCT
ap-1261	203	1	we	we	PRON
ap-1261	203	2	have	have	AUX
ap-1261	203	3	shown	show	VERB
ap-1261	203	4	theorem	theorem	VERB
ap-1261	203	5	3.1	3.1	NUM
ap-1261	203	6	any	any	DET
ap-1261	203	7	z2	z2	NOUN
ap-1261	203	8	-	-	PUNCT
ap-1261	203	9	grading	grading	NOUN
ap-1261	203	10	of	of	ADP
ap-1261	203	11	the	the	DET
ap-1261	203	12	lie	lie	NOUN
ap-1261	203	13	algebra	algebra	PROPN
ap-1261	203	14	sl(n	sl(n	NOUN
ap-1261	203	15	,	,	PUNCT
ap-1261	203	16	c	c	NOUN
ap-1261	203	17	)	)	PUNCT
ap-1261	203	18	obtained	obtain	VERB
ap-1261	203	19	by	by	ADP
ap-1261	203	20	an	an	DET
ap-1261	203	21	inner	inner	ADJ
ap-1261	203	22	automorphism	automorphism	NOUN
ap-1261	203	23	and	and	CCONJ
ap-1261	203	24	any	any	DET
ap-1261	203	25	irreducible	irreducible	ADJ
ap-1261	203	26	representation	representation	NOUN
ap-1261	203	27	of	of	ADP
ap-1261	203	28	sl(n	sl(n	ADJ
ap-1261	203	29	,	,	PUNCT
ap-1261	203	30	c	c	NOUN
ap-1261	203	31	)	)	PUNCT
ap-1261	203	32	are	be	AUX
ap-1261	203	33	compatible	compatible	ADJ
ap-1261	203	34	.	.	PUNCT
ap-1261	204	1	using	use	VERB
ap-1261	204	2	(	(	PUNCT
ap-1261	204	3	12	12	NUM
ap-1261	204	4	)	)	PUNCT
ap-1261	204	5	and	and	CCONJ
ap-1261	204	6	the	the	DET
ap-1261	204	7	explicit	explicit	ADJ
ap-1261	204	8	form	form	NOUN
ap-1261	204	9	of	of	ADP
ap-1261	204	10	the	the	DET
ap-1261	204	11	gel’fand	gel’fand	NOUN
ap-1261	204	12	-	-	PUNCT
ap-1261	204	13	tseitlin	tseitlin	NOUN
ap-1261	204	14	representation	representation	NOUN
ap-1261	204	15	we	we	PRON
ap-1261	204	16	obtain	obtain	VERB
ap-1261	204	17	for	for	ADP
ap-1261	204	18	any	any	DET
ap-1261	204	19	basis	basis	NOUN
ap-1261	204	20	vector	vector	NOUN
ap-1261	204	21	ξ(m	ξ(m	NOUN
ap-1261	204	22	)	)	PUNCT
ap-1261	204	23	r(xn	r(xn	NOUN
ap-1261	204	24	,	,	PUNCT
ap-1261	204	25	s)ξ(m	s)ξ(m	NOUN
ap-1261	204	26	)	)	PUNCT
ap-1261	204	27	=	=	VERB
ap-1261	205	1	iπ	iπ	INTJ
ap-1261	205	2	(	(	PUNCT
ap-1261	205	3	η(s	η(s	PROPN
ap-1261	205	4	)	)	PUNCT
ap-1261	205	5	n	n	PRON
ap-1261	205	6	rn(m	rn(m	NOUN
ap-1261	205	7	)	)	PUNCT
ap-1261	206	1	+	+	CCONJ
ap-1261	206	2	2	2	NUM
ap-1261	206	3	s−1∑	s−1∑	NUM
ap-1261	206	4	k=1	k=1	PUNCT
ap-1261	206	5	(	(	PUNCT
ap-1261	206	6	−1)k−1rn−s+k(m)−	−1)k−1rn−s+k(m)−	PROPN
ap-1261	206	7	rn−s(m)−	rn−s(m)−	PROPN
ap-1261	206	8	(	(	PUNCT
ap-1261	206	9	−1)η(s)rn(m	−1)η(s)rn(m	PROPN
ap-1261	206	10	)	)	PUNCT
ap-1261	206	11	)	)	PUNCT
ap-1261	206	12	ξ(m	ξ(m	NOUN
ap-1261	206	13	)	)	PUNCT
ap-1261	206	14	.	.	PUNCT
ap-1261	207	1	thus	thus	ADV
ap-1261	207	2	we	we	PRON
ap-1261	207	3	have	have	AUX
ap-1261	207	4	arrived	arrive	VERB
ap-1261	207	5	at	at	ADP
ap-1261	207	6	the	the	DET
ap-1261	207	7	explicit	explicit	ADJ
ap-1261	207	8	form	form	NOUN
ap-1261	207	9	of	of	ADP
ap-1261	207	10	the	the	DET
ap-1261	207	11	simulation	simulation	NOUN
ap-1261	207	12	matrix	matrix	NOUN
ap-1261	207	13	of	of	ADP
ap-1261	207	14	the	the	DET
ap-1261	207	15	automorphism	automorphism	NOUN
ap-1261	207	16	g	g	PROPN
ap-1261	207	17	=	=	SYM
ap-1261	207	18	adan	adan	PROPN
ap-1261	207	19	,	,	PUNCT
ap-1261	207	20	s	s	PART
ap-1261	207	21	ran	ran	NOUN
ap-1261	207	22	,	,	PUNCT
ap-1261	207	23	sξ(m	sξ(m	X
ap-1261	207	24	)	)	PUNCT
ap-1261	207	25	=	=	PUNCT
ap-1261	208	1	e	e	X
ap-1261	208	2	iπ	iπ	NOUN
ap-1261	208	3	(	(	PUNCT
ap-1261	208	4	(	(	PUNCT
ap-1261	208	5	η(s	η(s	PROPN
ap-1261	208	6	)	)	PUNCT
ap-1261	208	7	n	n	NUM
ap-1261	208	8	−1	−1	NOUN
ap-1261	208	9	)	)	PUNCT
ap-1261	208	10	rn(m)−rn−s(m	rn(m)−rn−s(m	NOUN
ap-1261	208	11	)	)	PUNCT
ap-1261	208	12	)	)	PUNCT
ap-1261	209	1	ξ(m	ξ(m	NOUN
ap-1261	209	2	)	)	PUNCT
ap-1261	209	3	35	35	NUM
ap-1261	209	4	acta	acta	PROPN
ap-1261	209	5	polytechnica	polytechnica	PROPN
ap-1261	209	6	vol	vol	NOUN
ap-1261	209	7	.	.	PROPN
ap-1261	210	1	50	50	NUM
ap-1261	210	2	no	no	NOUN
ap-1261	210	3	.	.	PUNCT
ap-1261	211	1	5/2010	5/2010	NUM
ap-1261	211	2	3.2	3.2	NUM
ap-1261	211	3	outer	outer	ADJ
ap-1261	211	4	automorphism	automorphism	NOUN
ap-1261	211	5	of	of	ADP
ap-1261	211	6	order	order	NOUN
ap-1261	211	7	two	two	NUM
ap-1261	211	8	as	as	SCONJ
ap-1261	211	9	explained	explain	VERB
ap-1261	211	10	at	at	ADP
ap-1261	211	11	the	the	DET
ap-1261	211	12	beginning	beginning	NOUN
ap-1261	211	13	of	of	ADP
ap-1261	211	14	section	section	NOUN
ap-1261	211	15	3	3	NUM
ap-1261	211	16	,	,	PUNCT
ap-1261	211	17	any	any	DET
ap-1261	211	18	outer	outer	ADJ
ap-1261	211	19	automorphism	automorphism	NOUN
ap-1261	211	20	of	of	ADP
ap-1261	211	21	order	order	NOUN
ap-1261	211	22	two	two	NUM
ap-1261	211	23	on	on	ADP
ap-1261	211	24	sl(n	sl(n	ADJ
ap-1261	211	25	,	,	PUNCT
ap-1261	211	26	c	c	X
ap-1261	211	27	)	)	PUNCT
ap-1261	211	28	is	be	AUX
ap-1261	211	29	up	up	ADP
ap-1261	211	30	to	to	PART
ap-1261	211	31	equivalence	equivalence	VERB
ap-1261	211	32	the	the	DET
ap-1261	211	33	automorphism	automorphism	NOUN
ap-1261	211	34	outi(x	outi(x	NOUN
ap-1261	211	35	)	)	PUNCT
ap-1261	211	36	=	=	SYM
ap-1261	211	37	−xt	−xt	X
ap-1261	211	38	,	,	PUNCT
ap-1261	211	39	and	and	CCONJ
ap-1261	211	40	thus	thus	ADV
ap-1261	211	41	we	we	PRON
ap-1261	211	42	will	will	AUX
ap-1261	211	43	focus	focus	VERB
ap-1261	211	44	only	only	ADV
ap-1261	211	45	on	on	ADP
ap-1261	211	46	it	it	PRON
ap-1261	211	47	without	without	ADP
ap-1261	211	48	loss	loss	NOUN
ap-1261	211	49	of	of	ADP
ap-1261	211	50	generality	generality	NOUN
ap-1261	211	51	.	.	PUNCT
ap-1261	212	1	it	it	PRON
ap-1261	212	2	is	be	AUX
ap-1261	212	3	well	well	ADV
ap-1261	212	4	known	know	VERB
ap-1261	212	5	that	that	SCONJ
ap-1261	212	6	for	for	ADP
ap-1261	212	7	an	an	DET
ap-1261	212	8	irreducible	irreducible	ADJ
ap-1261	212	9	representation	representation	NOUN
ap-1261	212	10	r	r	NOUN
ap-1261	212	11	characterized	characterize	VERB
ap-1261	212	12	in	in	ADP
ap-1261	212	13	the	the	DET
ap-1261	212	14	gel’fand	gel’fand	NOUN
ap-1261	212	15	-	-	PUNCT
ap-1261	212	16	tseitlin	tseitlin	NOUN
ap-1261	212	17	formalism	formalism	NOUN
ap-1261	212	18	by	by	ADP
ap-1261	212	19	the	the	DET
ap-1261	212	20	n	n	CCONJ
ap-1261	212	21	-	-	PUNCT
ap-1261	212	22	tuple	tuple	NOUN
ap-1261	212	23	(	(	PUNCT
ap-1261	212	24	m1,n	m1,n	PROPN
ap-1261	212	25	,	,	PUNCT
ap-1261	212	26	m2,n	m2,n	PROPN
ap-1261	212	27	,	,	PUNCT
ap-1261	212	28	.	.	PUNCT
ap-1261	212	29	.	.	PUNCT
ap-1261	213	1	.	.	PUNCT
ap-1261	214	1	,	,	PUNCT
ap-1261	214	2	mn	mn	PROPN
ap-1261	214	3	,	,	PUNCT
ap-1261	214	4	n	n	CCONJ
ap-1261	214	5	)	)	PUNCT
ap-1261	214	6	,	,	PUNCT
ap-1261	214	7	the	the	DET
ap-1261	214	8	mapping	mapping	NOUN
ap-1261	214	9	−rt	−rt	NOUN
ap-1261	214	10	(	(	PUNCT
ap-1261	214	11	to	to	ADP
ap-1261	214	12	minus	minus	CCONJ
ap-1261	214	13	transposed	transpose	VERB
ap-1261	214	14	matrices	matrix	NOUN
ap-1261	214	15	)	)	PUNCT
ap-1261	214	16	is	be	AUX
ap-1261	214	17	also	also	ADV
ap-1261	214	18	an	an	DET
ap-1261	214	19	irreducible	irreducible	ADJ
ap-1261	214	20	representation	representation	NOUN
ap-1261	214	21	.	.	PUNCT
ap-1261	215	1	this	this	DET
ap-1261	215	2	representation	representation	NOUN
ap-1261	215	3	is	be	AUX
ap-1261	215	4	equivalent	equivalent	ADJ
ap-1261	215	5	to	to	ADP
ap-1261	215	6	the	the	DET
ap-1261	215	7	contragredient	contragredient	NOUN
ap-1261	215	8	representation	representation	PROPN
ap-1261	215	9	rc	rc	PROPN
ap-1261	215	10	,	,	PUNCT
ap-1261	215	11	which	which	PRON
ap-1261	215	12	is	be	AUX
ap-1261	215	13	characterized	characterize	VERB
ap-1261	215	14	by	by	ADP
ap-1261	215	15	the	the	DET
ap-1261	215	16	n	n	CCONJ
ap-1261	215	17	-	-	PUNCT
ap-1261	215	18	tuple	tuple	NOUN
ap-1261	215	19	(	(	PUNCT
ap-1261	215	20	m′	m′	NUM
ap-1261	215	21	1,n	1,n	NUM
ap-1261	215	22	,	,	PUNCT
ap-1261	215	23	m′	m′	NOUN
ap-1261	215	24	2,n	2,n	NUM
ap-1261	215	25	,	,	PUNCT
ap-1261	215	26	.	.	PUNCT
ap-1261	215	27	.	.	PUNCT
ap-1261	216	1	.	.	PUNCT
ap-1261	217	1	,	,	PUNCT
ap-1261	217	2	m′	m′	NOUN
ap-1261	217	3	n	n	CCONJ
ap-1261	217	4	,	,	PUNCT
ap-1261	217	5	n	n	CCONJ
ap-1261	217	6	)	)	PUNCT
ap-1261	217	7	,	,	PUNCT
ap-1261	217	8	where	where	SCONJ
ap-1261	217	9	m′	m′	PROPN
ap-1261	217	10	i	i	PRON
ap-1261	217	11	,	,	PUNCT
ap-1261	217	12	n	n	PROPN
ap-1261	217	13	=	=	SYM
ap-1261	217	14	m1,n	m1,n	PROPN
ap-1261	217	15	−	−	PROPN
ap-1261	217	16	mn−i+1,n	mn−i+1,n	PROPN
ap-1261	217	17	for	for	ADP
ap-1261	217	18	i	i	PRON
ap-1261	217	19	=	=	NOUN
ap-1261	217	20	1	1	NUM
ap-1261	217	21	,	,	PUNCT
ap-1261	217	22	2	2	NUM
ap-1261	217	23	,	,	PUNCT
ap-1261	217	24	.	.	PUNCT
ap-1261	217	25	.	.	PUNCT
ap-1261	218	1	.	.	PUNCT
ap-1261	219	1	,	,	PUNCT
ap-1261	219	2	n	n	X
ap-1261	219	3	.	.	PUNCT
ap-1261	220	1	let	let	VERB
ap-1261	220	2	us	we	PRON
ap-1261	220	3	consider	consider	VERB
ap-1261	220	4	a	a	DET
ap-1261	220	5	triangular	triangular	NOUN
ap-1261	220	6	patternm	patternm	NOUN
ap-1261	220	7	filled	fill	VERB
ap-1261	220	8	by	by	ADP
ap-1261	220	9	indices	index	NOUN
ap-1261	220	10	mi	mi	PROPN
ap-1261	220	11	,	,	PUNCT
ap-1261	220	12	j	j	PROPN
ap-1261	220	13	,	,	PUNCT
ap-1261	220	14	1	1	NUM
ap-1261	220	15	≤	≤	NUM
ap-1261	220	16	i	i	X
ap-1261	220	17	≤	≤	NUM
ap-1261	220	18	j	j	PROPN
ap-1261	220	19	≤	≤	NUM
ap-1261	220	20	n	n	CCONJ
ap-1261	220	21	,	,	PUNCT
ap-1261	220	22	and	and	CCONJ
ap-1261	220	23	associated	associate	VERB
ap-1261	220	24	with	with	ADP
ap-1261	220	25	the	the	DET
ap-1261	220	26	basis	basis	NOUN
ap-1261	220	27	vector	vector	NOUN
ap-1261	220	28	ξ(m	ξ(m	NOUN
ap-1261	220	29	)	)	PUNCT
ap-1261	220	30	of	of	ADP
ap-1261	220	31	representation	representation	NOUN
ap-1261	220	32	r.	r.	PROPN
ap-1261	220	33	to	to	ADP
ap-1261	220	34	any	any	DET
ap-1261	220	35	such	such	ADJ
ap-1261	220	36	pattern	pattern	NOUN
ap-1261	220	37	m	m	PRON
ap-1261	220	38	,	,	PUNCT
ap-1261	220	39	we	we	PRON
ap-1261	220	40	may	may	AUX
ap-1261	220	41	assign	assign	VERB
ap-1261	220	42	the	the	DET
ap-1261	220	43	unique	unique	ADJ
ap-1261	220	44	triangular	triangular	NOUN
ap-1261	220	45	pattern	pattern	NOUN
ap-1261	220	46	m′	m′	NOUN
ap-1261	220	47	with	with	ADP
ap-1261	220	48	indices	index	NOUN
ap-1261	220	49	m′	m′	PROPN
ap-1261	220	50	i	i	PRON
ap-1261	220	51	,	,	PUNCT
ap-1261	220	52	j	j	PROPN
ap-1261	220	53	:	:	PUNCT
ap-1261	220	54	=	=	SYM
ap-1261	220	55	m1,n	m1,n	PROPN
ap-1261	220	56	−	−	PROPN
ap-1261	220	57	mj−i+1,j	mj−i+1,j	PROPN
ap-1261	220	58	.	.	PUNCT
ap-1261	221	1	it	it	PRON
ap-1261	221	2	is	be	AUX
ap-1261	221	3	easy	easy	ADJ
ap-1261	221	4	to	to	PART
ap-1261	221	5	check	check	VERB
ap-1261	221	6	that	that	DET
ap-1261	221	7	m′	m′	NOUN
ap-1261	221	8	i	i	PRON
ap-1261	221	9	,	,	PUNCT
ap-1261	221	10	j	j	PROPN
ap-1261	221	11	satisfies	satisfy	VERB
ap-1261	221	12	the	the	DET
ap-1261	221	13	necessary	necessary	ADJ
ap-1261	221	14	inequalities	inequality	NOUN
ap-1261	221	15	for	for	ADP
ap-1261	221	16	m	m	PROPN
ap-1261	221	17	′	′	NUM
ap-1261	221	18	to	to	PART
ap-1261	221	19	be	be	AUX
ap-1261	221	20	a	a	DET
ap-1261	221	21	correct	correct	ADJ
ap-1261	221	22	pattern	pattern	NOUN
ap-1261	221	23	of	of	ADP
ap-1261	221	24	the	the	DET
ap-1261	221	25	contragredient	contragredient	NOUN
ap-1261	221	26	representation	representation	PROPN
ap-1261	221	27	rc	rc	PROPN
ap-1261	221	28	.	.	PUNCT
ap-1261	222	1	let	let	VERB
ap-1261	222	2	us	we	PRON
ap-1261	222	3	define	define	VERB
ap-1261	222	4	the	the	DET
ap-1261	222	5	linear	linear	ADJ
ap-1261	222	6	mapping	mapping	NOUN
ap-1261	222	7	j	j	PROPN
ap-1261	222	8	of	of	ADP
