id	sid	tid	token	lemma	pos
ap-3511	1	1	acta	acta	PROPN
ap-3511	1	2	polytechnica	polytechnica	PROPN
ap-3511	1	3	doi:10.14311	doi:10.14311	PROPN
ap-3511	1	4	/	/	SYM
ap-3511	1	5	ap.2016.56.0440	ap.2016.56.0440	PROPN
ap-3511	1	6	acta	acta	PROPN
ap-3511	1	7	polytechnica	polytechnica	PROPN
ap-3511	1	8	56(6):440–447	56(6):440–447	PROPN
ap-3511	1	9	,	,	PUNCT
ap-3511	1	10	2016	2016	NUM
ap-3511	1	11	©	©	PROPN
ap-3511	1	12	czech	czech	PROPN
ap-3511	1	13	technical	technical	PROPN
ap-3511	1	14	university	university	PROPN
ap-3511	1	15	in	in	ADP
ap-3511	1	16	prague	prague	PROPN
ap-3511	1	17	,	,	PUNCT
ap-3511	1	18	2016	2016	NUM
ap-3511	1	19	available	available	ADJ
ap-3511	1	20	online	online	ADV
ap-3511	1	21	at	at	ADP
ap-3511	1	22	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-3511	1	23	on	on	ADP
ap-3511	1	24	generalization	generalization	NOUN
ap-3511	1	25	of	of	ADP
ap-3511	1	26	special	special	ADJ
ap-3511	1	27	functions	function	NOUN
ap-3511	1	28	related	relate	VERB
ap-3511	1	29	to	to	ADP
ap-3511	1	30	weyl	weyl	VERB
ap-3511	1	31	groups	group	NOUN
ap-3511	1	32	lenka	lenka	PROPN
ap-3511	1	33	hákováa,∗	hákováa,∗	PROPN
ap-3511	1	34	,	,	PUNCT
ap-3511	1	35	agnieszka	agnieszka	PROPN
ap-3511	1	36	tereszkiewiczb	tereszkiewiczb	PROPN
ap-3511	1	37	a	a	DET
ap-3511	1	38	department	department	NOUN
ap-3511	1	39	of	of	ADP
ap-3511	1	40	mathematics	mathematic	NOUN
ap-3511	1	41	,	,	PUNCT
ap-3511	1	42	faculty	faculty	NOUN
ap-3511	1	43	of	of	ADP
ap-3511	1	44	chemical	chemical	ADJ
ap-3511	1	45	engineering	engineering	NOUN
ap-3511	1	46	,	,	PUNCT
ap-3511	1	47	university	university	NOUN
ap-3511	1	48	of	of	ADP
ap-3511	1	49	chemistry	chemistry	NOUN
ap-3511	1	50	and	and	CCONJ
ap-3511	1	51	technology	technology	NOUN
ap-3511	1	52	,	,	PUNCT
ap-3511	1	53	prague	prague	PROPN
ap-3511	1	54	,	,	PUNCT
ap-3511	1	55	technická	technická	NOUN
ap-3511	1	56	5	5	NUM
ap-3511	1	57	,	,	PUNCT
ap-3511	1	58	cz-166	cz-166	NOUN
ap-3511	1	59	28	28	NUM
ap-3511	1	60	prague	prague	PROPN
ap-3511	1	61	,	,	PUNCT
ap-3511	1	62	czech	czech	PROPN
ap-3511	1	63	republic	republic	PROPN
ap-3511	1	64	b	b	PROPN
ap-3511	1	65	institute	institute	PROPN
ap-3511	1	66	of	of	ADP
ap-3511	1	67	mathematics	mathematics	PROPN
ap-3511	1	68	,	,	PUNCT
ap-3511	1	69	university	university	NOUN
ap-3511	1	70	of	of	ADP
ap-3511	1	71	bialystok	bialystok	ADJ
ap-3511	1	72	,	,	PUNCT
ap-3511	1	73	ciolkowskiego	ciolkowskiego	NOUN
ap-3511	1	74	1	1	NUM
ap-3511	1	75	m	m	PROPN
ap-3511	1	76	,	,	PUNCT
ap-3511	1	77	15	15	NUM
ap-3511	1	78	-	-	SYM
ap-3511	1	79	245	245	NUM
ap-3511	1	80	bialystok	bialystok	ADJ
ap-3511	1	81	,	,	PUNCT
ap-3511	1	82	poland	poland	PROPN
ap-3511	1	83	∗	∗	NOUN
ap-3511	1	84	corresponding	correspond	VERB