ap-1261	222	9	the	the	DET
ap-1261	222	10	representation	representation	NOUN
ap-1261	222	11	space	space	NOUN
ap-1261	222	12	of	of	ADP
ap-1261	222	13	r	r	NOUN
ap-1261	222	14	onto	onto	ADP
ap-1261	222	15	the	the	DET
ap-1261	222	16	representation	representation	NOUN
ap-1261	222	17	space	space	NOUN
ap-1261	222	18	of	of	ADP
ap-1261	222	19	rc	rc	PROPN
ap-1261	222	20	by	by	ADP
ap-1261	222	21	j	j	PROPN
ap-1261	222	22	ξ(m	ξ(m	PROPN
ap-1261	222	23	)	)	PUNCT
ap-1261	222	24	:	:	PUNCT
ap-1261	223	1	=	=	SYM
ap-1261	223	2	(	(	PUNCT
ap-1261	223	3	−1	−1	NOUN
ap-1261	223	4	)	)	PUNCT
ap-1261	223	5	∑	∑	PROPN
ap-1261	223	6	i	i	PROPN
ap-1261	223	7	,	,	PUNCT
ap-1261	223	8	j	j	PROPN
ap-1261	223	9	mi	mi	PROPN
ap-1261	223	10	,	,	PUNCT
ap-1261	223	11	j	j	PROPN
ap-1261	223	12	ξ(m′	ξ(m′	NUM
ap-1261	223	13	)	)	PUNCT
ap-1261	223	14	.	.	PUNCT
ap-1261	224	1	on	on	ADP
ap-1261	224	2	the	the	DET
ap-1261	224	3	other	other	ADJ
ap-1261	224	4	hand	hand	NOUN
ap-1261	224	5	,	,	PUNCT
ap-1261	224	6	from	from	ADP
ap-1261	224	7	the	the	DET
ap-1261	224	8	formulae	formulae	NOUN
ap-1261	224	9	in	in	ADP
ap-1261	224	10	the	the	DET
ap-1261	224	11	appendix	appendix	ADJ
ap-1261	224	12	one	one	NUM
ap-1261	224	13	sees	see	VERB
ap-1261	224	14	that	that	SCONJ
ap-1261	224	15	rt	rt	PROPN
ap-1261	224	16	(	(	PUNCT
ap-1261	224	17	eij	eij	PROPN
ap-1261	224	18	)	)	PUNCT
ap-1261	224	19	=	=	PRON
ap-1261	224	20	r(eji	r(eji	NOUN
ap-1261	224	21	)	)	PUNCT
ap-1261	224	22	=	=	SYM
ap-1261	224	23	r(e	r(e	NOUN
ap-1261	224	24	t	t	X
ap-1261	224	25	ij	ij	PROPN
ap-1261	224	26	)	)	PUNCT
ap-1261	224	27	.	.	PUNCT
ap-1261	225	1	(	(	PUNCT
ap-1261	225	2	13	13	X
ap-1261	225	3	)	)	PUNCT
ap-1261	225	4	using	use	VERB
ap-1261	225	5	this	this	DET
ap-1261	225	6	fact	fact	NOUN
ap-1261	225	7	one	one	PRON
ap-1261	225	8	can	can	AUX
ap-1261	225	9	prove	prove	VERB
ap-1261	225	10	by	by	ADP
ap-1261	225	11	direct	direct	ADJ
ap-1261	225	12	verification	verification	NOUN
ap-1261	225	13	that	that	PRON
ap-1261	225	14	the	the	DET
ap-1261	225	15	mapping	mapping	NOUN
ap-1261	225	16	j	j	PROPN
ap-1261	225	17	satisfies	satisfy	VERB
ap-1261	225	18	−	−	PROPN
ap-1261	225	19	j	j	PROPN
ap-1261	225	20	rt	rt	PROPN
ap-1261	225	21	(	(	PUNCT
ap-1261	225	22	x	x	NOUN
ap-1261	225	23	)	)	PUNCT
ap-1261	225	24	=	=	SYM
ap-1261	225	25	rc(x)j	rc(x)j	PROPN
ap-1261	225	26	for	for	ADP
ap-1261	225	27	any	any	DET
ap-1261	225	28	x	x	SYM
ap-1261	225	29	∈	∈	PROPN
ap-1261	225	30	sl(n	sl(n	NOUN
ap-1261	225	31	,	,	PUNCT
ap-1261	225	32	c	c	NOUN
ap-1261	225	33	)	)	PUNCT
ap-1261	225	34	.	.	PUNCT
ap-1261	226	1	(	(	PUNCT
ap-1261	226	2	14	14	NUM
ap-1261	226	3	)	)	PUNCT
ap-1261	226	4	let	let	VERB
ap-1261	226	5	us	we	PRON
ap-1261	226	6	return	return	VERB
ap-1261	226	7	to	to	ADP
ap-1261	226	8	our	our	PRON
ap-1261	226	9	original	original	ADJ
ap-1261	226	10	task	task	NOUN
ap-1261	226	11	.	.	PUNCT
ap-1261	227	1	we	we	PRON
ap-1261	227	2	are	be	AUX
ap-1261	227	3	looking	look	VERB
ap-1261	227	4	for	for	ADP
ap-1261	227	5	the	the	DET
ap-1261	227	6	simulation	simulation	NOUN
ap-1261	227	7	matrix	matrix	NOUN
ap-1261	227	8	of	of	ADP
ap-1261	227	9	the	the	DET
ap-1261	227	10	automorphism	automorphism	NOUN
ap-1261	227	11	g	g	PROPN
ap-1261	227	12	=	=	SYM
ap-1261	227	13	outi	outi	PROPN
ap-1261	227	14	,	,	PUNCT
ap-1261	227	15	i.e.	i.e.	X
ap-1261	227	16	,	,	PUNCT
ap-1261	227	17	we	we	PRON
ap-1261	227	18	are	be	AUX
ap-1261	227	19	looking	look	VERB
ap-1261	227	20	for	for	ADP
ap-1261	227	21	a	a	DET
ap-1261	227	22	matrix	matrix	NOUN
ap-1261	227	23	rg	rg	NOUN
ap-1261	227	24	of	of	ADP
ap-1261	227	25	order	order	NOUN
ap-1261	227	26	two	two	NUM
ap-1261	227	27	such	such	ADJ
ap-1261	227	28	that	that	DET
ap-1261	227	29	r(outi(x	r(outi(x	NOUN
ap-1261	227	30	)	)	PUNCT
ap-1261	227	31	)	)	PUNCT
ap-1261	228	1	=	=	NOUN
ap-1261	228	2	−r(xt	−r(xt	NOUN
ap-1261	228	3	)	)	PUNCT
ap-1261	228	4	=	=	PUNCT
ap-1261	229	1	rgr(x)r−1	rgr(x)r−1	NUM
ap-1261	229	2	g	g	NOUN
ap-1261	229	3	.	.	PUNCT
ap-1261	230	1	according	accord	VERB
ap-1261	230	2	to	to	ADP
ap-1261	230	3	(	(	PUNCT
ap-1261	230	4	13	13	NUM
ap-1261	230	5	)	)	PUNCT
ap-1261	230	6	,	,	PUNCT
ap-1261	230	7	we	we	PRON
ap-1261	230	8	have	have	VERB
ap-1261	230	9	r(xt	r(xt	NOUN
ap-1261	230	10	)	)	PUNCT
ap-1261	231	1	=	=	SYM
ap-1261	231	2	rt	rt	PROPN
ap-1261	231	3	(	(	PUNCT
ap-1261	231	4	x	x	NOUN
ap-1261	231	5	)	)	PUNCT
ap-1261	231	6	and	and	CCONJ
ap-1261	231	7	therefore	therefore	ADV
ap-1261	231	8	the	the	DET
ap-1261	231	9	existence	existence	NOUN
ap-1261	231	10	of	of	ADP
ap-1261	231	11	the	the	DET
ap-1261	231	12	simulation	simulation	NOUN
ap-1261	231	13	matrix	matrix	NOUN
ap-1261	231	14	rg	rg	PROPN
ap-1261	231	15	means	mean	VERB
ap-1261	231	16	equivalence	equivalence	NOUN
ap-1261	231	17	of	of	ADP
ap-1261	231	18	the	the	DET
ap-1261	231	19	representations	representation	NOUN
ap-1261	231	20	r	r	NOUN
ap-1261	231	21	and	and	CCONJ
ap-1261	231	22	−rt	−rt	NOUN
ap-1261	231	23	,	,	PUNCT
ap-1261	231	24	i.e.	i.e.	X
ap-1261	231	25	equivalence	equivalence	NOUN
ap-1261	231	26	of	of	ADP
ap-1261	231	27	r	r	NOUN
ap-1261	231	28	and	and	CCONJ
ap-1261	231	29	its	its	PRON
ap-1261	231	30	contragredient	contragredient	NOUN
ap-1261	231	31	representation	representation	PROPN
ap-1261	231	32	rc	rc	PROPN
ap-1261	231	33	.	.	PUNCT
ap-1261	232	1	the	the	DET
ap-1261	232	2	gel’fand	gel’fand	NOUN
ap-1261	232	3	-	-	PUNCT
ap-1261	232	4	tseitlin	tseitlin	NOUN
ap-1261	232	5	result	result	NOUN
ap-1261	232	6	states	state	VERB
ap-1261	232	7	that	that	SCONJ
ap-1261	232	8	this	this	PRON
ap-1261	232	9	is	be	AUX
ap-1261	232	10	possible	possible	ADJ
ap-1261	232	11	if	if	SCONJ
ap-1261	232	12	and	and	CCONJ
ap-1261	232	13	only	only	ADV
ap-1261	232	14	if	if	SCONJ
ap-1261	232	15	n	n	NUM
ap-1261	232	16	-	-	PUNCT
ap-1261	232	17	tuples	tuple	NOUN
ap-1261	232	18	(	(	PUNCT
ap-1261	232	19	m1,n	m1,n	PROPN
ap-1261	232	20	,	,	PUNCT
ap-1261	232	21	m2,n	m2,n	PROPN
ap-1261	232	22	,	,	PUNCT
ap-1261	232	23	.	.	PUNCT
ap-1261	232	24	.	.	PUNCT
ap-1261	232	25	.	.	PUNCT
ap-1261	233	1	,	,	PUNCT
ap-1261	233	2	mn	mn	PROPN
ap-1261	233	3	,	,	PUNCT
ap-1261	233	4	n	n	CCONJ
ap-1261	233	5	)	)	PUNCT
ap-1261	233	6	and	and	CCONJ
ap-1261	233	7	(	(	PUNCT
ap-1261	233	8	m′	m′	NUM
ap-1261	233	9	1,n	1,n	NUM
ap-1261	233	10	,	,	PUNCT
ap-1261	233	11	m′	m′	NOUN
ap-1261	233	12	2,n	2,n	NUM
ap-1261	233	13	,	,	PUNCT
ap-1261	233	14	.	.	PUNCT
ap-1261	233	15	.	.	PUNCT
ap-1261	233	16	.	.	PUNCT
ap-1261	234	1	,	,	PUNCT
ap-1261	234	2	m′	m′	NOUN
ap-1261	234	3	n	n	CCONJ
ap-1261	234	4	,	,	PUNCT
ap-1261	234	5	n	n	CCONJ
ap-1261	234	6	)	)	PUNCT
ap-1261	234	7	coincide	coincide	NOUN
ap-1261	234	8	.	.	PUNCT
ap-1261	235	1	in	in	ADP
ap-1261	235	2	this	this	DET
ap-1261	235	3	case	case	NOUN
ap-1261	235	4	the	the	DET
ap-1261	235	5	simulation	simulation	NOUN
ap-1261	235	6	matrix	matrix	NOUN
ap-1261	235	7	rg	rg	PROPN
ap-1261	235	8	is	be	AUX
ap-1261	235	9	equal	equal	ADJ
ap-1261	235	10	to	to	ADP
ap-1261	235	11	j	j	PROPN
ap-1261	235	12	.	.	PUNCT
ap-1261	236	1	we	we	PRON
ap-1261	236	2	have	have	AUX
ap-1261	236	3	deduced	deduce	VERB
ap-1261	236	4	theorem	theorem	VERB
ap-1261	236	5	3.2	3.2	NUM
ap-1261	236	6	a	a	DET
ap-1261	236	7	z2	z2	NOUN
ap-1261	236	8	-	-	PUNCT
ap-1261	236	9	grading	grading	NOUN
ap-1261	236	10	of	of	ADP
ap-1261	236	11	the	the	DET
ap-1261	236	12	lie	lie	NOUN
ap-1261	236	13	algebra	algebra	PROPN
ap-1261	236	14	sl(n	sl(n	NOUN
ap-1261	236	15	,	,	PUNCT
ap-1261	236	16	c	c	NOUN
ap-1261	236	17	)	)	PUNCT
ap-1261	236	18	obtained	obtain	VERB
ap-1261	236	19	by	by	ADP
ap-1261	236	20	an	an	DET
ap-1261	236	21	outer	outer	ADJ
ap-1261	236	22	automorphism	automorphism	NOUN
ap-1261	236	23	outi	outi	NOUN
ap-1261	236	24	is	be	AUX
ap-1261	236	25	compatible	compatible	ADJ
ap-1261	236	26	with	with	ADP
ap-1261	236	27	an	an	DET
ap-1261	236	28	irreducible	irreducible	ADJ
ap-1261	236	29	representation	representation	NOUN
ap-1261	236	30	r	r	NOUN
ap-1261	236	31	of	of	ADP
ap-1261	236	32	sl(n	sl(n	ADJ
ap-1261	236	33	,	,	PUNCT
ap-1261	236	34	c	c	NOUN
ap-1261	236	35	)	)	PUNCT
ap-1261	237	1	if	if	SCONJ
ap-1261	237	2	and	and	CCONJ
ap-1261	237	3	only	only	ADV
ap-1261	237	4	if	if	SCONJ
ap-1261	237	5	the	the	DET
ap-1261	237	6	representation	representation	NOUN
ap-1261	237	7	is	be	AUX
ap-1261	237	8	self	self	NOUN
ap-1261	237	9	-	-	PUNCT
ap-1261	237	10	contragredient	contragredient	NOUN
ap-1261	237	11	.	.	PUNCT
ap-1261	238	1	if	if	SCONJ
ap-1261	238	2	we	we	PRON
ap-1261	238	3	do	do	AUX
ap-1261	238	4	not	not	PART
ap-1261	238	5	insist	insist	VERB
ap-1261	238	6	on	on	ADP
ap-1261	238	7	the	the	DET
ap-1261	238	8	irreducibility	irreducibility	NOUN
ap-1261	238	9	of	of	ADP
ap-1261	238	10	representation	representation	NOUN
ap-1261	238	11	r	r	NOUN
ap-1261	238	12	,	,	PUNCT
ap-1261	238	13	the	the	DET
ap-1261	238	14	class	class	NOUN
ap-1261	238	15	of	of	ADP
ap-1261	238	16	representations	representation	NOUN
ap-1261	238	17	compatible	compatible	ADJ
ap-1261	238	18	with	with	ADP
ap-1261	238	19	the	the	DET
ap-1261	238	20	z2grading	z2grading	NOUN
ap-1261	238	21	obtained	obtain	VERB
ap-1261	238	22	by	by	ADP
ap-1261	238	23	the	the	DET
ap-1261	238	24	automorphism	automorphism	NOUN
ap-1261	238	25	outi	outi	NOUN
ap-1261	238	26	is	be	AUX
ap-1261	238	27	larger	large	ADJ
ap-1261	238	28	.	.	PUNCT
ap-1261	239	1	of	of	ADP
ap-1261	239	2	course	course	ADV
ap-1261	239	3	,	,	PUNCT
ap-1261	239	4	if	if	SCONJ
ap-1261	239	5	for	for	ADP
ap-1261	239	6	a	a	DET
ap-1261	239	7	representation	representation	NOUN
ap-1261	239	8	r1	r1	NOUN
ap-1261	239	9	it	it	PRON
ap-1261	239	10	is	be	AUX
ap-1261	239	11	possible	possible	ADJ
ap-1261	239	12	to	to	PART
ap-1261	239	13	find	find	VERB
ap-1261	239	14	a	a	DET
ap-1261	239	15	simulation	simulation	NOUN
ap-1261	239	16	matrix	matrix	NOUN
ap-1261	239	17	r(1	r(1	PROPN
ap-1261	239	18	)	)	PUNCT
ap-1261	239	19	and	and	CCONJ
ap-1261	239	20	for	for	ADP
ap-1261	239	21	a	a	DET
ap-1261	239	22	representation	representation	NOUN
ap-1261	239	23	r2	r2	NOUN
ap-1261	239	24	a	a	DET
ap-1261	239	25	simulation	simulation	NOUN
ap-1261	239	26	matrix	matrix	NOUN
ap-1261	239	27	r(2	r(2	PROPN
ap-1261	239	28	)	)	PUNCT
ap-1261	239	29	,	,	PUNCT
ap-1261	239	30	then	then	ADV
ap-1261	239	31	the	the	DET
ap-1261	239	32	direct	direct	ADJ
ap-1261	239	33	sum	sum	NOUN
ap-1261	239	34	r(1)⊕r(2	r(1)⊕r(2	PROPN
ap-1261	239	35	)	)	PUNCT
ap-1261	239	36	is	be	AUX
ap-1261	239	37	the	the	DET
ap-1261	239	38	simulation	simulation	NOUN
ap-1261	239	39	matrix	matrix	NOUN
ap-1261	239	40	for	for	ADP
ap-1261	239	41	the	the	DET
ap-1261	239	42	direct	direct	ADJ
ap-1261	239	43	sum	sum	NOUN
ap-1261	239	44	r1⊕r2	r1⊕r2	NOUN
ap-1261	239	45	.	.	PUNCT
ap-1261	240	1	to	to	PART
ap-1261	240	2	avoid	avoid	VERB
ap-1261	240	3	a	a	DET
ap-1261	240	4	discussion	discussion	NOUN
ap-1261	240	5	of	of	ADP
ap-1261	240	6	all	all	DET
ap-1261	240	7	such	such	ADJ
ap-1261	240	8	obvious	obvious	ADJ
ap-1261	240	9	cases	case	NOUN
ap-1261	240	10	,	,	PUNCT
ap-1261	240	11	we	we	PRON
ap-1261	240	12	will	will	AUX
ap-1261	240	13	describe	describe	VERB
ap-1261	240	14	only	only	ADV
ap-1261	240	15	those	those	DET
ap-1261	240	16	representations	representation	NOUN
ap-1261	240	17	r	r	NOUN
ap-1261	240	18	with	with	ADP
ap-1261	240	19	simulation	simulation	NOUN
ap-1261	240	20	matrices	matrix	NOUN
ap-1261	240	21	r	r	NOUN
ap-1261	240	22	for	for	ADP
ap-1261	240	23	which	which	PRON
ap-1261	240	24	the	the	DET
ap-1261	240	25	operator	operator	NOUN
ap-1261	240	26	set	set	VERB
ap-1261	240	27	{	{	PUNCT
ap-1261	240	28	r	r	NOUN
ap-1261	240	29	}	}	PUNCT
ap-1261	240	30	∪	∪	ADJ
ap-1261	240	31	{	{	PUNCT
ap-1261	240	32	r(x	r(x	NOUN
ap-1261	240	33	)	)	PUNCT
ap-1261	241	1	|	|	ADV
ap-1261	241	2	x	x	SYM
ap-1261	241	3	∈	∈	PROPN
ap-1261	241	4	sl(n	sl(n	NOUN
ap-1261	241	5	,	,	PUNCT
ap-1261	241	6	c	c	NOUN
ap-1261	241	7	)	)	PUNCT
ap-1261	241	8	}	}	PUNCT
ap-1261	241	9	is	be	AUX
ap-1261	241	10	irreducible	irreducible	ADJ
ap-1261	241	11	,	,	PUNCT
ap-1261	241	12	whereas	whereas	SCONJ
ap-1261	241	13	the	the	DET
ap-1261	241	14	set	set	NOUN
ap-1261	241	15	{	{	PUNCT
ap-1261	241	16	r(x	r(x	NOUN
ap-1261	241	17	)	)	PUNCT
ap-1261	241	18	|	|	ADV
ap-1261	241	19	x	x	SYM
ap-1261	241	20	∈	∈	PROPN
ap-1261	241	21	sl(n	sl(n	NOUN
ap-1261	241	22	,	,	PUNCT
ap-1261	241	23	c	c	NOUN
ap-1261	241	24	)	)	PUNCT
ap-1261	241	25	}	}	PUNCT
ap-1261	241	26	is	be	AUX
ap-1261	241	27	reducible	reducible	ADJ
ap-1261	241	28	.	.	PUNCT
ap-1261	242	1	if	if	SCONJ
ap-1261	242	2	r0	r0	NOUN
ap-1261	242	3	is	be	AUX
ap-1261	242	4	a	a	DET
ap-1261	242	5	d	d	ADJ
ap-1261	242	6	-	-	ADJ
ap-1261	242	7	dimensional	dimensional	ADJ
ap-1261	242	8	irreducible	irreducible	ADJ
ap-1261	242	9	representation	representation	NOUN
ap-1261	242	10	of	of	ADP
ap-1261	242	11	sl(n	sl(n	ADJ
ap-1261	242	12	,	,	PUNCT
ap-1261	242	13	c	c	NOUN
ap-1261	242	14	)	)	PUNCT
ap-1261	242	15	then	then	ADV
ap-1261	242	16	the	the	DET
ap-1261	242	17	2d	2d	ADV
ap-1261	242	18	-	-	PUNCT
ap-1261	242	19	dimensional	dimensional	ADJ
ap-1261	242	20	representation	representation	NOUN
ap-1261	242	21	r	r	NOUN
ap-1261	242	22	:	:	PUNCT
ap-1261	242	23	=	=	SYM
ap-1261	242	24	r0	r0	PROPN
ap-1261	242	25	⊕	⊕	PROPN
ap-1261	242	26	(	(	PUNCT
ap-1261	242	27	−r	−r	PROPN
ap-1261	242	28	t	t	PROPN
ap-1261	242	29	0	0	NUM
ap-1261	242	30	)	)	PUNCT
ap-1261	242	31	assigns	assign	NOUN
ap-1261	242	32	to	to	ADP
ap-1261	242	33	x	x	SYM
ap-1261	242	34	the	the	DET
ap-1261	242	35	matrix	matrix	NOUN
ap-1261	242	36	r(x	r(x	NOUN
ap-1261	242	37	)	)	PUNCT
ap-1261	242	38	=	=	PRON
ap-1261	242	39	(	(	PUNCT
ap-1261	242	40	r0(x	r0(x	NOUN
ap-1261	242	41	)	)	PUNCT
ap-1261	242	42	0	0	NUM
ap-1261	242	43	0	0	NUM
ap-1261	243	1	−	−	PROPN
ap-1261	243	2	(	(	PUNCT
ap-1261	243	3	r0(x	r0(x	NOUN
ap-1261	243	4	)	)	PUNCT
ap-1261	243	5	)	)	PUNCT
ap-1261	244	1	t	t	NOUN
ap-1261	244	2	)	)	PUNCT
ap-1261	244	3	and	and	CCONJ
ap-1261	244	4	therefore	therefore	ADV
ap-1261	244	5	r(outi(x	r(outi(x	VERB
ap-1261	244	6	)	)	PUNCT
ap-1261	244	7	)	)	PUNCT
ap-1261	245	1	=	=	PRON
ap-1261	245	2	(	(	PUNCT
ap-1261	245	3	−	−	X
ap-1261	245	4	(	(	PUNCT
ap-1261	245	5	r0(x	r0(x	NOUN
ap-1261	245	6	)	)	PUNCT
ap-1261	245	7	)	)	PUNCT
ap-1261	246	1	t	t	NOUN
ap-1261	246	2	0	0	NUM
ap-1261	246	3	0	0	NUM
ap-1261	246	4	r0(x	r0(x	NOUN
ap-1261	246	5	)	)	PUNCT
ap-1261	246	6	)	)	PUNCT
ap-1261	247	1	=	=	PUNCT
ap-1261	247	2	(	(	PUNCT
ap-1261	247	3	0	0	NUM
ap-1261	247	4	i	i	NOUN
ap-1261	247	5	d	d	PROPN
ap-1261	247	6	i	i	PROPN
ap-1261	247	7	d	d	PROPN
ap-1261	247	8	0	0	NUM
ap-1261	247	9	)	)	PUNCT
ap-1261	247	10	r(x	r(x	PROPN
ap-1261	247	11	)	)	PUNCT
ap-1261	247	12	(	(	PUNCT
ap-1261	247	13	0	0	NUM
ap-1261	247	14	i	i	NOUN
ap-1261	247	15	d	d	PROPN
ap-1261	247	16	i	i	PROPN
ap-1261	247	17	d	d	PROPN
ap-1261	247	18	0	0	NUM
ap-1261	247	19	)	)	PUNCT
ap-1261	247	20	.	.	PUNCT
ap-1261	248	1	the	the	DET
ap-1261	248	2	matrix	matrix	NOUN
ap-1261	248	3	(	(	PUNCT
ap-1261	248	4	0	0	NUM
ap-1261	248	5	i	i	NOUN
ap-1261	248	6	d	d	PROPN
ap-1261	248	7	i	i	PROPN
ap-1261	248	8	d	d	PROPN
ap-1261	248	9	0	0	NUM
ap-1261	248	10	)	)	PUNCT
ap-1261	248	11	is	be	AUX
ap-1261	248	12	the	the	DET
ap-1261	248	13	simulation	simulation	NOUN
ap-1261	248	14	matrix	matrix	NOUN
ap-1261	248	15	of	of	ADP
ap-1261	248	16	outi	outi	NOUN
ap-1261	248	17	.	.	PUNCT
ap-1261	249	1	it	it	PRON
ap-1261	249	2	is	be	AUX
ap-1261	249	3	easy	easy	ADJ
ap-1261	249	4	to	to	PART
ap-1261	249	5	see	see	VERB
ap-1261	249	6	that	that	SCONJ
ap-1261	249	7	the	the	DET
ap-1261	249	8	simulation	simulation	NOUN
ap-1261	249	9	matrix	matrix	NOUN
ap-1261	249	10	together	together	ADV
ap-1261	249	11	with	with	ADP
ap-1261	249	12	all	all	DET
ap-1261	249	13	r(x	r(x	NOUN
ap-1261	249	14	)	)	PUNCT
ap-1261	249	15	form	form	VERB
ap-1261	249	16	an	an	DET
ap-1261	249	17	irreducible	irreducible	ADJ
ap-1261	249	18	set	set	NOUN
ap-1261	249	19	.	.	PUNCT
ap-1261	250	1	36	36	NUM
ap-1261	250	2	acta	acta	PROPN
ap-1261	250	3	polytechnica	polytechnica	PROPN
ap-1261	250	4	vol	vol	NOUN
ap-1261	250	5	.	.	PROPN
ap-1261	251	1	50	50	NUM
ap-1261	251	2	no	no	NOUN
ap-1261	251	3	.	.	PUNCT
ap-1261	252	1	5/2010	5/2010	NUM
ap-1261	252	2	3.3	3.3	NUM
ap-1261	252	3	z2	z2	NUM
ap-1261	252	4	-	-	PUNCT
ap-1261	252	5	grading	grading	NOUN
ap-1261	252	6	of	of	ADP
ap-1261	252	7	sl(3,c	sl(3,c	ADJ
ap-1261	252	8	)	)	PUNCT
ap-1261	252	9	let	let	VERB
ap-1261	252	10	us	we	PRON
ap-1261	252	11	illustrate	illustrate	VERB
ap-1261	252	12	the	the	DET
ap-1261	252	13	conclusions	conclusion	NOUN
ap-1261	252	14	of	of	ADP
ap-1261	252	15	the	the	DET
ap-1261	252	16	previous	previous	ADJ
ap-1261	252	17	sections	section	NOUN
ap-1261	252	18	on	on	ADP
ap-1261	252	19	the	the	DET
ap-1261	252	20	lie	lie	NOUN
ap-1261	252	21	algebra	algebra	PROPN
ap-1261	252	22	sl(3	sl(3	PROPN
ap-1261	252	23	,	,	PUNCT
ap-1261	252	24	c	c	NOUN
ap-1261	252	25	)	)	PUNCT
ap-1261	252	26	.	.	PUNCT
ap-1261	253	1	on	on	ADP
ap-1261	253	2	this	this	DET
ap-1261	253	3	algebra	algebra	NOUN
ap-1261	253	4	there	there	ADV
ap-1261	253	5	exist	exist	VERB
ap-1261	253	6	only	only	ADV
ap-1261	253	7	two	two	NUM
ap-1261	253	8	inequivalent	inequivalent	ADJ
ap-1261	253	9	automorphisms	automorphism	NOUN
ap-1261	253	10	of	of	ADP
ap-1261	253	11	order	order	NOUN
ap-1261	253	12	two	two	NUM
ap-1261	253	13	.	.	PUNCT
ap-1261	254	1	in	in	ADP
ap-1261	254	2	our	our	PRON
ap-1261	254	3	notation	notation	NOUN
ap-1261	254	4	g1	g1	NOUN
ap-1261	254	5	=	=	PUNCT
ap-1261	254	6	ada3,1	ada3,1	PROPN
ap-1261	254	7	with	with	ADP
ap-1261	254	8	a3,1	a3,1	PROPN
ap-1261	254	9	=	=	PUNCT
ap-1261	254	10	ω	ω	NUM
ap-1261	254	11	⎛⎜⎜⎝	⎛⎜⎜⎝	NOUN
ap-1261	254	12	1	1	NUM
ap-1261	254	13	0	0	NUM
ap-1261	254	14	0	0	NUM
ap-1261	254	15	0	0	NUM
ap-1261	254	16	1	1	NUM
ap-1261	254	17	0	0	NUM
ap-1261	254	18	0	0	NUM
ap-1261	254	19	0	0	NUM
ap-1261	254	20	−1	−1	NOUN
ap-1261	254	21	⎞⎟⎟⎠	⎞⎟⎟⎠	NOUN
ap-1261	254	22	,	,	PUNCT
ap-1261	254	23	where	where	SCONJ
ap-1261	254	24	ω	ω	NOUN
ap-1261	254	25	=	=	PUNCT
ap-1261	254	26	e	e	X
ap-1261	254	27	iπ	iπ	ADV
ap-1261	254	28	3	3	NUM
ap-1261	254	29	and	and	CCONJ
ap-1261	254	30	g2	g2	PROPN
ap-1261	254	31	=	=	PUNCT
ap-1261	255	1	outi	outi	PROPN
ap-1261	255	2	.	.	PUNCT
ap-1261	256	1	the	the	DET
ap-1261	256	2	corresponding	correspond	VERB
ap-1261	256	3	z2	z2	PROPN
ap-1261	256	4	-	-	PUNCT
ap-1261	256	5	gradings	grading	NOUN
ap-1261	256	6	are	be	AUX
ap-1261	256	7	γ1	γ1	NOUN
ap-1261	256	8	:	:	PUNCT
ap-1261	257	1	sl(3	sl(3	NOUN
ap-1261	257	2	,	,	PUNCT
ap-1261	257	3	c	c	NOUN
ap-1261	257	4	)	)	PUNCT
ap-1261	257	5	=	=	PRON
ap-1261	257	6	{	{	PUNCT
ap-1261	257	7	⎛⎜⎜⎝	⎛⎜⎜⎝	NOUN
ap-1261	257	8	a	a	DET
ap-1261	257	9	b	b	NOUN
ap-1261	257	10	0	0	NUM
ap-1261	257	11	c	c	NOUN
ap-1261	257	12	d	d	NOUN
ap-1261	257	13	0	0	NUM
ap-1261	257	14	0	0	NUM
ap-1261	257	15	0	0	NUM
ap-1261	257	16	−a	−a	NOUN
ap-1261	258	1	−	−	PROPN
ap-1261	259	1	d	d	PRON
ap-1261	259	2	⎞⎟⎟⎠∣∣∣	⎞⎟⎟⎠∣∣∣	NOUN
ap-1261	259	3	a	a	DET
ap-1261	259	4	,	,	PUNCT
ap-1261	259	5	b	b	NOUN
ap-1261	259	6	,	,	PUNCT
ap-1261	259	7	c	c	NOUN
ap-1261	259	8	,	,	PUNCT
ap-1261	259	9	d	d	PROPN
ap-1261	259	10	∈	∈	PROPN
ap-1261	259	11	c	c	X
ap-1261	259	12	}	}	PUNCT
ap-1261	259	13	⊕	⊕	PROPN
ap-1261	259	14	{	{	PUNCT
ap-1261	259	15	⎛⎜⎜⎝	⎛⎜⎜⎝	NOUN
ap-1261	259	16	0	0	NUM
ap-1261	259	17	0	0	NUM
ap-1261	259	18	a	a	DET
ap-1261	259	19	0	0	NUM
ap-1261	259	20	0	0	NUM
ap-1261	259	21	b	b	NOUN
ap-1261	259	22	c	c	NOUN
ap-1261	259	23	d	d	SYM
ap-1261	259	24	0	0	NUM
ap-1261	259	25	⎞⎟⎟⎠∣∣∣	⎞⎟⎟⎠∣∣∣	NOUN
ap-1261	259	26	a	a	DET
ap-1261	259	27	,	,	PUNCT
ap-1261	259	28	b	b	NOUN
ap-1261	259	29	,	,	PUNCT
ap-1261	259	30	c	c	NOUN
ap-1261	259	31	,	,	PUNCT
ap-1261	259	32	d	d	PROPN
ap-1261	259	33	∈	∈	PROPN
ap-1261	259	34	c	c	X
ap-1261	259	35	}	}	PUNCT
ap-1261	259	36	,	,	PUNCT
ap-1261	259	37	γ2	γ2	PROPN
ap-1261	259	38	:	:	PUNCT
ap-1261	259	39	sl(3	sl(3	NOUN
ap-1261	259	40	,	,	PUNCT
ap-1261	259	41	c	c	NOUN
ap-1261	259	42	)	)	PUNCT
ap-1261	259	43	=	=	PRON
ap-1261	259	44	{	{	PUNCT
ap-1261	259	45	⎛⎜⎜⎝	⎛⎜⎜⎝	NOUN
ap-1261	259	46	0	0	NUM
ap-1261	259	47	a	a	DET
ap-1261	259	48	b	b	NOUN
ap-1261	259	49	−a	−a	NOUN
ap-1261	259	50	0	0	PUNCT
ap-1261	260	1	c	c	NOUN
ap-1261	260	2	−b	−b	NOUN
ap-1261	260	3	−c	−c	NOUN
ap-1261	260	4	0	0	NUM
ap-1261	260	5	⎞⎟⎟⎠∣∣∣	⎞⎟⎟⎠∣∣∣	NOUN
ap-1261	260	6	a	a	DET
ap-1261	260	7	,	,	PUNCT
ap-1261	260	8	b	b	NOUN
ap-1261	260	9	,	,	PUNCT
ap-1261	260	10	c	c	PROPN
ap-1261	260	11	∈	∈	PROPN
ap-1261	260	12	c	c	PROPN
ap-1261	260	13	}	}	PUNCT
ap-1261	260	14	⊕	⊕	PROPN
ap-1261	260	15	{	{	PUNCT
ap-1261	260	16	⎛⎜⎜⎝	⎛⎜⎜⎝	NOUN
ap-1261	260	17	a	a	DET
ap-1261	260	18	b	b	NOUN
ap-1261	260	19	c	c	NOUN
ap-1261	260	20	b	b	PROPN
ap-1261	260	21	d	d	X
ap-1261	260	22	e	e	X
ap-1261	260	23	c	c	NOUN
ap-1261	260	24	e	e	NOUN
ap-1261	260	25	−a	−a	ADV
ap-1261	260	26	−	−	PROPN
ap-1261	261	1	d	d	PRON
ap-1261	261	2	⎞⎟⎟⎠∣∣∣	⎞⎟⎟⎠∣∣∣	NOUN
ap-1261	261	3	a	a	DET
ap-1261	261	4	,	,	PUNCT
ap-1261	261	5	b	b	NOUN
ap-1261	261	6	,	,	PUNCT
ap-1261	261	7	c	c	NOUN
ap-1261	261	8	,	,	PUNCT
ap-1261	261	9	d	d	NOUN
ap-1261	261	10	,	,	PUNCT
ap-1261	261	11	e	e	PROPN
ap-1261	261	12	∈	∈	PROPN
ap-1261	261	13	c	c	PROPN
ap-1261	261	14	}	}	PUNCT
ap-1261	261	15	.	.	PUNCT
ap-1261	262	1	the	the	DET
ap-1261	262	2	first	first	ADJ
ap-1261	262	3	grading	grade	VERB
ap-1261	262	4	γ1	γ1	NOUN
ap-1261	262	5	is	be	AUX
ap-1261	262	6	compatible	compatible	ADJ
ap-1261	262	7	with	with	ADP
ap-1261	262	8	any	any	DET
ap-1261	262	9	irreducible	irreducible	ADJ
ap-1261	262	10	representation	representation	NOUN
ap-1261	262	11	.	.	PUNCT
ap-1261	263	1	the	the	DET
ap-1261	263	2	simulation	simulation	NOUN
ap-1261	263	3	matrix	matrix	NOUN
ap-1261	263	4	rg1	rg1	PROPN
ap-1261	263	5	of	of	ADP
ap-1261	263	6	the	the	DET
ap-1261	263	7	automorphism	automorphism	NOUN
ap-1261	263	8	g1	g1	NOUN
ap-1261	263	9	=	=	SYM
ap-1261	264	1	ada31	ada31	NOUN
ap-1261	264	2	acts	act	VERB
ap-1261	264	3	on	on	ADP
ap-1261	264	4	the	the	DET
ap-1261	264	5	gel’fand	gel’fand	NOUN
ap-1261	264	6	-	-	PUNCT
ap-1261	264	7	tseitlin	tseitlin	NOUN
ap-1261	264	8	triangular	triangular	NOUN
ap-1261	264	9	patterns	pattern	NOUN
ap-1261	264	10	as	as	SCONJ
ap-1261	264	11	follows	follow	VERB
ap-1261	265	1	rg1	rg1	PROPN
ap-1261	265	2	⎛⎜⎜⎝	⎛⎜⎜⎝	NOUN
ap-1261	265	3	m1,3	m1,3	PROPN
ap-1261	265	4	m2,3	m2,3	PROPN
ap-1261	265	5	0	0	PUNCT
ap-1261	266	1	m1,2	m1,2	ADJ
ap-1261	266	2	m2,2	m2,2	PROPN
ap-1261	266	3	m1,1	m1,1	PROPN
ap-1261	266	4	⎞⎟⎟⎠	⎞⎟⎟⎠	NOUN
ap-1261	266	5	=	=	SYM
ap-1261	266	6	e−	e−	NUM
ap-1261	266	7	2iπ	2iπ	NOUN
ap-1261	266	8	3	3	NUM
ap-1261	266	9	(	(	PUNCT