ap-3511	1	85	author	author	NOUN
ap-3511	1	86	:	:	PUNCT
ap-3511	1	87	lenka.hakova@vscht.cz	lenka.hakova@vscht.cz	PROPN
ap-3511	1	88	abstract	abstract	NOUN
ap-3511	1	89	.	.	PUNCT
ap-3511	2	1	weyl	weyl	PROPN
ap-3511	2	2	group	group	PROPN
ap-3511	2	3	orbit	orbit	NOUN
ap-3511	2	4	functions	function	NOUN
ap-3511	2	5	are	be	AUX
ap-3511	2	6	defined	define	VERB
ap-3511	2	7	in	in	ADP
ap-3511	2	8	the	the	DET
ap-3511	2	9	context	context	NOUN
ap-3511	2	10	of	of	ADP
ap-3511	2	11	weyl	weyl	VERB
ap-3511	2	12	groups	group	NOUN
ap-3511	2	13	of	of	ADP
ap-3511	2	14	simple	simple	ADJ
ap-3511	2	15	lie	lie	NOUN
ap-3511	2	16	algebras	algebra	NOUN
ap-3511	2	17	.	.	PUNCT
ap-3511	3	1	they	they	PRON
ap-3511	3	2	are	be	AUX
ap-3511	3	3	multivariable	multivariable	ADJ
ap-3511	3	4	complex	complex	ADJ
ap-3511	3	5	functions	function	NOUN
ap-3511	3	6	possessing	possess	VERB
ap-3511	3	7	remarkable	remarkable	ADJ
ap-3511	3	8	properties	property	NOUN
ap-3511	3	9	such	such	ADJ
ap-3511	3	10	as	as	ADP
ap-3511	3	11	(	(	PUNCT
ap-3511	3	12	anti)invariance	anti)invariance	NOUN
ap-3511	3	13	with	with	ADP
ap-3511	3	14	respect	respect	NOUN
ap-3511	3	15	to	to	ADP
ap-3511	3	16	the	the	DET
ap-3511	3	17	corresponding	corresponding	ADJ
ap-3511	3	18	weyl	weyl	VERB
ap-3511	3	19	group	group	NOUN
ap-3511	3	20	,	,	PUNCT
ap-3511	3	21	continuous	continuous	ADJ
ap-3511	3	22	and	and	CCONJ
ap-3511	3	23	discrete	discrete	ADJ
ap-3511	3	24	orthogonality	orthogonality	NOUN
ap-3511	3	25	.	.	PUNCT
ap-3511	4	1	a	a	DET
ap-3511	4	2	crucial	crucial	ADJ
ap-3511	4	3	tool	tool	NOUN
ap-3511	4	4	in	in	ADP
ap-3511	4	5	their	their	PRON
ap-3511	4	6	definition	definition	NOUN
ap-3511	4	7	are	be	AUX
ap-3511	4	8	so	so	ADV
ap-3511	4	9	-	-	PUNCT
ap-3511	4	10	called	call	VERB
ap-3511	4	11	sign	sign	NOUN
ap-3511	4	12	homomorphisms	homomorphism	NOUN
ap-3511	4	13	,	,	PUNCT
ap-3511	4	14	which	which	PRON
ap-3511	4	15	coincide	coincide	VERB
ap-3511	4	16	with	with	ADP
ap-3511	4	17	one	one	NUM
ap-3511	4	18	-	-	PUNCT
ap-3511	4	19	dimensional	dimensional	ADJ
ap-3511	4	20	irreducible	irreducible	ADJ
ap-3511	4	21	representations	representation	NOUN
ap-3511	4	22	.	.	PUNCT
ap-3511	5	1	in	in	ADP
ap-3511	5	2	this	this	DET
ap-3511	5	3	work	work	NOUN
ap-3511	5	4	we	we	PRON
ap-3511	5	5	generalize	generalize	VERB
ap-3511	5	6	the	the	DET
ap-3511	5	7	definition	definition	NOUN
ap-3511	5	8	of	of	ADP
ap-3511	5	9	orbit	orbit	NOUN
ap-3511	5	10	functions	function	NOUN
ap-3511	5	11	using	use	VERB
ap-3511	5	12	characters	character	NOUN
ap-3511	5	13	of	of	ADP
ap-3511	5	14	irreducible	irreducible	ADJ
ap-3511	5	15	representations	representation	NOUN
ap-3511	5	16	of	of	ADP
ap-3511	5	17	higher	high	ADJ