ap-1261	266	10	m1,3+m2,3)e−iπ(m1,2+m2,2	m1,3+m2,3)e−iπ(m1,2+m2,2	NOUN
ap-1261	266	11	)	)	PUNCT
ap-1261	267	1	⎛⎜⎜⎝	⎛⎜⎜⎝	NOUN
ap-1261	267	2	m1,3	m1,3	NOUN
ap-1261	267	3	m2,3	m2,3	NOUN
ap-1261	267	4	0	0	PUNCT
ap-1261	268	1	m1,2	m1,2	ADJ
ap-1261	268	2	m2,2	m2,2	PROPN
ap-1261	268	3	m1,1	m1,1	PROPN
ap-1261	268	4	⎞⎟⎟⎠	⎞⎟⎟⎠	NOUN
ap-1261	268	5	.	.	PUNCT
ap-1261	269	1	the	the	DET
ap-1261	269	2	irreducible	irreducible	ADJ
ap-1261	269	3	representations	representation	NOUN
ap-1261	269	4	compatible	compatible	ADJ
ap-1261	269	5	with	with	ADP
ap-1261	269	6	the	the	DET
ap-1261	269	7	second	second	ADJ
ap-1261	269	8	grading	grading	NOUN
ap-1261	269	9	are	be	AUX
ap-1261	269	10	only	only	ADV
ap-1261	269	11	self	self	NOUN
ap-1261	269	12	-	-	PUNCT
ap-1261	269	13	contragredient	contragredient	NOUN
ap-1261	269	14	representations	representation	NOUN
ap-1261	269	15	,	,	PUNCT
ap-1261	269	16	i.e.	i.e.	X
ap-1261	269	17	,	,	PUNCT
ap-1261	269	18	representations	representation	VERB
ap-1261	269	19	r	r	NOUN
ap-1261	269	20	=	=	SYM
ap-1261	269	21	r(2	r(2	PROPN
ap-1261	269	22	�	�	PROPN
ap-1261	269	23	,	,	PUNCT
ap-1261	269	24	�	�	PROPN
ap-1261	269	25	,	,	PUNCT
ap-1261	269	26	0	0	NUM
ap-1261	269	27	)	)	PUNCT
ap-1261	269	28	.	.	PUNCT
ap-1261	270	1	in	in	ADP
ap-1261	270	2	such	such	ADJ
ap-1261	270	3	representation	representation	NOUN
ap-1261	270	4	,	,	PUNCT
ap-1261	270	5	the	the	DET
ap-1261	270	6	operator	operator	NOUN
ap-1261	270	7	j	j	PROPN
ap-1261	270	8	is	be	AUX
ap-1261	270	9	defined	define	VERB
ap-1261	270	10	by	by	ADP
ap-1261	270	11	j	j	PROPN
ap-1261	270	12	⎛⎜⎜⎝	⎛⎜⎜⎝	PROPN
ap-1261	270	13	2	2	NUM
ap-1261	270	14	�	�	PROPN
ap-1261	270	15	�	�	PROPN
ap-1261	270	16	0	0	NUM
ap-1261	270	17	m1,2	m1,2	PROPN
ap-1261	270	18	m2,2	m2,2	PROPN
ap-1261	270	19	m1,1	m1,1	PROPN
ap-1261	271	1	⎞⎟⎟⎠	⎞⎟⎟⎠	NOUN
ap-1261	271	2	=	=	SYM
ap-1261	271	3	(	(	PUNCT
ap-1261	271	4	−1	−1	NOUN
ap-1261	271	5	)	)	PUNCT
ap-1261	272	1	+	+	NOUN
ap-1261	272	2	m1,2+m2,2+m1,1	m1,2+m2,2+m1,1	NOUN
ap-1261	272	3	⎛⎜⎜⎝	⎛⎜⎜⎝	NOUN
ap-1261	272	4	2	2	NUM
ap-1261	272	5	�	�	PROPN
ap-1261	272	6	�	�	PROPN
ap-1261	272	7	0	0	NUM
ap-1261	272	8	2	2	NUM
ap-1261	272	9	�	�	NOUN
ap-1261	272	10	−	−	NOUN
ap-1261	272	11	m2,2	m2,2	PROPN
ap-1261	272	12	2	2	NUM
ap-1261	272	13	�	�	PROPN
ap-1261	272	14	−	−	PROPN
ap-1261	272	15	m1,2	m1,2	ADJ
ap-1261	272	16	2	2	NUM
ap-1261	272	17	�	�	NOUN
ap-1261	272	18	−	−	PROPN
ap-1261	272	19	m1,1	m1,1	NOUN
ap-1261	272	20	⎞⎟⎟⎠	⎞⎟⎟⎠	NOUN
ap-1261	272	21	.	.	PUNCT
ap-1261	273	1	the	the	DET
ap-1261	273	2	lowest	lowest	ADV
ap-1261	273	3	-	-	PUNCT
ap-1261	273	4	dimensional	dimensional	ADJ
ap-1261	273	5	non	non	ADJ
ap-1261	273	6	-	-	ADJ
ap-1261	273	7	trivial	trivial	ADJ
ap-1261	273	8	self	self	NOUN
ap-1261	273	9	-	-	PUNCT
ap-1261	273	10	contragredient	contragredient	NOUN
ap-1261	273	11	representation	representation	NOUN
ap-1261	273	12	is	be	AUX
ap-1261	273	13	r	r	NOUN
ap-1261	273	14	=	=	PUNCT
ap-1261	273	15	r(2	r(2	NOUN
ap-1261	273	16	,	,	PUNCT
ap-1261	273	17	1	1	NUM
ap-1261	273	18	,	,	PUNCT
ap-1261	273	19	0	0	NUM
ap-1261	273	20	)	)	PUNCT
ap-1261	273	21	,	,	PUNCT
ap-1261	273	22	in	in	ADP
ap-1261	273	23	fact	fact	NOUN
ap-1261	273	24	,	,	PUNCT
ap-1261	273	25	the	the	DET
ap-1261	273	26	adjoint	adjoint	PROPN
ap-1261	273	27	representation	representation	NOUN
ap-1261	273	28	.	.	PUNCT
ap-1261	274	1	its	its	PRON
ap-1261	274	2	dimension	dimension	NOUN
ap-1261	274	3	is	be	AUX
ap-1261	274	4	8	8	NUM
ap-1261	274	5	and	and	CCONJ
ap-1261	274	6	has	have	VERB
ap-1261	274	7	the	the	DET
ap-1261	274	8	following	follow	VERB
ap-1261	274	9	explicit	explicit	ADJ
ap-1261	274	10	form	form	NOUN
ap-1261	274	11	on	on	ADP
ap-1261	274	12	the	the	DET
ap-1261	274	13	basis	basis	NOUN
ap-1261	274	14	vectors	vector	NOUN
ap-1261	274	15	:	:	PUNCT
ap-1261	275	1	rg2	rg2	NOUN
ap-1261	275	2	⎛⎜⎜⎝	⎛⎜⎜⎝	NOUN
ap-1261	275	3	2	2	NUM
ap-1261	275	4	1	1	NUM
ap-1261	275	5	0	0	NUM
ap-1261	275	6	2	2	NUM
ap-1261	275	7	1	1	NUM
ap-1261	275	8	2	2	NUM
ap-1261	275	9	⎞⎟⎟⎠	⎞⎟⎟⎠	NOUN
ap-1261	275	10	=	=	NOUN
ap-1261	275	11	⎛⎜⎜⎝	⎛⎜⎜⎝	NOUN
ap-1261	275	12	2	2	NUM
ap-1261	275	13	1	1	NUM
ap-1261	275	14	0	0	NUM
ap-1261	275	15	1	1	NUM
ap-1261	275	16	0	0	NUM
ap-1261	275	17	0	0	NUM
ap-1261	275	18	⎞⎟⎟⎠	⎞⎟⎟⎠	NOUN
ap-1261	275	19	,	,	PUNCT
ap-1261	275	20	rg2	rg2	NOUN
ap-1261	275	21	⎛⎜⎜⎝	⎛⎜⎜⎝	NOUN
ap-1261	275	22	2	2	NUM
ap-1261	275	23	1	1	NUM
ap-1261	275	24	0	0	NUM
ap-1261	275	25	1	1	NUM
ap-1261	275	26	0	0	NUM
ap-1261	275	27	0	0	NUM
ap-1261	275	28	⎞⎟⎟⎠	⎞⎟⎟⎠	NOUN
ap-1261	275	29	=	=	NOUN
ap-1261	275	30	⎛⎜⎜⎝	⎛⎜⎜⎝	NOUN
ap-1261	275	31	2	2	NUM
ap-1261	275	32	1	1	NUM
ap-1261	275	33	0	0	NUM
ap-1261	275	34	2	2	NUM
ap-1261	275	35	1	1	NUM
ap-1261	275	36	2	2	NUM
ap-1261	275	37	⎞⎟⎟⎠	⎞⎟⎟⎠	NOUN
ap-1261	275	38	,	,	PUNCT
ap-1261	275	39	rg2	rg2	NOUN
ap-1261	275	40	⎛⎜⎜⎝	⎛⎜⎜⎝	NOUN
ap-1261	275	41	2	2	NUM
ap-1261	275	42	1	1	NUM
ap-1261	275	43	0	0	NUM
ap-1261	275	44	2	2	NUM
ap-1261	275	45	1	1	NUM
ap-1261	275	46	1	1	NUM
ap-1261	275	47	⎞⎟⎟⎠	⎞⎟⎟⎠	NOUN
ap-1261	275	48	=	=	SYM
ap-1261	275	49	−	−	PROPN
ap-1261	275	50	⎛⎜⎜⎝	⎛⎜⎜⎝	NOUN
ap-1261	275	51	2	2	NUM
ap-1261	275	52	1	1	NUM
ap-1261	275	53	0	0	NUM
ap-1261	275	54	1	1	NUM
ap-1261	275	55	0	0	NUM
ap-1261	275	56	1	1	NUM
ap-1261	275	57	⎞⎟⎟⎠	⎞⎟⎟⎠	NOUN
ap-1261	275	58	,	,	PUNCT
ap-1261	275	59	rg2	rg2	NOUN
ap-1261	275	60	⎛⎜⎜⎝	⎛⎜⎜⎝	NOUN
ap-1261	275	61	2	2	NUM
ap-1261	275	62	1	1	NUM
ap-1261	275	63	0	0	NUM
ap-1261	275	64	1	1	NUM
ap-1261	275	65	0	0	NUM
ap-1261	275	66	1	1	NUM
ap-1261	275	67	⎞⎟⎟⎠	⎞⎟⎟⎠	NOUN
ap-1261	275	68	=	=	SYM
ap-1261	275	69	−	−	PROPN
ap-1261	275	70	⎛⎜⎜⎝	⎛⎜⎜⎝	NOUN
ap-1261	275	71	2	2	NUM
ap-1261	275	72	1	1	NUM
ap-1261	275	73	0	0	NUM
ap-1261	275	74	2	2	NUM
ap-1261	275	75	1	1	NUM
ap-1261	275	76	1	1	NUM
ap-1261	275	77	⎞⎟⎟⎠	⎞⎟⎟⎠	NOUN
ap-1261	275	78	,	,	PUNCT
ap-1261	275	79	rg2	rg2	NOUN
ap-1261	275	80	⎛⎜⎜⎝	⎛⎜⎜⎝	NOUN
ap-1261	275	81	2	2	NUM
ap-1261	275	82	1	1	NUM
ap-1261	275	83	0	0	NUM
ap-1261	275	84	2	2	NUM
ap-1261	275	85	0	0	NUM
ap-1261	275	86	2	2	NUM
ap-1261	275	87	⎞⎟⎟⎠	⎞⎟⎟⎠	NOUN
ap-1261	275	88	=	=	SYM
ap-1261	275	89	−	−	PROPN
ap-1261	275	90	⎛⎜⎜⎝	⎛⎜⎜⎝	NOUN
ap-1261	275	91	2	2	NUM
ap-1261	275	92	1	1	NUM
ap-1261	275	93	0	0	NUM
ap-1261	275	94	2	2	NUM
ap-1261	275	95	0	0	NUM
ap-1261	275	96	0	0	NUM
ap-1261	275	97	⎞⎟⎟⎠	⎞⎟⎟⎠	NOUN
ap-1261	275	98	,	,	PUNCT
ap-1261	275	99	rg2	rg2	NOUN
ap-1261	275	100	⎛⎜⎜⎝	⎛⎜⎜⎝	NOUN
ap-1261	275	101	2	2	NUM
ap-1261	275	102	1	1	NUM
ap-1261	275	103	0	0	NUM
ap-1261	275	104	2	2	NUM
ap-1261	275	105	0	0	NUM
ap-1261	275	106	0	0	NUM
ap-1261	275	107	⎞⎟⎟⎠	⎞⎟⎟⎠	NOUN
ap-1261	275	108	=	=	SYM
ap-1261	275	109	−	−	PROPN
ap-1261	275	110	⎛⎜⎜⎝	⎛⎜⎜⎝	NOUN
ap-1261	275	111	2	2	NUM
ap-1261	275	112	1	1	NUM
ap-1261	275	113	0	0	NUM
ap-1261	275	114	2	2	NUM
ap-1261	275	115	0	0	NUM
ap-1261	275	116	2	2	NUM
ap-1261	275	117	⎞⎟⎟⎠	⎞⎟⎟⎠	NOUN
ap-1261	275	118	,	,	PUNCT
ap-1261	275	119	rg2	rg2	NOUN
ap-1261	275	120	⎛⎜⎜⎝	⎛⎜⎜⎝	NOUN
ap-1261	275	121	2	2	NUM
ap-1261	275	122	1	1	NUM
ap-1261	275	123	0	0	NUM
ap-1261	275	124	1	1	NUM
ap-1261	275	125	1	1	NUM
ap-1261	275	126	1	1	NUM
ap-1261	275	127	⎞⎟⎟⎠	⎞⎟⎟⎠	NOUN
ap-1261	275	128	=	=	NOUN
ap-1261	275	129	⎛⎜⎜⎝	⎛⎜⎜⎝	NOUN
ap-1261	275	130	2	2	NUM
ap-1261	275	131	1	1	NUM
ap-1261	275	132	0	0	NUM
ap-1261	275	133	1	1	NUM
ap-1261	275	134	1	1	NUM
ap-1261	275	135	1	1	NUM
ap-1261	275	136	⎞⎟⎟⎠	⎞⎟⎟⎠	NOUN
ap-1261	275	137	,	,	PUNCT
ap-1261	275	138	rg2	rg2	NOUN
ap-1261	275	139	⎛⎜⎜⎝	⎛⎜⎜⎝	NOUN
ap-1261	275	140	2	2	NUM
ap-1261	275	141	1	1	NUM
ap-1261	275	142	0	0	NUM
ap-1261	275	143	2	2	NUM
ap-1261	275	144	0	0	NUM
ap-1261	275	145	1	1	NUM
ap-1261	275	146	⎞⎟⎟⎠	⎞⎟⎟⎠	NOUN
ap-1261	275	147	=	=	NOUN
ap-1261	275	148	⎛⎜⎜⎝	⎛⎜⎜⎝	NOUN
ap-1261	275	149	2	2	NUM
ap-1261	275	150	1	1	NUM
ap-1261	275	151	0	0	NUM
ap-1261	275	152	2	2	NUM
ap-1261	275	153	0	0	NUM
ap-1261	275	154	1	1	NUM
ap-1261	275	155	⎞⎟⎟⎠	⎞⎟⎟⎠	NOUN
ap-1261	275	156	.	.	PUNCT
ap-1261	276	1	if	if	SCONJ
ap-1261	276	2	the	the	DET
ap-1261	276	3	representation	representation	NOUN
ap-1261	276	4	r	r	NOUN
ap-1261	276	5	=	=	SYM
ap-1261	276	6	r(m13	r(m13	NOUN
ap-1261	276	7	,	,	PUNCT
ap-1261	276	8	m23	m23	NOUN
ap-1261	276	9	,	,	PUNCT
ap-1261	276	10	0	0	NUM
ap-1261	276	11	)	)	PUNCT
ap-1261	276	12	is	be	AUX
ap-1261	276	13	not	not	PART
ap-1261	276	14	self	self	NOUN
ap-1261	276	15	-	-	PUNCT
ap-1261	276	16	contragredient	contragredient	NOUN
ap-1261	276	17	,	,	PUNCT
ap-1261	276	18	then	then	ADV
ap-1261	276	19	grading	grade	VERB
ap-1261	276	20	γ2	γ2	NOUN
ap-1261	276	21	is	be	AUX
ap-1261	276	22	compatible	compatible	ADJ
ap-1261	276	23	with	with	ADP
ap-1261	276	24	the	the	DET
ap-1261	276	25	reducible	reducible	ADJ
ap-1261	276	26	representation	representation	NOUN
ap-1261	276	27	r⊕(x	r⊕(x	NOUN
ap-1261	276	28	)	)	PUNCT
ap-1261	276	29	:	:	PUNCT
ap-1261	277	1	=	=	SYM
ap-1261	277	2	(	(	PUNCT
ap-1261	277	3	r(x	r(x	PROPN
ap-1261	277	4	)	)	PUNCT
ap-1261	277	5	0	0	NUM
ap-1261	277	6	0	0	NUM
ap-1261	278	1	−	−	PROPN
ap-1261	278	2	(	(	PUNCT
ap-1261	278	3	r(x	r(x	PROPN
ap-1261	278	4	)	)	PUNCT
ap-1261	278	5	)	)	PUNCT
ap-1261	279	1	t	t	NOUN
ap-1261	279	2	)	)	PUNCT
ap-1261	279	3	and	and	CCONJ
ap-1261	279	4	the	the	DET
ap-1261	279	5	corresponding	corresponding	ADJ
ap-1261	279	6	simulation	simulation	NOUN
ap-1261	279	7	matrix	matrix	NOUN
ap-1261	279	8	on	on	ADP
ap-1261	279	9	the	the	DET
ap-1261	279	10	double	double	ADJ
ap-1261	279	11	-	-	PUNCT
ap-1261	279	12	dimensional	dimensional	ADJ
ap-1261	279	13	space	space	NOUN
ap-1261	279	14	is	be	AUX
ap-1261	279	15	j	j	NOUN
ap-1261	279	16	=	=	PUNCT
ap-1261	279	17	σ1⊗	σ1⊗	PUNCT
ap-1261	280	1	i	i	PROPN
ap-1261	280	2	,	,	PUNCT
ap-1261	280	3	where	where	SCONJ
ap-1261	280	4	i	i	PRON
ap-1261	280	5	is	be	AUX
ap-1261	280	6	the	the	DET
ap-1261	280	7	identity	identity	NOUN
ap-1261	280	8	operator	operator	NOUN
ap-1261	280	9	on	on	ADP
ap-1261	280	10	the	the	DET
ap-1261	280	11	representation	representation	NOUN
ap-1261	280	12	space	space	NOUN
ap-1261	280	13	of	of	ADP
ap-1261	280	14	representation	representation	NOUN
ap-1261	280	15	r	r	NOUN
ap-1261	280	16	and	and	CCONJ
ap-1261	280	17	σ1	σ1	PROPN
ap-1261	280	18	denotes	denote	VERB
ap-1261	280	19	the	the	DET
ap-1261	280	20	first	first	ADJ
ap-1261	280	21	pauli	pauli	PROPN
ap-1261	280	22	matrix	matrix	NOUN
ap-1261	280	23	.	.	PUNCT
ap-1261	281	1	37	37	NUM
ap-1261	281	2	acta	acta	PROPN
ap-1261	281	3	polytechnica	polytechnica	PROPN
ap-1261	281	4	vol	vol	NOUN
ap-1261	281	5	.	.	PROPN
ap-1261	281	6	50	50	NUM
ap-1261	281	7	no	no	NOUN
ap-1261	281	8	.	.	PUNCT
ap-1261	282	1	5/2010	5/2010	NUM
ap-1261	282	2	4	4	NUM
ap-1261	282	3	conclusions	conclusion	NOUN
ap-1261	282	4	since	since	SCONJ
ap-1261	282	5	basic	basic	ADJ
ap-1261	282	6	concepts	concept	NOUN
ap-1261	282	7	connected	connect	VERB
ap-1261	282	8	with	with	ADP
ap-1261	282	9	gradings	grading	NOUN
ap-1261	282	10	of	of	ADP
ap-1261	282	11	lie	lie	NOUN
ap-1261	282	12	algebras	algebra	NOUN
ap-1261	282	13	were	be	AUX
ap-1261	282	14	laid	lay	VERB
ap-1261	282	15	down	down	ADP
ap-1261	282	16	already	already	ADV
ap-1261	282	17	in	in	ADP
ap-1261	282	18	the	the	DET
ap-1261	282	19	work	work	NOUN
ap-1261	282	20	of	of	ADP
ap-1261	282	21	j.	j.	PROPN
ap-1261	282	22	patera	patera	PROPN
ap-1261	282	23	and	and	CCONJ
ap-1261	282	24	h.	h.	PROPN
ap-1261	282	25	zassenhaus	zassenhaus	PROPN
ap-1261	283	1	[	[	X
ap-1261	283	2	16	16	NUM