ap-3511	5	18	dimensions	dimension	NOUN
ap-3511	5	19	.	.	PUNCT
ap-3511	6	1	we	we	PRON
ap-3511	6	2	describe	describe	VERB
ap-3511	6	3	their	their	PRON
ap-3511	6	4	properties	property	NOUN
ap-3511	6	5	and	and	CCONJ
ap-3511	6	6	give	give	VERB
ap-3511	6	7	examples	example	NOUN
ap-3511	6	8	for	for	ADP
ap-3511	6	9	weyl	weyl	VERB
ap-3511	6	10	groups	group	NOUN
ap-3511	6	11	of	of	ADP
ap-3511	6	12	rank	rank	NOUN
ap-3511	6	13	2	2	NUM
ap-3511	6	14	and	and	CCONJ
ap-3511	6	15	3	3	NUM
ap-3511	6	16	.	.	PUNCT
ap-3511	7	1	keywords	keyword	NOUN
ap-3511	7	2	:	:	PUNCT
ap-3511	7	3	weyl	weyl	VERB
ap-3511	7	4	groups	group	NOUN
ap-3511	7	5	,	,	PUNCT
ap-3511	7	6	characters	character	NOUN
ap-3511	7	7	,	,	PUNCT
ap-3511	7	8	special	special	ADJ
ap-3511	7	9	functions	function	NOUN
ap-3511	7	10	.	.	PUNCT
ap-3511	8	1	1	1	X
ap-3511	8	2	.	.	X
ap-3511	8	3	introduction	introduction	NOUN
ap-3511	8	4	we	we	PRON
ap-3511	8	5	consider	consider	VERB
ap-3511	8	6	simple	simple	ADJ
ap-3511	8	7	lie	lie	NOUN
ap-3511	8	8	algebras	algebra	NOUN
ap-3511	8	9	,	,	PUNCT
ap-3511	8	10	i.e.	i.e.	X
ap-3511	8	11	,	,	PUNCT
ap-3511	8	12	the	the	DET
ap-3511	8	13	infinite	infinite	ADJ
ap-3511	8	14	families	family	NOUN
ap-3511	8	15	an	an	PRON
ap-3511	8	16	,	,	PUNCT
ap-3511	8	17	bn	bn	NOUN
ap-3511	8	18	,	,	PUNCT
ap-3511	8	19	cn	cn	PROPN
ap-3511	8	20	and	and	CCONJ
ap-3511	8	21	dn	dn	NOUN
ap-3511	8	22	and	and	CCONJ
ap-3511	8	23	exceptional	exceptional	ADJ
ap-3511	8	24	algebras	algebras	PROPN
ap-3511	8	25	g2	g2	PROPN
ap-3511	8	26	,	,	PUNCT
ap-3511	8	27	f4	f4	PROPN
ap-3511	8	28	,	,	PUNCT
ap-3511	8	29	e6	e6	NOUN
ap-3511	8	30	,	,	PUNCT
ap-3511	8	31	e7	e7	PROPN
ap-3511	8	32	and	and	CCONJ
ap-3511	8	33	e8	e8	PROPN
ap-3511	8	34	.	.	PUNCT
ap-3511	9	1	several	several	ADJ
ap-3511	9	2	families	family	NOUN
ap-3511	9	3	of	of	ADP
ap-3511	9	4	multivariable	multivariable	ADJ
ap-3511	9	5	special	special	ADJ
ap-3511	9	6	functions	function	NOUN
ap-3511	9	7	–	–	PUNCT
ap-3511	9	8	orbit	orbit	NOUN
ap-3511	9	9	functions	function	NOUN
ap-3511	9	10	–	–	PUNCT
ap-3511	9	11	are	be	AUX
ap-3511	9	12	defined	define	VERB
ap-3511	9	13	with	with	ADP
ap-3511	9	14	respect	respect	NOUN
ap-3511	9	15	to	to	ADP
ap-3511	9	16	related	relate	VERB
ap-3511	9	17	weyl	weyl	VERB
ap-3511	9	18	groups	group	NOUN
ap-3511	9	19	;	;	PUNCT
ap-3511	9	20	see	see	VERB
ap-3511	9	21	(	(	PUNCT
ap-3511	9	22	5	5	NUM
ap-3511	9	23	)	)	PUNCT
ap-3511	9	24	.	.	PUNCT
ap-3511	10	1	these	these	DET
ap-3511	10	2	functions	function	NOUN
ap-3511	10	3	are	be	AUX
ap-3511	10	4	called	call	VERB
ap-3511	10	5	c	c	PROPN
ap-3511	10	6	–	–	PUNCT
ap-3511	10	7	,	,	PUNCT
ap-3511	10	8	s	s	X
ap-3511	10	9	–	–	PUNCT
ap-3511	10	10	,	,	PUNCT