ap-1261	283	3	]	]	PUNCT
ap-1261	283	4	,	,	PUNCT
ap-1261	283	5	including	include	VERB
ap-1261	283	6	the	the	DET
ap-1261	283	7	notion	notion	NOUN
ap-1261	283	8	of	of	ADP
ap-1261	283	9	compatibly	compatibly	ADV
ap-1261	283	10	graded	grade	VERB
ap-1261	283	11	representation	representation	NOUN
ap-1261	283	12	,	,	PUNCT
ap-1261	283	13	it	it	PRON
ap-1261	283	14	is	be	AUX
ap-1261	283	15	really	really	ADV
ap-1261	283	16	surprising	surprising	ADJ
ap-1261	283	17	that	that	SCONJ
ap-1261	283	18	there	there	PRON
ap-1261	283	19	does	do	AUX
ap-1261	283	20	not	not	PART
ap-1261	283	21	yet	yet	ADV
ap-1261	283	22	exist	exist	VERB
ap-1261	283	23	a	a	DET
ap-1261	283	24	theory	theory	NOUN
ap-1261	283	25	of	of	ADP
ap-1261	283	26	representations	representation	NOUN
ap-1261	283	27	of	of	ADP
ap-1261	283	28	graded	grade	VERB
ap-1261	283	29	lie	lie	NOUN
ap-1261	283	30	algebras	algebra	NOUN
ap-1261	283	31	compatible	compatible	ADJ
ap-1261	283	32	with	with	ADP
ap-1261	283	33	a	a	DET
ap-1261	283	34	given	give	VERB
ap-1261	283	35	grading	grading	NOUN
ap-1261	283	36	.	.	PUNCT
ap-1261	284	1	this	this	DET
ap-1261	284	2	work	work	NOUN
ap-1261	284	3	is	be	AUX
ap-1261	284	4	devoted	devote	VERB
ap-1261	284	5	to	to	ADP
ap-1261	284	6	first	first	ADJ
ap-1261	284	7	steps	step	NOUN
ap-1261	284	8	in	in	ADP
ap-1261	284	9	investigating	investigate	VERB
ap-1261	284	10	which	which	DET
ap-1261	284	11	irreducible	irreducible	ADJ
ap-1261	284	12	representations	representation	NOUN
ap-1261	284	13	of	of	ADP
ap-1261	284	14	a	a	DET
ap-1261	284	15	lie	lie	NOUN
ap-1261	284	16	algebra	algebra	NOUN
ap-1261	284	17	l	l	NOUN
ap-1261	284	18	are	be	AUX
ap-1261	284	19	compatible	compatible	ADJ
ap-1261	284	20	with	with	ADP
ap-1261	284	21	its	its	PRON
ap-1261	284	22	g	g	NOUN
ap-1261	284	23	-	-	PUNCT
ap-1261	284	24	grading	grade	VERB
ap-1261	284	25	,	,	PUNCT
ap-1261	284	26	at	at	ADP
ap-1261	284	27	least	least	ADJ
ap-1261	284	28	in	in	ADP
ap-1261	284	29	a	a	DET
ap-1261	284	30	rather	rather	ADV
ap-1261	284	31	restricted	restricted	ADJ
ap-1261	284	32	framework	framework	NOUN
ap-1261	284	33	.	.	PUNCT
ap-1261	285	1	the	the	DET
ap-1261	285	2	main	main	ADJ
ap-1261	285	3	contribution	contribution	NOUN
ap-1261	285	4	of	of	ADP
ap-1261	285	5	the	the	DET
ap-1261	285	6	paper	paper	NOUN
ap-1261	285	7	consists	consist	VERB
ap-1261	285	8	in	in	ADP
ap-1261	285	9	elucidating	elucidating	NOUN
ap-1261	285	10	which	which	PRON
ap-1261	285	11	representations	representation	NOUN
ap-1261	285	12	of	of	ADP
ap-1261	285	13	classical	classical	ADJ
ap-1261	285	14	lie	lie	NOUN
ap-1261	285	15	algebras	algebra	NOUN
ap-1261	285	16	of	of	ADP
ap-1261	285	17	type	type	NOUN
ap-1261	285	18	a	a	PRON
ap-1261	285	19	are	be	AUX
ap-1261	285	20	compatible	compatible	ADJ
ap-1261	285	21	with	with	ADP
ap-1261	285	22	a	a	DET
ap-1261	285	23	z2	z2	NOUN
ap-1261	285	24	-	-	PUNCT
ap-1261	285	25	grading	grade	VERB
ap-1261	285	26	.	.	PUNCT
ap-1261	286	1	concretely	concretely	ADV
ap-1261	286	2	,	,	PUNCT
ap-1261	286	3	the	the	DET
ap-1261	286	4	results	result	NOUN
ap-1261	286	5	are	be	AUX
ap-1261	286	6	as	as	SCONJ
ap-1261	286	7	follows	follow	VERB
ap-1261	286	8	:	:	PUNCT
ap-1261	286	9	if	if	SCONJ
ap-1261	286	10	the	the	DET
ap-1261	286	11	involutive	involutive	ADJ
ap-1261	286	12	automorphism	automorphism	NOUN
ap-1261	286	13	producing	produce	VERB
ap-1261	286	14	the	the	DET
ap-1261	286	15	z2	z2	NOUN
ap-1261	286	16	-	-	PUNCT
ap-1261	286	17	grading	grading	NOUN
ap-1261	286	18	is	be	AUX
ap-1261	286	19	inner	inner	ADJ
ap-1261	286	20	,	,	PUNCT
ap-1261	286	21	then	then	ADV
ap-1261	286	22	every	every	DET
ap-1261	286	23	irreducible	irreducible	ADJ
ap-1261	286	24	finite	finite	ADJ
ap-1261	286	25	-	-	ADJ
ap-1261	286	26	dimensional	dimensional	ADJ
ap-1261	286	27	representation	representation	NOUN
ap-1261	286	28	is	be	AUX
ap-1261	286	29	compatible	compatible	ADJ
ap-1261	286	30	with	with	ADP
ap-1261	286	31	the	the	DET
ap-1261	286	32	grading	grading	NOUN
ap-1261	286	33	,	,	PUNCT
ap-1261	286	34	but	but	CCONJ
ap-1261	286	35	if	if	SCONJ
ap-1261	286	36	the	the	DET
ap-1261	286	37	automorphism	automorphism	NOUN
ap-1261	286	38	producing	produce	VERB
ap-1261	286	39	the	the	DET
ap-1261	286	40	grading	grading	NOUN
ap-1261	286	41	is	be	AUX
ap-1261	286	42	not	not	PART
ap-1261	286	43	inner	inner	ADJ
ap-1261	286	44	,	,	PUNCT
ap-1261	286	45	then	then	ADV
ap-1261	286	46	the	the	DET
ap-1261	286	47	only	only	ADJ
ap-1261	286	48	irreducible	irreducible	ADJ
ap-1261	286	49	finite	finite	ADJ
ap-1261	286	50	-	-	ADJ
ap-1261	286	51	dimensional	dimensional	ADJ
ap-1261	286	52	representations	representation	NOUN
ap-1261	286	53	compatible	compatible	ADJ
ap-1261	286	54	with	with	ADP
ap-1261	286	55	the	the	DET
ap-1261	286	56	grading	grading	NOUN
ap-1261	286	57	are	be	AUX
ap-1261	286	58	the	the	DET
ap-1261	286	59	self	self	NOUN
ap-1261	286	60	-	-	PUNCT
ap-1261	286	61	contragredient	contragredient	NOUN
ap-1261	286	62	ones	one	NOUN
ap-1261	286	63	.	.	PUNCT
ap-1261	287	1	for	for	ADP
ap-1261	287	2	the	the	DET
ap-1261	287	3	outer	outer	ADJ
ap-1261	287	4	automorphism	automorphism	NOUN
ap-1261	287	5	there	there	PRON
ap-1261	287	6	is	be	VERB
ap-1261	287	7	also	also	ADV
ap-1261	287	8	a	a	DET
ap-1261	287	9	possibility	possibility	NOUN
ap-1261	287	10	of	of	ADP
ap-1261	287	11	reducible	reducible	ADJ
ap-1261	287	12	representations	representation	NOUN
ap-1261	287	13	involving	involve	VERB
ap-1261	287	14	pairs	pair	NOUN
ap-1261	287	15	of	of	ADP
ap-1261	287	16	mutually	mutually	ADV
ap-1261	287	17	contragredient	contragredient	ADJ
ap-1261	287	18	irreducible	irreducible	ADJ
ap-1261	287	19	representations	representation	NOUN
ap-1261	287	20	.	.	PUNCT
ap-1261	288	1	thus	thus	ADV
ap-1261	288	2	it	it	PRON
ap-1261	288	3	is	be	AUX
ap-1261	288	4	not	not	PART
ap-1261	288	5	generally	generally	ADV
ap-1261	288	6	true	true	ADJ
ap-1261	288	7	that	that	SCONJ
ap-1261	288	8	every	every	DET
ap-1261	288	9	irreducible	irreducible	ADJ
ap-1261	288	10	representation	representation	NOUN
ap-1261	288	11	can	can	AUX
ap-1261	288	12	be	be	AUX
ap-1261	288	13	compatibly	compatibly	ADV
ap-1261	288	14	graded	grade	VERB
ap-1261	288	15	.	.	PUNCT
ap-1261	289	1	the	the	DET
ap-1261	289	2	sl(3	sl(3	PROPN
ap-1261	289	3	,	,	PUNCT
ap-1261	289	4	c)-case	c)-case	NOUN
ap-1261	289	5	is	be	AUX
ap-1261	289	6	enclosed	enclose	VERB
ap-1261	289	7	to	to	PART
ap-1261	289	8	illustrate	illustrate	VERB
ap-1261	289	9	the	the	DET
ap-1261	289	10	process	process	NOUN
ap-1261	289	11	.	.	PUNCT
ap-1261	290	1	one	one	NUM
ap-1261	290	2	of	of	ADP
ap-1261	290	3	our	our	PRON
ap-1261	290	4	future	future	ADJ
ap-1261	290	5	goals	goal	NOUN
ap-1261	290	6	is	be	AUX
ap-1261	290	7	to	to	PART
ap-1261	290	8	enlarge	enlarge	VERB
ap-1261	290	9	the	the	DET
ap-1261	290	10	family	family	NOUN
ap-1261	290	11	of	of	ADP
ap-1261	290	12	gradings	grading	NOUN
ap-1261	290	13	of	of	ADP
ap-1261	290	14	l	l	NOUN
ap-1261	290	15	for	for	ADP
ap-1261	290	16	which	which	PRON
ap-1261	290	17	one	one	PRON
ap-1261	290	18	can	can	AUX
ap-1261	290	19	decide	decide	VERB
ap-1261	290	20	about	about	ADP
ap-1261	290	21	compatibility	compatibility	NOUN
ap-1261	290	22	with	with	ADP
ap-1261	290	23	representations	representation	NOUN
ap-1261	290	24	of	of	ADP
ap-1261	290	25	l.	l.	NOUN
ap-1261	290	26	another	another	DET
ap-1261	290	27	goal	goal	NOUN
ap-1261	290	28	is	be	AUX
ap-1261	290	29	to	to	PART
ap-1261	290	30	study	study	VERB
ap-1261	290	31	representations	representation	NOUN
ap-1261	290	32	of	of	ADP
ap-1261	290	33	physical	physical	ADJ
ap-1261	290	34	interest	interest	NOUN
ap-1261	290	35	of	of	ADP
ap-1261	290	36	the	the	DET
ap-1261	290	37	so	so	ADV
ap-1261	290	38	-	-	PUNCT
ap-1261	290	39	called	call	VERB
ap-1261	290	40	kinematical	kinematical	ADJ
ap-1261	290	41	groups	group	NOUN
ap-1261	290	42	of	of	ADP
ap-1261	290	43	space	space	NOUN
ap-1261	290	44	-	-	PUNCT
ap-1261	290	45	times	time	NOUN
ap-1261	290	46	.	.	PUNCT
ap-1261	291	1	the	the	DET
ap-1261	291	2	possible	possible	ADJ
ap-1261	291	3	lie	lie	NOUN
ap-1261	291	4	algebras	algebras	PROPN
ap-1261	291	5	l	l	PROPN
ap-1261	291	6	of	of	ADP
ap-1261	291	7	these	these	DET
ap-1261	291	8	groups	group	NOUN
ap-1261	291	9	were	be	AUX
ap-1261	291	10	classified	classify	VERB
ap-1261	291	11	in	in	ADP
ap-1261	291	12	[	[	X
ap-1261	291	13	1	1	NUM
ap-1261	291	14	]	]	PUNCT
ap-1261	291	15	.	.	PUNCT
ap-1261	292	1	a	a	DET
ap-1261	292	2	rather	rather	ADV
ap-1261	292	3	remarkable	remarkable	ADJ
ap-1261	292	4	fact	fact	NOUN
ap-1261	292	5	was	be	AUX
ap-1261	292	6	found	find	VERB
ap-1261	292	7	there	there	ADV
ap-1261	292	8	that	that	SCONJ
ap-1261	292	9	very	very	ADV
ap-1261	292	10	simple	simple	ADJ
ap-1261	292	11	conditions	condition	NOUN
ap-1261	292	12	imposed	impose	VERB
ap-1261	292	13	by	by	ADP
ap-1261	292	14	space	space	NOUN
ap-1261	292	15	inversion	inversion	NOUN
ap-1261	292	16	and	and	CCONJ
ap-1261	292	17	time	time	NOUN
ap-1261	292	18	reversal	reversal	NOUN
ap-1261	292	19	on	on	ADP
ap-1261	292	20	the	the	DET
ap-1261	292	21	generators	generator	NOUN
ap-1261	292	22	very	very	ADV
ap-1261	292	23	severely	severely	ADV
ap-1261	292	24	constrain	constrain	VERB
ap-1261	292	25	the	the	DET
ap-1261	292	26	possible	possible	ADJ
ap-1261	292	27	lie	lie	NOUN
ap-1261	292	28	algebras	algebra	NOUN
ap-1261	292	29	.	.	PUNCT
ap-1261	293	1	this	this	DET
ap-1261	293	2	result	result	NOUN
ap-1261	293	3	was	be	AUX
ap-1261	293	4	confirmed	confirm	VERB
ap-1261	293	5	in	in	ADP
ap-1261	293	6	[	[	X
ap-1261	293	7	12	12	NUM
ap-1261	293	8	]	]	PUNCT
ap-1261	293	9	from	from	ADP
ap-1261	293	10	the	the	DET
ap-1261	293	11	corresponding	correspond	VERB
ap-1261	293	12	z2	z2	PROPN
ap-1261	293	13	×	×	PROPN
ap-1261	293	14	z2	z2	NUM
ap-1261	293	15	-	-	PUNCT
ap-1261	293	16	contractions	contraction	NOUN
ap-1261	293	17	of	of	ADP
ap-1261	293	18	the	the	DET
ap-1261	293	19	de	de	PROPN
ap-1261	293	20	sitter	sitter	PROPN
ap-1261	293	21	lie	lie	NOUN
ap-1261	293	22	algebras	algebras	PROPN
ap-1261	293	23	.	.	PUNCT
ap-1261	294	1	from	from	ADP
ap-1261	294	2	this	this	DET
ap-1261	294	3	point	point	NOUN
ap-1261	294	4	of	of	ADP
ap-1261	294	5	view	view	NOUN
ap-1261	294	6	it	it	PRON
ap-1261	294	7	would	would	AUX
ap-1261	294	8	be	be	AUX
ap-1261	294	9	useful	useful	ADJ
ap-1261	294	10	to	to	PART
ap-1261	294	11	identify	identify	VERB
ap-1261	294	12	the	the	DET
ap-1261	294	13	gradings	grading	NOUN
ap-1261	294	14	implicitly	implicitly	ADV
ap-1261	294	15	present	present	ADJ
ap-1261	294	16	for	for	ADP
ap-1261	294	17	instance	instance	NOUN
ap-1261	294	18	in	in	ADP
ap-1261	294	19	[	[	X
ap-1261	294	20	3	3	NUM
ap-1261	294	21	,	,	PUNCT
ap-1261	294	22	18	18	NUM
ap-1261	294	23	]	]	PUNCT
ap-1261	294	24	and	and	CCONJ
ap-1261	294	25	in	in	ADP
ap-1261	294	26	other	other	ADJ
ap-1261	294	27	papers	paper	NOUN
ap-1261	294	28	where	where	SCONJ
ap-1261	294	29	contractions	contraction	NOUN
ap-1261	294	30	of	of	ADP
ap-1261	294	31	representations	representation	NOUN
ap-1261	294	32	are	be	AUX
ap-1261	294	33	studied	study	VERB
ap-1261	294	34	.	.	PUNCT
ap-1261	295	1	acknowledgement	acknowledgement	NOUN
ap-1261	295	2	the	the	DET
ap-1261	295	3	authors	author	NOUN
ap-1261	295	4	would	would	AUX
ap-1261	295	5	like	like	VERB
ap-1261	295	6	to	to	PART
ap-1261	295	7	express	express	VERB
ap-1261	295	8	their	their	PRON
ap-1261	295	9	gratitude	gratitude	NOUN
ap-1261	295	10	to	to	ADP
ap-1261	295	11	the	the	DET
ap-1261	295	12	referees	referee	NOUN
ap-1261	295	13	for	for	ADP
ap-1261	295	14	their	their	PRON
ap-1261	295	15	careful	careful	ADJ
ap-1261	295	16	reading	reading	NOUN
ap-1261	295	17	of	of	ADP
ap-1261	295	18	the	the	DET
ap-1261	295	19	manuscript	manuscript	NOUN
ap-1261	295	20	and	and	CCONJ
ap-1261	295	21	for	for	ADP
ap-1261	295	22	their	their	PRON
ap-1261	295	23	valuable	valuable	ADJ
ap-1261	295	24	critical	critical	ADJ
ap-1261	295	25	comments	comment	NOUN
ap-1261	295	26	,	,	PUNCT
ap-1261	295	27	which	which	PRON
ap-1261	295	28	have	have	AUX
ap-1261	295	29	helped	help	VERB
ap-1261	295	30	to	to	PART
ap-1261	295	31	improve	improve	VERB
ap-1261	295	32	the	the	DET
ap-1261	295	33	presentation	presentation	NOUN
ap-1261	295	34	.	.	PUNCT
ap-1261	296	1	we	we	PRON
ap-1261	296	2	are	be	AUX
ap-1261	296	3	grateful	grateful	ADJ
ap-1261	296	4	to	to	PART
ap-1261	296	5	vyacheslav	vyacheslav	NOUN
ap-1261	296	6	futorny	futorny	VERB
ap-1261	296	7	for	for	ADP
ap-1261	296	8	fruitful	fruitful	ADJ
ap-1261	296	9	discussions	discussion	NOUN
ap-1261	296	10	on	on	ADP
ap-1261	296	11	relations	relation	NOUN
ap-1261	296	12	between	between	ADP
ap-1261	296	13	the	the	DET
ap-1261	296	14	notions	notion	NOUN
ap-1261	296	15	of	of	ADP
ap-1261	296	16	grading	grading	NOUN
ap-1261	296	17	and	and	CCONJ
ap-1261	296	18	group	group	NOUN
ap-1261	296	19	grading	grading	NOUN
ap-1261	296	20	,	,	PUNCT
ap-1261	296	21	and	and	CCONJ
ap-1261	296	22	to	to	ADP
ap-1261	296	23	jiří	jiří	NOUN
ap-1261	296	24	patera	patera	NOUN
ap-1261	296	25	for	for	ADP
ap-1261	296	26	introducing	introduce	VERB
ap-1261	296	27	us	we	PRON
ap-1261	296	28	to	to	ADP
ap-1261	296	29	the	the	DET
ap-1261	296	30	problems	problem	NOUN
ap-1261	296	31	connected	connect	VERB
ap-1261	296	32	with	with	ADP
ap-1261	296	33	representations	representation	NOUN
ap-1261	296	34	of	of	ADP
ap-1261	296	35	contracted	contract	VERB
ap-1261	296	36	lie	lie	NOUN
ap-1261	296	37	algebras	algebra	NOUN
ap-1261	296	38	.	.	PUNCT
ap-1261	297	1	we	we	PRON
ap-1261	297	2	acknowledge	acknowledge	VERB
ap-1261	297	3	financial	financial	ADJ
ap-1261	297	4	support	support	NOUN
ap-1261	297	5	from	from	ADP
ap-1261	297	6	the	the	DET
ap-1261	297	7	grants	grant	NOUN
ap-1261	297	8	msm6840770039	msm6840770039	NOUN
ap-1261	297	9	and	and	CCONJ
ap-1261	297	10	lc06002	lc06002	NOUN
ap-1261	297	11	of	of	ADP
ap-1261	297	12	the	the	DET
ap-1261	297	13	ministry	ministry	PROPN
ap-1261	297	14	of	of	ADP
ap-1261	297	15	education	education	PROPN
ap-1261	297	16	,	,	PUNCT
ap-1261	297	17	youth	youth	NOUN
ap-1261	297	18	,	,	PUNCT
ap-1261	297	19	and	and	CCONJ
ap-1261	297	20	sports	sport	NOUN
ap-1261	297	21	of	of	ADP
ap-1261	297	22	the	the	DET
ap-1261	297	23	czech	czech	PROPN
ap-1261	297	24	republic	republic	NOUN
ap-1261	297	25	.	.	PUNCT
ap-1261	298	1	appendix	appendix	NOUN
ap-1261	298	2	.	.	PUNCT
ap-1261	299	1	the	the	DET
ap-1261	299	2	gel’fand	gel’fand	NOUN
ap-1261	299	3	-	-	PUNCT
ap-1261	299	4	tseitlin	tseitlin	NOUN
ap-1261	299	5	formalism	formalism	NOUN
ap-1261	299	6	let	let	VERB
ap-1261	299	7	us	we	PRON
ap-1261	299	8	give	give	VERB
ap-1261	299	9	an	an	DET
ap-1261	299	10	explicit	explicit	ADJ
ap-1261	299	11	description	description	NOUN
ap-1261	299	12	of	of	ADP
ap-1261	299	13	the	the	DET
ap-1261	299	14	irreducible	irreducible	ADJ
ap-1261	299	15	representations	representation	NOUN
ap-1261	299	16	of	of	ADP
ap-1261	299	17	gl(n	gl(n	PROPN
ap-1261	299	18	,	,	PUNCT
ap-1261	299	19	c	c	NOUN
ap-1261	299	20	)	)	PUNCT
ap-1261	299	21	in	in	ADP
ap-1261	299	22	the	the	DET
ap-1261	299	23	gel’fand	gel’fand	NOUN
ap-1261	299	24	-	-	PUNCT
ap-1261	299	25	tseitlin	tseitlin	NOUN
ap-1261	299	26	formalism	formalism	NOUN
ap-1261	299	27	[	[	X
ap-1261	299	28	4	4	NUM
ap-1261	299	29	,	,	PUNCT
ap-1261	299	30	10	10	NUM
ap-1261	299	31	,	,	PUNCT
ap-1261	299	32	2	2	NUM
ap-1261	299	33	]	]	PUNCT
ap-1261	299	34	.	.	PUNCT
ap-1261	300	1	any	any	DET
ap-1261	300	2	irreducible	irreducible	ADJ
ap-1261	300	3	representation	representation	NOUN
ap-1261	300	4	r	r	NOUN
ap-1261	300	5	of	of	ADP
ap-1261	300	6	gl(n	gl(n	PROPN
ap-1261	300	7	,	,	PUNCT
ap-1261	300	8	c	c	X
ap-1261	300	9	)	)	PUNCT
ap-1261	300	10	is	be	AUX
ap-1261	300	11	in	in	ADP
ap-1261	300	12	one	one	NUM
ap-1261	300	13	-	-	PUNCT
ap-1261	300	14	to	to	ADP
ap-1261	300	15	-	-	PUNCT
ap-1261	300	16	one	one	NUM
ap-1261	300	17	correspondence	correspondence	NOUN
ap-1261	300	18	with	with	ADP
ap-1261	300	19	an	an	DET
ap-1261	300	20	n	n	CCONJ
ap-1261	300	21	-	-	PUNCT
ap-1261	300	22	tuple	tuple	NOUN
ap-1261	300	23	(	(	PUNCT
ap-1261	300	24	m1,n	m1,n	PROPN
ap-1261	300	25	,	,	PUNCT
ap-1261	300	26	m2,n	m2,n	PROPN
ap-1261	300	27	,	,	PUNCT
ap-1261	300	28	.	.	PUNCT
ap-1261	300	29	.	.	PUNCT
ap-1261	301	1	.	.	PUNCT
ap-1261	302	1	,	,	PUNCT
ap-1261	302	2	mn	mn	PROPN
ap-1261	302	3	,	,	PUNCT
ap-1261	302	4	n	n	CCONJ
ap-1261	302	5	)	)	PUNCT
ap-1261	302	6	of	of	ADP
ap-1261	302	7	non	non	ADJ
ap-1261	302	8	-	-	ADJ
ap-1261	302	9	negative	negative	ADJ
ap-1261	302	10	integer	integer	NOUN
ap-1261	302	11	parameters	parameter	NOUN
ap-1261	302	12	m1,n	m1,n	PROPN
ap-1261	302	13	≥	≥	NUM
ap-1261	302	14	m2,n	m2,n	PROPN
ap-1261	302	15	≥	≥	NOUN
ap-1261	302	16	.	.	PUNCT
ap-1261	302	17	.	.	PUNCT
ap-1261	303	1	.	.	PUNCT
ap-1261	304	1	≥	≥	PROPN
ap-1261	304	2	mn	mn	PROPN
ap-1261	304	3	,	,	PUNCT
ap-1261	304	4	n	n	PRON
ap-1261	304	5	≥	≥	NOUN
ap-1261	304	6	0	0	NUM
ap-1261	304	7	.	.	PUNCT
ap-1261	305	1	since	since	SCONJ
ap-1261	305	2	any	any	DET
ap-1261	305	3	ek	ek	NOUN
ap-1261	305	4	can	can	AUX
ap-1261	305	5	be	be	AUX
ap-1261	305	6	obtained	obtain	VERB
ap-1261	305	7	by	by	ADP
ap-1261	305	8	commutation	commutation	NOUN
ap-1261	305	9	relations	relation	NOUN
ap-1261	305	10	from	from	ADP
ap-1261	305	11	ek	ek	PROPN
ap-1261	305	12	,	,	PUNCT
ap-1261	305	13	k	k	PROPN
ap-1261	305	14	,	,	PUNCT
ap-1261	305	15	ek	ek	PROPN
ap-1261	305	16	,	,	PUNCT
ap-1261	305	17	k−1	k−1	PROPN
ap-1261	305	18	and	and	CCONJ
ap-1261	305	19	ek−1,k	ek−1,k	PROPN
ap-1261	305	20	,	,	PUNCT
ap-1261	305	21	only	only	ADV
ap-1261	305	22	formulas	formula	NOUN
ap-1261	305	23	for	for	ADP
ap-1261	305	24	r(ek	r(ek	NOUN
ap-1261	305	25	,	,	PUNCT
ap-1261	305	26	k	k	NOUN
ap-1261	305	27	)	)	PUNCT
ap-1261	305	28	,	,	PUNCT
ap-1261	305	29	r(ek	r(ek	NOUN
ap-1261	305	30	,	,	PUNCT
ap-1261	305	31	k−1	k−1	PROPN
ap-1261	305	32	)	)	PUNCT
ap-1261	305	33	and	and	CCONJ
ap-1261	305	34	r(ek−1,k	r(ek−1,k	PROPN
ap-1261	305	35	)	)	PUNCT
ap-1261	305	36	are	be	AUX
ap-1261	305	37	needed	need	VERB
ap-1261	305	38	:	:	PUNCT
ap-1261	305	39	r(ek	r(ek	NOUN
ap-1261	305	40	,	,	PUNCT
ap-1261	305	41	k)ξ(m	k)ξ(m	NOUN
ap-1261	305	42	)	)	PUNCT
ap-1261	306	1	=	=	PRON
ap-1261	306	2	(	(	PUNCT
ap-1261	306	3	rk	rk	NOUN
ap-1261	306	4	−	−	PROPN
ap-1261	306	5	rk−1)ξ(m	rk−1)ξ(m	PROPN
ap-1261	306	6	)	)	PUNCT
ap-1261	306	7	,	,	PUNCT
ap-1261	306	8	where	where	SCONJ
ap-1261	306	9	rk	rk	NOUN
ap-1261	306	10	=	=	SYM
ap-1261	306	11	m1,k	m1,k	PROPN
ap-1261	306	12	+	+	AUX
ap-1261	306	13	.	.	PUNCT
ap-1261	306	14	.	.	PUNCT
ap-1261	307	1	.+mk	.+mk	PROPN
ap-1261	307	2	,	,	PUNCT
ap-1261	307	3	k	k	PROPN
ap-1261	307	4	for	for	ADP
ap-1261	307	5	k	k	PROPN
ap-1261	307	6	=	=	SYM
ap-1261	307	7	1	1	NUM
ap-1261	307	8	,	,	PUNCT
ap-1261	307	9	2	2	NUM
ap-1261	307	10	,	,	PUNCT
ap-1261	307	11	.	.	PUNCT
ap-1261	307	12	.	.	PUNCT
ap-1261	308	1	.	.	PUNCT
ap-1261	309	1	,	,	PUNCT
ap-1261	309	2	n	n	NOUN
ap-1261	309	3	and	and	CCONJ
ap-1261	309	4	r0	r0	NOUN
ap-1261	309	5	=	=	SYM
ap-1261	309	6	0	0	NUM
ap-1261	309	7	,	,	PUNCT
ap-1261	309	8	r(ek	r(ek	NOUN
ap-1261	309	9	,	,	PUNCT
ap-1261	309	10	k−1)ξ(m	k−1)ξ(m	NUM
ap-1261	309	11	)	)	PUNCT
ap-1261	310	1	=	=	SYM
ap-1261	310	2	a1k−1ξ(m	a1k−1ξ(m	NOUN
ap-1261	310	3	1	1	NUM
ap-1261	310	4	k−1	k−1	PROPN
ap-1261	310	5	)	)	PUNCT
ap-1261	310	6	+	+	CCONJ
ap-1261	310	7	.	.	PUNCT
ap-1261	310	8	.	.	PUNCT
ap-1261	311	1	.+	.+	PROPN
ap-1261	311	2	ak−1	ak−1	PROPN
ap-1261	311	3	k−1ξ(m	k−1ξ(m	PROPN
ap-1261	311	4	k−1	k−1	PROPN
ap-1261	311	5	k−1	k−1	PROPN
ap-1261	311	6	)	)	PUNCT
ap-1261	311	7	,	,	PUNCT
ap-1261	311	8	where	where	SCONJ
ap-1261	311	9	mj	mj	PROPN
ap-1261	311	10	k−1	k−1	PROPN
ap-1261	311	11	denotes	denote	VERB
ap-1261	311	12	the	the	DET
ap-1261	311	13	triangular	triangular	NOUN
ap-1261	311	14	pattern	pattern	NOUN
ap-1261	311	15	obtained	obtain	VERB
ap-1261	311	16	from	from	ADP
ap-1261	311	17	m	m	PROPN
ap-1261	311	18	replacing	replace	VERB
ap-1261	311	19	mj	mj	PRON
ap-1261	311	20	,	,	PUNCT
ap-1261	311	21	k−1	k−1	PROPN
ap-1261	311	22	by	by	ADP
ap-1261	311	23	mj	mj	PROPN
ap-1261	311	24	,	,	PUNCT
ap-1261	311	25	k−1	k−1	PROPN
ap-1261	311	26	−	−	PROPN
ap-1261	311	27	1	1	NUM
ap-1261	311	28	,	,	PUNCT
ap-1261	311	29	aj	aj	PROPN
ap-1261	311	30	k−1	k−1	PROPN
ap-1261	311	31	=	=	PUNCT
ap-1261	312	1	[	[	PUNCT
ap-1261	312	2	−	−	X
ap-1261	312	3	∏k	∏k	X
ap-1261	312	4	i=1(mi	i=1(mi	NOUN
ap-1261	312	5	,	,	PUNCT
ap-1261	312	6	k	k	PROPN
ap-1261	312	7	−	−	PROPN
ap-1261	312	8	mj	mj	PROPN
ap-1261	312	9	,	,	PUNCT
ap-1261	312	10	k−1	k−1	PROPN
ap-1261	312	11	−	−	PROPN
ap-1261	312	12	i+	i+	NOUN
ap-1261	312	13	j	j	NOUN
ap-1261	312	14	+	+	CCONJ
ap-1261	312	15	1	1	X
ap-1261	312	16	)	)	PUNCT
ap-1261	312	17	∏k−2	∏k−2	PROPN
ap-1261	312	18	i=1	i=1	PROPN
ap-1261	312	19	(	(	PUNCT
ap-1261	312	20	mi	mi	PROPN
ap-1261	312	21	,	,	PUNCT
ap-1261	312	22	k−2	k−2	PROPN
ap-1261	312	23	−	−	PROPN
ap-1261	312	24	mj	mj	PROPN
ap-1261	312	25	,	,	PUNCT
ap-1261	312	26	k−1	k−1	PROPN
ap-1261	312	27	−	−	PROPN
ap-1261	312	28	i+	i+	PUNCT
ap-1261	312	29	j)∏	j)∏	PROPN
ap-1261	312	30	i	i	PRON
ap-1261	312	31	�	�	NOUN
ap-1261	312	32	=j(mi	=j(mi	NOUN
ap-1261	312	33	,	,	PUNCT
ap-1261	312	34	k−1	k−1	PROPN
ap-1261	312	35	−	−	PROPN
ap-1261	312	36	mj	mj	PROPN
ap-1261	312	37	,	,	PUNCT
ap-1261	312	38	k−1	k−1	PROPN
ap-1261	312	39	−	−	PROPN
ap-1261	312	40	i+	i+	NOUN
ap-1261	312	41	j	j	PROPN
ap-1261	312	42	+	+	PROPN
ap-1261	312	43	1)(mi	1)(mi	NUM
ap-1261	312	44	,	,	PUNCT
ap-1261	312	45	k−1	k−1	PROPN
ap-1261	312	46	−	−	PROPN
ap-1261	312	47	mj	mj	PROPN
ap-1261	312	48	,	,	PUNCT
ap-1261	312	49	k−1	k−1	PROPN
ap-1261	312	50	−	−	PROPN
ap-1261	312	51	i+	i+	X
ap-1261	312	52	j	j	PROPN
ap-1261	312	53	)	)	PUNCT
ap-1261	312	54	]	]	PUNCT
ap-1261	312	55	1/2	1/2	NUM
ap-1261	312	56	and	and	CCONJ
ap-1261	312	57	r(ek−1,k)ξ(m	r(ek−1,k)ξ(m	NOUN
ap-1261	312	58	)	)	PUNCT
ap-1261	312	59	=	=	PRON
ap-1261	312	60	b1k−1ξ(m	b1k−1ξ(m	NOUN
ap-1261	312	61	1	1	NUM
ap-1261	312	62	k−1	k−1	PROPN
ap-1261	312	63	)	)	PUNCT
ap-1261	312	64	+	+	CCONJ
ap-1261	312	65	.	.	PUNCT
ap-1261	312	66	.	.	PUNCT
ap-1261	313	1	.+	.+	NOUN
ap-1261	314	1	bk−1	bk−1	ADJ
ap-1261	314	2	k−1ξ(m	k−1ξ(m	NOUN
ap-1261	314	3	k−1	k−1	PROPN
ap-1261	314	4	k−1	k−1	PROPN
ap-1261	314	5	)	)	PUNCT
ap-1261	314	6	,	,	PUNCT
ap-1261	314	7	where	where	SCONJ
ap-1261	314	8	mj	mj	PROPN
ap-1261	314	9	k−1	k−1	PROPN
ap-1261	314	10	denotes	denote	VERB
ap-1261	314	11	the	the	DET
ap-1261	314	12	triangular	triangular	NOUN
ap-1261	314	13	pattern	pattern	NOUN
ap-1261	314	14	obtained	obtain	VERB
ap-1261	314	15	from	from	ADP
ap-1261	314	16	m	m	PROPN
ap-1261	314	17	replacing	replace	VERB
ap-1261	314	18	mj	mj	PRON
ap-1261	314	19	,	,	PUNCT
ap-1261	314	20	k−1	k−1	PROPN
ap-1261	314	21	by	by	ADP
ap-1261	314	22	mj	mj	PROPN
ap-1261	314	23	,	,	PUNCT
ap-1261	314	24	k−1	k−1	PROPN
ap-1261	314	25	+	+	PROPN
ap-1261	314	26	1	1	NUM
ap-1261	314	27	,	,	PUNCT
ap-1261	314	28	and	and	CCONJ
ap-1261	314	29	bj	bj	VERB
ap-1261	314	30	k−1	k−1	PROPN
ap-1261	314	31	=	=	PUNCT
ap-1261	314	32	[	[	PUNCT
ap-1261	314	33	−	−	X
ap-1261	314	34	∏k	∏k	X
ap-1261	314	35	i=1(mik	i=1(mik	PROPN
ap-1261	314	36	−	−	PROPN
ap-1261	314	37	mj	mj	PROPN
ap-1261	314	38	,	,	PUNCT
ap-1261	314	39	k−1	k−1	PROPN
ap-1261	314	40	−	−	PROPN
ap-1261	314	41	i+	i+	PRON
ap-1261	314	42	j	j	PROPN
ap-1261	314	43	)	)	PUNCT
ap-1261	314	44	∏k−2	∏k−2	PROPN
ap-1261	314	45	i=1	i=1	PROPN
ap-1261	314	46	(	(	PUNCT
ap-1261	314	47	mi	mi	PROPN
ap-1261	314	48	,	,	PUNCT
ap-1261	314	49	k−2	k−2	PROPN
ap-1261	314	50	−	−	PROPN
ap-1261	314	51	mj	mj	PROPN
ap-1261	314	52	,	,	PUNCT
ap-1261	314	53	k−1	k−1	PROPN
ap-1261	314	54	−	−	PROPN
ap-1261	314	55	i+	i+	NUM
ap-1261	315	1	j	j	NOUN
ap-1261	315	2	−	−	PROPN
ap-1261	315	3	1)∏	1)∏	NUM
ap-1261	315	4	i	i	NOUN
ap-1261	315	5	�	�	VERB
ap-1261	315	6	=j(mi	=j(mi	NOUN
ap-1261	315	7	,	,	PUNCT
ap-1261	315	8	k−1	k−1	PROPN
ap-1261	315	9	−	−	PROPN
ap-1261	315	10	mj	mj	PROPN
ap-1261	315	11	,	,	PUNCT
ap-1261	315	12	k−1	k−1	PROPN
ap-1261	315	13	−	−	PROPN
ap-1261	315	14	i+	i+	SYM
ap-1261	315	15	j)(mi	j)(mi	PROPN
ap-1261	315	16	,	,	PUNCT
ap-1261	315	17	k−1	k−1	PROPN
ap-1261	315	18	−	−	PROPN
ap-1261	316	1	mj	mj	PROPN
ap-1261	316	2	,	,	PUNCT
ap-1261	316	3	k−1	k−1	PROPN
ap-1261	316	4	−	−	PROPN
ap-1261	316	5	i+	i+	NUM
ap-1261	316	6	j	j	NOUN
ap-1261	316	7	−	−	PROPN
ap-1261	316	8	1	1	NUM
ap-1261	316	9	)	)	PUNCT
ap-1261	316	10	]	]	PUNCT
ap-1261	316	11	1/2	1/2	NUM
ap-1261	316	12	.	.	PUNCT
ap-1261	317	1	38	38	NUM
ap-1261	317	2	acta	acta	PROPN
ap-1261	317	3	polytechnica	polytechnica	PROPN
ap-1261	317	4	vol	vol	NOUN
ap-1261	317	5	.	.	PUNCT
ap-1261	318	1	50	50	NUM
ap-1261	318	2	no	no	NOUN
ap-1261	318	3	.	.	PUNCT
ap-1261	319	1	5/2010	5/2010	NUM
ap-1261	319	2	references	reference	NOUN
ap-1261	319	3	[	[	X
ap-1261	319	4	1	1	NUM
ap-1261	319	5	]	]	PUNCT
ap-1261	319	6	bacry	bacry	NOUN
ap-1261	319	7	,	,	PUNCT
ap-1261	319	8	h.	h.	PROPN
ap-1261	319	9	,	,	PUNCT
ap-1261	319	10	lévy	lévy	NOUN
ap-1261	319	11	-	-	PUNCT
ap-1261	319	12	leblond	leblond	NOUN
ap-1261	319	13	,	,	PUNCT
ap-1261	319	14	j.-m	j.-m	NOUN
ap-1261	319	15	.	.	PUNCT
ap-1261	319	16	:	:	PUNCT
ap-1261	320	1	possible	possible	ADJ
ap-1261	320	2	kinematics	kinematic	NOUN
ap-1261	320	3	,	,	PUNCT
ap-1261	320	4	j.	j.	PROPN
ap-1261	320	5	math	math	PROPN
ap-1261	320	6	.	.	PUNCT
ap-1261	321	1	phys	phy	NOUN
ap-1261	321	2	.	.	PUNCT
ap-1261	322	1	9	9	NUM
ap-1261	322	2	(	(	PUNCT
ap-1261	322	3	1968	1968	NUM
ap-1261	322	4	)	)	PUNCT
ap-1261	322	5	,	,	PUNCT
ap-1261	322	6	1	1	NUM
ap-1261	322	7	605–1614	605–1614	NUM
ap-1261	322	8	.	.	PUNCT
ap-1261	323	1	[	[	X
ap-1261	323	2	2	2	NUM
ap-1261	323	3	]	]	PUNCT
ap-1261	323	4	barut	barut	NOUN
ap-1261	323	5	,	,	PUNCT
ap-1261	323	6	a.	a.	NOUN
ap-1261	323	7	o.	o.	PROPN
ap-1261	323	8	,	,	PUNCT
ap-1261	323	9	raczka	raczka	PROPN
ap-1261	323	10	,	,	PUNCT
ap-1261	323	11	r.	r.	PROPN
ap-1261	323	12	:	:	PUNCT
ap-1261	323	13	theory	theory	NOUN
ap-1261	323	14	of	of	ADP
ap-1261	323	15	group	group	NOUN
ap-1261	323	16	representations	representation	NOUN
ap-1261	323	17	and	and	CCONJ
ap-1261	323	18	applications	application	NOUN
ap-1261	323	19	,	,	PUNCT
ap-1261	323	20	world	world	NOUN
ap-1261	323	21	scientific	scientific	PROPN
ap-1261	323	22	,	,	PUNCT
ap-1261	323	23	singapore	singapore	PROPN
ap-1261	323	24	,	,	PUNCT
ap-1261	323	25	2000	2000	NUM
ap-1261	323	26	,	,	PUNCT
ap-1261	323	27	chap	chap	NOUN
ap-1261	323	28	.	.	PUNCT
ap-1261	324	1	10	10	NUM
ap-1261	324	2	.	.	PUNCT
ap-1261	325	1	[	[	X
ap-1261	325	2	3	3	NUM
ap-1261	325	3	]	]	X
ap-1261	325	4	de	de	X
ap-1261	325	5	bièvre	bièvre	PROPN
ap-1261	325	6	,	,	PUNCT
ap-1261	325	7	s.	s.	PROPN
ap-1261	325	8	,	,	PUNCT
ap-1261	325	9	cishahayo	cishahayo	PROPN
ap-1261	325	10	,	,	PUNCT
ap-1261	325	11	c.	c.	PROPN
ap-1261	325	12	:	:	PUNCT
ap-1261	325	13	on	on	ADP
ap-1261	325	14	the	the	DET
ap-1261	325	15	contraction	contraction	NOUN
ap-1261	325	16	of	of	ADP
ap-1261	325	17	the	the	DET
ap-1261	325	18	discrete	discrete	ADJ
ap-1261	325	19	series	series	NOUN
ap-1261	325	20	of	of	ADP
ap-1261	325	21	su(1,1	su(1,1	PROPN
ap-1261	325	22	)	)	PUNCT
ap-1261	325	23	,	,	PUNCT
ap-1261	325	24	ann	ann	PROPN
ap-1261	325	25	.	.	PROPN
ap-1261	325	26	inst	inst	PROPN
ap-1261	325	27	.	.	PUNCT
ap-1261	326	1	fourier	fourier	PROPN
ap-1261	326	2	,	,	PUNCT
ap-1261	326	3	43	43	NUM
ap-1261	326	4	(	(	PUNCT
ap-1261	326	5	1993	1993	NUM
ap-1261	326	6	)	)	PUNCT
ap-1261	326	7	,	,	PUNCT
ap-1261	326	8	551–567	551–567	NUM
ap-1261	326	9	.	.	PUNCT
ap-1261	327	1	[	[	X
ap-1261	327	2	4	4	NUM
ap-1261	327	3	]	]	X
ap-1261	327	4	gel’fand	gel’fand	PROPN
ap-1261	327	5	,	,	PUNCT
ap-1261	327	6	i.	i.	NOUN
ap-1261	327	7	m.	m.	PROPN
ap-1261	327	8	,	,	PUNCT
ap-1261	327	9	tseitlin	tseitlin	NOUN
ap-1261	327	10	,	,	PUNCT
ap-1261	327	11	m.	m.	NOUN
ap-1261	327	12	l.	l.	PROPN
ap-1261	327	13	:	:	PUNCT
ap-1261	327	14	finite	finite	ADJ
ap-1261	327	15	-	-	ADJ
ap-1261	327	16	dimensional	dimensional	ADJ
ap-1261	327	17	representations	representation	NOUN
ap-1261	327	18	of	of	ADP
ap-1261	327	19	the	the	DET
ap-1261	327	20	group	group	NOUN
ap-1261	327	21	of	of	ADP
ap-1261	327	22	unimodular	unimodular	ADJ
ap-1261	327	23	matrices	matrix	NOUN
ap-1261	327	24	,	,	PUNCT
ap-1261	327	25	dokl	dokl	NOUN
ap-1261	327	26	.	.	PUNCT
ap-1261	327	27	akad	akad	PROPN
ap-1261	327	28	.	.	PUNCT
ap-1261	328	1	nauk	nauk	NOUN
ap-1261	328	2	sssr	sssr	NOUN
ap-1261	328	3	71	71	NUM
ap-1261	328	4	(	(	PUNCT
ap-1261	328	5	1950	1950	NUM
ap-1261	328	6	)	)	PUNCT
ap-1261	328	7	,	,	PUNCT
ap-1261	328	8	825–828	825–828	NUM
ap-1261	328	9	.	.	PUNCT
ap-1261	329	1	[	[	X
ap-1261	329	2	5	5	NUM
ap-1261	329	3	]	]	X
ap-1261	329	4	gilmore	gilmore	PROPN
ap-1261	329	5	,	,	PUNCT
ap-1261	329	6	r.	r.	PROPN
ap-1261	329	7	:	:	PUNCT
ap-1261	329	8	lie	lie	NOUN
ap-1261	329	9	groups	group	NOUN
ap-1261	329	10	,	,	PUNCT
ap-1261	329	11	lie	lie	NOUN
ap-1261	329	12	algebras	algebra	NOUN
ap-1261	329	13	,	,	PUNCT
ap-1261	329	14	and	and	CCONJ
ap-1261	329	15	some	some	PRON
ap-1261	329	16	of	of	ADP
ap-1261	329	17	their	their	PRON
ap-1261	329	18	applications	application	NOUN
ap-1261	329	19	,	,	PUNCT
ap-1261	329	20	wiley	wiley	NOUN
ap-1261	329	21	,	,	PUNCT
ap-1261	329	22	new	new	PROPN
ap-1261	329	23	york	york	PROPN
ap-1261	329	24	1974	1974	NUM
ap-1261	329	25	,	,	PUNCT
ap-1261	329	26	chap	chap	NOUN
ap-1261	329	27	.	.	PUNCT
ap-1261	330	1	10	10	NUM
ap-1261	330	2	.	.	PUNCT
ap-1261	331	1	[	[	X
ap-1261	331	2	6	6	NUM
ap-1261	331	3	]	]	X
ap-1261	331	4	havlíček	havlíček	NOUN
ap-1261	331	5	,	,	PUNCT
ap-1261	331	6	m.	m.	NOUN
ap-1261	331	7	,	,	PUNCT
ap-1261	331	8	patera	patera	NOUN
ap-1261	331	9	,	,	PUNCT
ap-1261	331	10	j.	j.	PROPN
ap-1261	331	11	,	,	PUNCT
ap-1261	331	12	pelantová	pelantová	PROPN
ap-1261	331	13	,	,	PUNCT
ap-1261	331	14	e.	e.	PROPN
ap-1261	331	15	:	:	PUNCT
ap-1261	331	16	on	on	ADP
ap-1261	331	17	lie	lie	PROPN
ap-1261	331	18	gradings	gradings	PROPN
ap-1261	331	19	ii	ii	PROPN
ap-1261	331	20	,	,	PUNCT
ap-1261	331	21	lin	lin	PROPN
ap-1261	331	22	.	.	PUNCT
ap-1261	332	1	alg	alg	PROPN
ap-1261	332	2	.	.	PUNCT
ap-1261	333	1	appl	appl	PROPN
ap-1261	333	2	.	.	PROPN
ap-1261	334	1	277	277	NUM
ap-1261	334	2	(	(	PUNCT
ap-1261	334	3	1998	1998	NUM
ap-1261	334	4	)	)	PUNCT
ap-1261	334	5	,	,	PUNCT
ap-1261	334	6	97–125	97–125	NUM
ap-1261	334	7	.	.	PUNCT
ap-1261	335	1	[	[	X
ap-1261	335	2	7	7	NUM
ap-1261	335	3	]	]	X
ap-1261	335	4	helgason	helgason	NOUN
ap-1261	335	5	,	,	PUNCT
ap-1261	335	6	s.	s.	PROPN
ap-1261	335	7	:	:	PUNCT
ap-1261	335	8	differential	differential	ADJ
ap-1261	335	9	geometry	geometry	NOUN
ap-1261	335	10	,	,	PUNCT
ap-1261	335	11	lie	lie	NOUN
ap-1261	335	12	groups	group	NOUN
ap-1261	335	13	,	,	PUNCT
ap-1261	335	14	and	and	CCONJ
ap-1261	335	15	symmetric	symmetric	ADJ
ap-1261	335	16	spaces	space	NOUN
ap-1261	335	17	.	.	PUNCT
ap-1261	336	1	academic	academic	ADJ
ap-1261	336	2	press	press	NOUN
ap-1261	336	3	,	,	PUNCT
ap-1261	336	4	new	new	PROPN
ap-1261	336	5	york	york	PROPN
ap-1261	336	6	1978	1978	NUM
ap-1261	336	7	.	.	PUNCT
ap-1261	337	1	[	[	X
ap-1261	337	2	8	8	NUM
ap-1261	337	3	]	]	SYM
ap-1261	337	4	inönü	inönü	ADJ
ap-1261	337	5	,	,	PUNCT
ap-1261	337	6	e.	e.	PROPN
ap-1261	337	7	,	,	PUNCT
ap-1261	337	8	wigner	wigner	NOUN
ap-1261	337	9	,	,	PUNCT
ap-1261	337	10	e.	e.	PROPN
ap-1261	337	11	p.	p.	PROPN
ap-1261	337	12	:	:	PUNCT
ap-1261	337	13	on	on	ADP
ap-1261	337	14	the	the	DET
ap-1261	337	15	contraction	contraction	NOUN
ap-1261	337	16	of	of	ADP
ap-1261	337	17	groups	group	NOUN
ap-1261	337	18	and	and	CCONJ
ap-1261	337	19	their	their	PRON
ap-1261	337	20	representations	representation	NOUN
ap-1261	337	21	,	,	PUNCT
ap-1261	337	22	proc	proc	NOUN
ap-1261	337	23	.	.	PUNCT
ap-1261	338	1	nat	nat	PROPN
ap-1261	338	2	.	.	PUNCT
ap-1261	339	1	acad	acad	PROPN
ap-1261	339	2	.	.	PUNCT
ap-1261	340	1	sci	sci	PROPN
ap-1261	340	2	.	.	PUNCT
ap-1261	340	3	u.s.a	u.s.a	PROPN
ap-1261	340	4	.	.	PROPN
ap-1261	340	5	39	39	NUM
ap-1261	340	6	(	(	PUNCT
ap-1261	340	7	1952	1952	NUM
ap-1261	340	8	)	)	PUNCT
ap-1261	340	9	,	,	PUNCT
ap-1261	340	10	510–525	510–525	NUM
ap-1261	340	11	.	.	PUNCT
ap-1261	341	1	[	[	X
ap-1261	341	2	9	9	NUM
ap-1261	341	3	]	]	X
ap-1261	341	4	kac	kac	PROPN
ap-1261	341	5	,	,	PUNCT
ap-1261	341	6	v.	v.	PROPN
ap-1261	341	7	g.	g.	PROPN
ap-1261	341	8	:	:	PUNCT
ap-1261	341	9	automorphisms	automorphisms	PROPN
ap-1261	341	10	of	of	ADP
ap-1261	341	11	finite	finite	ADJ
ap-1261	341	12	order	order	NOUN
ap-1261	341	13	of	of	ADP
ap-1261	341	14	semisimple	semisimple	ADJ
ap-1261	341	15	lie	lie	NOUN
ap-1261	341	16	algebras	algebra	NOUN
ap-1261	341	17	,	,	PUNCT
ap-1261	341	18	funct	funct	ADJ
ap-1261	341	19	.	.	PUNCT
ap-1261	342	1	anal	anal	PROPN
ap-1261	342	2	.	.	PUNCT
ap-1261	343	1	appl	appl	PROPN
ap-1261	343	2	.	.	PROPN
ap-1261	344	1	3	3	NUM
ap-1261	344	2	(	(	PUNCT
ap-1261	344	3	1969	1969	NUM
ap-1261	344	4	)	)	PUNCT
ap-1261	344	5	,	,	PUNCT
ap-1261	344	6	252–254	252–254	NUM
ap-1261	344	7	.	.	PUNCT
ap-1261	345	1	[	[	X
ap-1261	345	2	10	10	NUM
ap-1261	345	3	]	]	X
ap-1261	345	4	lemire	lemire	PROPN
ap-1261	345	5	,	,	PUNCT
ap-1261	345	6	f.	f.	PROPN
ap-1261	345	7	,	,	PUNCT
ap-1261	345	8	patera	patera	NOUN
ap-1261	345	9	,	,	PUNCT
ap-1261	345	10	j.	j.	PROPN
ap-1261	345	11	:	:	PUNCT
ap-1261	345	12	formal	formal	ADJ
ap-1261	345	13	analytic	analytic	ADJ
ap-1261	345	14	continuation	continuation	NOUN
ap-1261	345	15	of	of	ADP
ap-1261	345	16	gel’fand	gel’fand	PROPN
ap-1261	345	17	’s	’s	PART
ap-1261	345	18	finite	finite	ADJ
ap-1261	345	19	dimensional	dimensional	ADJ
ap-1261	345	20	representations	representation	NOUN
ap-1261	345	21	of	of	ADP
ap-1261	345	22	gl(n	gl(n	NUM
ap-1261	345	23	,	,	PUNCT
ap-1261	345	24	c	c	NOUN
ap-1261	345	25	)	)	PUNCT
ap-1261	345	26	,	,	PUNCT
ap-1261	345	27	j.	j.	PROPN
ap-1261	345	28	math	math	PROPN
ap-1261	345	29	.	.	PUNCT
ap-1261	346	1	phys	phy	NOUN
ap-1261	346	2	.	.	PUNCT
ap-1261	347	1	20	20	NUM
ap-1261	347	2	(	(	PUNCT
ap-1261	347	3	1979	1979	NUM
ap-1261	347	4	)	)	PUNCT
ap-1261	347	5	,	,	PUNCT
ap-1261	347	6	820–829	820–829	NUM
ap-1261	347	7	.	.	PUNCT
ap-1261	348	1	[	[	X
ap-1261	348	2	11	11	NUM
ap-1261	348	3	]	]	SYM
ap-1261	348	4	de	de	X
ap-1261	348	5	montigny	montigny	PROPN
ap-1261	348	6	,	,	PUNCT
ap-1261	348	7	m.	m.	NOUN
ap-1261	348	8	,	,	PUNCT
ap-1261	348	9	patera	patera	NOUN
ap-1261	348	10	,	,	PUNCT
ap-1261	348	11	j.	j.	PROPN
ap-1261	348	12	:	:	PUNCT
ap-1261	348	13	discrete	discrete	ADJ
ap-1261	348	14	and	and	CCONJ
ap-1261	348	15	continuous	continuous	ADJ
ap-1261	348	16	graded	grade	VERB
ap-1261	348	17	contractions	contraction	NOUN
ap-1261	348	18	of	of	ADP
ap-1261	348	19	lie	lie	NOUN
ap-1261	348	20	algebras	algebra	NOUN
ap-1261	348	21	and	and	CCONJ
ap-1261	348	22	superalgebras	superalgebras	PROPN
ap-1261	348	23	,	,	PUNCT
ap-1261	348	24	j.	j.	PROPN
ap-1261	348	25	phys	phys	PROPN
ap-1261	348	26	.	.	PUNCT
ap-1261	349	1	a	a	DET
ap-1261	349	2	:	:	PUNCT
ap-1261	349	3	math	math	NOUN
ap-1261	349	4	.	.	PUNCT
ap-1261	350	1	gen	gen	PROPN
ap-1261	350	2	.	.	PROPN
ap-1261	350	3	24	24	NUM
ap-1261	350	4	(	(	PUNCT
ap-1261	350	5	1991	1991	NUM
ap-1261	350	6	)	)	PUNCT
ap-1261	350	7	,	,	PUNCT
ap-1261	350	8	525–549	525–549	NUM
ap-1261	350	9	.	.	PUNCT
ap-1261	351	1	[	[	X
ap-1261	351	2	12	12	NUM
ap-1261	351	3	]	]	X
ap-1261	351	4	de	de	X
ap-1261	351	5	montigny	montigny	PROPN
ap-1261	351	6	,	,	PUNCT
ap-1261	351	7	m.	m.	NOUN
ap-1261	351	8	,	,	PUNCT
ap-1261	351	9	patera	patera	NOUN
ap-1261	351	10	,	,	PUNCT
ap-1261	351	11	j.	j.	PROPN
ap-1261	351	12	,	,	PUNCT
ap-1261	351	13	tolar	tolar	PROPN
ap-1261	351	14	,	,	PUNCT
ap-1261	351	15	j.	j.	PROPN
ap-1261	351	16	:	:	PUNCT
ap-1261	351	17	graded	grade	VERB
ap-1261	351	18	contractions	contraction	NOUN
ap-1261	351	19	and	and	CCONJ
ap-1261	351	20	kinematical	kinematical	ADJ
ap-1261	351	21	groups	group	NOUN
ap-1261	351	22	of	of	ADP
ap-1261	351	23	space	space	NOUN
ap-1261	351	24	-	-	PUNCT
ap-1261	351	25	time	time	NOUN
ap-1261	351	26	,	,	PUNCT
ap-1261	351	27	j.	j.	PROPN
ap-1261	351	28	math	math	PROPN
ap-1261	351	29	.	.	PUNCT
ap-1261	352	1	phys	phy	NOUN
ap-1261	352	2	.	.	PUNCT
ap-1261	353	1	35	35	NUM
ap-1261	353	2	(	(	PUNCT
ap-1261	353	3	1994	1994	NUM
ap-1261	353	4	)	)	PUNCT
ap-1261	353	5	,	,	PUNCT
ap-1261	353	6	405–425	405–425	NUM
ap-1261	353	7	.	.	PUNCT
ap-1261	354	1	[	[	X
ap-1261	354	2	13	13	NUM
ap-1261	354	3	]	]	X
ap-1261	354	4	moody	moody	PROPN
ap-1261	354	5	,	,	PUNCT
ap-1261	354	6	r.	r.	PROPN
ap-1261	354	7	v.	v.	PROPN
ap-1261	354	8	,	,	PUNCT
ap-1261	354	9	patera	patera	NOUN
ap-1261	354	10	,	,	PUNCT
ap-1261	354	11	j.	j.	PROPN
ap-1261	354	12	:	:	PUNCT
ap-1261	354	13	discrete	discrete	ADJ
ap-1261	354	14	and	and	CCONJ
ap-1261	354	15	continuous	continuous	ADJ
ap-1261	354	16	graded	grade	VERB
ap-1261	354	17	contractions	contraction	NOUN
ap-1261	354	18	of	of	ADP
ap-1261	354	19	representations	representation	NOUN
ap-1261	354	20	of	of	ADP
ap-1261	354	21	lie	lie	NOUN
ap-1261	354	22	algebras	algebra	NOUN
ap-1261	354	23	,	,	PUNCT
ap-1261	354	24	j.	j.	PROPN
ap-1261	354	25	phys	phys	PROPN
ap-1261	354	26	.	.	PUNCT
ap-1261	355	1	a	a	DET
ap-1261	355	2	:	:	PUNCT
ap-1261	355	3	math	math	NOUN
ap-1261	355	4	.	.	PUNCT
ap-1261	356	1	gen	gen	PROPN
ap-1261	356	2	.	.	PROPN
ap-1261	356	3	24	24	NUM
ap-1261	356	4	(	(	PUNCT
ap-1261	356	5	1991	1991	NUM
ap-1261	356	6	)	)	PUNCT
ap-1261	356	7	,	,	PUNCT
ap-1261	356	8	2	2	NUM
ap-1261	356	9	227–2258	227–2258	NUM
ap-1261	356	10	.	.	PUNCT
ap-1261	357	1	[	[	X
ap-1261	357	2	14	14	NUM
ap-1261	357	3	]	]	PUNCT
ap-1261	357	4	patera	patera	NOUN
ap-1261	357	5	,	,	PUNCT
ap-1261	357	6	j.	j.	PROPN
ap-1261	357	7	:	:	PUNCT
ap-1261	357	8	graded	grade	VERB
ap-1261	357	9	contractions	contraction	NOUN
ap-1261	357	10	of	of	ADP
ap-1261	357	11	lie	lie	NOUN
ap-1261	357	12	algebras	algebra	NOUN
ap-1261	357	13	,	,	PUNCT
ap-1261	357	14	representations	representation	NOUN
ap-1261	357	15	and	and	CCONJ
ap-1261	357	16	tensor	tensor	NOUN
ap-1261	357	17	products	product	NOUN
ap-1261	357	18	,	,	PUNCT
ap-1261	357	19	aip	aip	PROPN
ap-1261	357	20	conference	conference	NOUN
ap-1261	357	21	proceedings	proceeding	NOUN
ap-1261	357	22	,	,	PUNCT
ap-1261	357	23	vol	vol	NOUN
ap-1261	357	24	.	.	PROPN
ap-1261	357	25	266	266	NUM
ap-1261	357	26	(	(	PUNCT
ap-1261	357	27	1992	1992	NUM
ap-1261	357	28	)	)	PUNCT
ap-1261	357	29	,	,	PUNCT
ap-1261	357	30	46–54	46–54	NUM
ap-1261	357	31	.	.	PUNCT
ap-1261	358	1	[	[	X
ap-1261	358	2	15	15	NUM
ap-1261	358	3	]	]	X
ap-1261	358	4	patera	patera	NOUN
ap-1261	358	5	,	,	PUNCT
ap-1261	358	6	j.	j.	PROPN
ap-1261	358	7	,	,	PUNCT
ap-1261	358	8	tolar	tolar	PROPN
ap-1261	358	9	,	,	PUNCT
ap-1261	358	10	j.	j.	PROPN
ap-1261	358	11	:	:	PUNCT
ap-1261	358	12	on	on	ADP
ap-1261	358	13	gradings	grading	NOUN
ap-1261	358	14	of	of	ADP
ap-1261	358	15	lie	lie	NOUN
ap-1261	358	16	algebras	algebra	NOUN
ap-1261	358	17	and	and	CCONJ
ap-1261	358	18	their	their	PRON
ap-1261	358	19	representations	representation	NOUN
ap-1261	358	20	,	,	PUNCT
ap-1261	358	21	in	in	ADP
ap-1261	358	22	lie	lie	NOUN
ap-1261	358	23	theory	theory	NOUN
ap-1261	358	24	and	and	CCONJ
ap-1261	358	25	its	its	PRON
ap-1261	358	26	applications	application	NOUN
ap-1261	358	27	in	in	ADP
ap-1261	358	28	physics	physics	PROPN
ap-1261	358	29	ii	ii	PROPN
ap-1261	358	30	,	,	PUNCT
ap-1261	358	31	(	(	PUNCT
ap-1261	358	32	eds	ed	NOUN
ap-1261	358	33	.	.	PUNCT
ap-1261	359	1	h.-d	h.-d	PROPN
ap-1261	359	2	.	.	PUNCT
ap-1261	360	1	doebner	doebner	PROPN
ap-1261	360	2	,	,	PUNCT
ap-1261	360	3	v.	v.	PROPN
ap-1261	360	4	k.	k.	PROPN
ap-1261	360	5	dobrev	dobrev	PROPN
ap-1261	360	6	,	,	PUNCT
ap-1261	360	7	j.	j.	PROPN
ap-1261	360	8	hilgert	hilgert	PROPN
ap-1261	360	9	)	)	PUNCT
ap-1261	360	10	,	,	PUNCT
ap-1261	360	11	world	world	NOUN
ap-1261	360	12	scientific	scientific	PROPN
ap-1261	360	13	,	,	PUNCT
ap-1261	360	14	singapore	singapore	PROPN
ap-1261	360	15	1998	1998	NUM
ap-1261	360	16	,	,	PUNCT
ap-1261	360	17	109–118	109–118	NUM
ap-1261	360	18	.	.	PUNCT
ap-1261	361	1	[	[	X
ap-1261	361	2	16	16	NUM
ap-1261	361	3	]	]	PUNCT
ap-1261	361	4	patera	patera	NOUN
ap-1261	361	5	,	,	PUNCT
ap-1261	361	6	j.	j.	PROPN
ap-1261	361	7	,	,	PUNCT
ap-1261	361	8	zassenhaus	zassenhaus	PROPN
ap-1261	361	9	,	,	PUNCT
ap-1261	361	10	h.	h.	PROPN
ap-1261	361	11	:	:	PUNCT
ap-1261	361	12	on	on	ADP
ap-1261	361	13	lie	lie	NOUN
ap-1261	361	14	gradings	grading	NOUN
ap-1261	362	1	i	i	PRON
ap-1261	362	2	,	,	PUNCT
ap-1261	362	3	lin	lin	PROPN
ap-1261	362	4	.	.	PUNCT
ap-1261	363	1	alg	alg	PROPN
ap-1261	363	2	.	.	PUNCT
ap-1261	363	3	appl	appl	PROPN
ap-1261	363	4	.	.	PUNCT
ap-1261	364	1	112	112	NUM
ap-1261	364	2	(	(	PUNCT
ap-1261	364	3	1989	1989	NUM
ap-1261	364	4	)	)	PUNCT
ap-1261	364	5	,	,	PUNCT
ap-1261	364	6	87–159	87–159	PROPN
ap-1261	364	7	.	.	PUNCT
ap-1261	365	1	[	[	X
ap-1261	365	2	17	17	NUM
ap-1261	365	3	]	]	PUNCT
ap-1261	365	4	patera	patera	NOUN
ap-1261	365	5	,	,	PUNCT
ap-1261	365	6	j.	j.	PROPN
ap-1261	365	7	,	,	PUNCT
ap-1261	365	8	zassenhaus	zassenhaus	PROPN
ap-1261	365	9	,	,	PUNCT
ap-1261	365	10	h.	h.	PROPN
ap-1261	365	11	:	:	PUNCT
ap-1261	365	12	the	the	DET
ap-1261	365	13	pauli	pauli	PROPN
ap-1261	365	14	matrices	matrice	VERB
ap-1261	365	15	in	in	ADP
ap-1261	365	16	n	n	ADP
ap-1261	365	17	dimensions	dimension	NOUN
ap-1261	365	18	and	and	CCONJ
ap-1261	365	19	finest	fine	ADJ
ap-1261	365	20	gradings	grading	NOUN
ap-1261	365	21	of	of	ADP
ap-1261	365	22	simple	simple	ADJ
ap-1261	365	23	lie	lie	NOUN
ap-1261	365	24	algebras	algebra	NOUN
ap-1261	365	25	of	of	ADP
ap-1261	365	26	type	type	NOUN
ap-1261	365	27	an−1	an−1	ADJ
ap-1261	365	28	,	,	PUNCT
ap-1261	365	29	j.	j.	PROPN
ap-1261	365	30	math	math	PROPN
ap-1261	365	31	.	.	PUNCT
ap-1261	366	1	phys	phy	NOUN
ap-1261	366	2	.	.	PUNCT
ap-1261	367	1	29	29	NUM
ap-1261	367	2	(	(	PUNCT
ap-1261	367	3	1988	1988	NUM
ap-1261	367	4	)	)	PUNCT
ap-1261	367	5	,	,	PUNCT
ap-1261	367	6	665–673	665–673	NUM
ap-1261	367	7	.	.	PUNCT
ap-1261	368	1	[	[	X
ap-1261	368	2	18	18	NUM
ap-1261	368	3	]	]	PUNCT
ap-1261	368	4	ström	ström	PROPN
ap-1261	368	5	,	,	PUNCT
ap-1261	368	6	s.	s.	PROPN
ap-1261	368	7	:	:	PUNCT
ap-1261	368	8	construction	construction	NOUN
ap-1261	368	9	of	of	ADP
ap-1261	368	10	representations	representation	NOUN
ap-1261	368	11	of	of	ADP
ap-1261	368	12	the	the	DET
ap-1261	368	13	inhomogeneous	inhomogeneous	ADJ
ap-1261	368	14	lorentz	lorentz	PROPN
ap-1261	368	15	group	group	NOUN
ap-1261	368	16	by	by	ADP
ap-1261	368	17	means	mean	NOUN
ap-1261	368	18	of	of	ADP
ap-1261	368	19	contraction	contraction	NOUN
ap-1261	368	20	of	of	ADP
ap-1261	368	21	representations	representation	NOUN
ap-1261	368	22	of	of	ADP
ap-1261	368	23	the	the	DET
ap-1261	368	24	(	(	PUNCT
ap-1261	368	25	1	1	NUM
ap-1261	368	26	+	+	NOUN
ap-1261	368	27	4	4	NUM
ap-1261	368	28	)	)	PUNCT
ap-1261	368	29	de	de	PROPN
ap-1261	368	30	sitter	sitter	NOUN
ap-1261	368	31	group	group	NOUN
ap-1261	368	32	,	,	PUNCT
ap-1261	368	33	arkiv	arkiv	ADP
ap-1261	368	34	för	för	NOUN
ap-1261	368	35	fysik	fysik	NOUN
ap-1261	368	36	30	30	NUM
ap-1261	368	37	(	(	PUNCT
ap-1261	368	38	1965	1965	NUM
ap-1261	368	39	)	)	PUNCT
ap-1261	368	40	,	,	PUNCT
ap-1261	368	41	455–472	455–472	NUM
ap-1261	368	42	.	.	PUNCT
ap-1261	369	1	prof	prof	PROPN
ap-1261	369	2	.	.	PUNCT
ap-1261	370	1	ing	ing	PROPN
ap-1261	370	2	.	.	PUNCT
ap-1261	371	1	miloslav	miloslav	PROPN
ap-1261	371	2	havlíček	havlíček	PROPN
ap-1261	371	3	,	,	PUNCT
ap-1261	371	4	drsc	drsc	PROPN
ap-1261	371	5	.	.	PUNCT
ap-1261	372	1	e	e	X
ap-1261	372	2	-	-	NOUN
ap-1261	372	3	mail	mail	NOUN
ap-1261	372	4	:	:	PUNCT
ap-1261	372	5	miloslav.havlicek@fjfi.cvut.cz	miloslav.havlicek@fjfi.cvut.cz	PROPN
ap-1261	372	6	prof	prof	PROPN
ap-1261	372	7	.	.	PUNCT
ap-1261	373	1	ing	ing	PROPN
ap-1261	373	2	.	.	PUNCT
ap-1261	374	1	edita	edita	PROPN
ap-1261	374	2	pelantová	pelantová	PROPN
ap-1261	374	3	,	,	PUNCT
ap-1261	374	4	csc	csc	PROPN
ap-1261	374	5	.	.	PROPN
ap-1261	375	1	e	e	X
ap-1261	375	2	-	-	NOUN
ap-1261	375	3	mail	mail	NOUN
ap-1261	375	4	:	:	PUNCT
ap-1261	375	5	edita.pelantova@fjfi.cvut.cz	edita.pelantova@fjfi.cvut.cz	NOUN
ap-1261	375	6	prof	prof	PROPN
ap-1261	375	7	.	.	PUNCT
ap-1261	376	1	ing	ing	PROPN
ap-1261	376	2	.	.	PROPN
ap-1261	377	1	jiří	jiří	PROPN
ap-1261	377	2	tolar	tolar	PROPN
ap-1261	377	3	,	,	PUNCT
ap-1261	377	4	drsc	drsc	PROPN
ap-1261	377	5	.	.	PUNCT
ap-1261	378	1	e	e	X
ap-1261	378	2	-	-	NOUN
ap-1261	378	3	mail	mail	NOUN
ap-1261	378	4	:	:	PUNCT
ap-1261	378	5	jiri.tolar@fjfi.cvut.cz	jiri.tolar@fjfi.cvut.cz	VERB
ap-1261	378	6	doppler	doppler	NOUN
ap-1261	378	7	institute	institute	NOUN
ap-1261	378	8	,	,	PUNCT
ap-1261	378	9	faculty	faculty	NOUN
ap-1261	378	10	of	of	ADP
ap-1261	378	11	nuclear	nuclear	ADJ
ap-1261	378	12	sciences	science	NOUN
ap-1261	378	13	and	and	CCONJ
ap-1261	378	14	physical	physical	ADJ
ap-1261	378	15	engineering	engineering	NOUN
ap-1261	378	16	czech	czech	PROPN
ap-1261	378	17	technical	technical	PROPN
ap-1261	378	18	university	university	PROPN
ap-1261	378	19	in	in	ADP
ap-1261	378	20	prague	prague	PROPN
ap-1261	378	21	,	,	PUNCT
ap-1261	378	22	czech	czech	PROPN
ap-1261	378	23	republic	republic	NOUN
ap-1261	378	24	39	39	NUM