ap-3511	10	11	ss	ss	NOUN
ap-3511	10	12	–	–	PUNCT
ap-3511	10	13	and	and	CCONJ
ap-3511	10	14	sl	sl	NOUN
ap-3511	10	15	–	–	PUNCT
ap-3511	10	16	functions	function	NOUN
ap-3511	10	17	and	and	CCONJ
ap-3511	10	18	they	they	PRON
ap-3511	10	19	have	have	AUX
ap-3511	10	20	been	be	AUX
ap-3511	10	21	described	describe	VERB
ap-3511	10	22	in	in	ADP
ap-3511	10	23	many	many	ADJ
ap-3511	10	24	papers	paper	NOUN
ap-3511	10	25	;	;	PUNCT
ap-3511	10	26	see	see	VERB
ap-3511	10	27	[	[	X
ap-3511	10	28	1]–[6	1]–[6	X
ap-3511	10	29	]	]	X
ap-3511	10	30	.	.	PUNCT
ap-3511	11	1	in	in	ADP
ap-3511	11	2	[	[	X
ap-3511	11	3	7	7	X
ap-3511	11	4	]	]	PUNCT
ap-3511	11	5	we	we	PRON
ap-3511	11	6	studied	study	VERB
ap-3511	11	7	a	a	DET
ap-3511	11	8	generalization	generalization	NOUN
ap-3511	11	9	of	of	ADP
ap-3511	11	10	c	c	PROPN
ap-3511	11	11	–	–	PUNCT
ap-3511	11	12	and	and	CCONJ
ap-3511	11	13	s	s	PROPN
ap-3511	11	14	–	–	PUNCT
ap-3511	11	15	functions	function	NOUN
ap-3511	11	16	of	of	ADP
ap-3511	11	17	weyl	weyl	VERB
ap-3511	11	18	groups	group	NOUN
ap-3511	11	19	of	of	ADP
ap-3511	11	20	an	an	DET
ap-3511	11	21	using	use	VERB
ap-3511	11	22	immanants	immanant	NOUN
ap-3511	11	23	of	of	ADP
ap-3511	11	24	a	a	DET
ap-3511	11	25	certain	certain	ADJ
ap-3511	11	26	matrix	matrix	NOUN
ap-3511	11	27	a	a	PRON
ap-3511	11	28	with	with	ADP
ap-3511	11	29	exponential	exponential	ADJ
ap-3511	11	30	entries	entry	NOUN
ap-3511	11	31	.	.	PUNCT
ap-3511	12	1	immanants	immanant	NOUN
ap-3511	12	2	are	be	AUX
ap-3511	12	3	functions	function	NOUN
ap-3511	12	4	defined	define	VERB
ap-3511	12	5	on	on	ADP
ap-3511	12	6	the	the	DET
ap-3511	12	7	set	set	NOUN
ap-3511	12	8	of	of	ADP
ap-3511	12	9	squared	square	VERB
ap-3511	12	10	matrix	matrix	NOUN
ap-3511	12	11	of	of	ADP
ap-3511	12	12	order	order	NOUN
ap-3511	12	13	n.	n.	NOUN
ap-3511	12	14	they	they	PRON
ap-3511	12	15	are	be	AUX
ap-3511	12	16	related	relate	VERB
ap-3511	12	17	to	to	ADP
ap-3511	12	18	irreducible	irreducible	ADJ
ap-3511	12	19	characters	character	NOUN
ap-3511	12	20	of	of	ADP
ap-3511	12	21	the	the	DET
ap-3511	12	22	symmetry	symmetry	NOUN
ap-3511	12	23	group	group	PROPN
ap-3511	12	24	sn	sn	PROPN
ap-3511	12	25	,	,	PUNCT
ap-3511	12	26	among	among	ADP
ap-3511	12	27	them	they	PRON
ap-3511	12	28	the	the	DET
ap-3511	12	29	standard	standard	ADJ
ap-3511	12	30	determinant	determinant	ADJ
ap-3511	12	31	and	and	CCONJ
ap-3511	12	32	permanent	permanent	ADJ
ap-3511	12	33	.	.	PUNCT
ap-3511	13	1	in	in	ADP
ap-3511	13	2	the	the	DET
ap-3511	13	3	paper	paper	NOUN
ap-3511	13	4	we	we	PRON
ap-3511	13	5	reviewed	review	VERB
ap-3511	13	6	the	the	DET
ap-3511	13	7	fact	fact	NOUN
ap-3511	13	8	that	that	SCONJ
ap-3511	13	9	the	the	DET
ap-3511	13	10	c	c	NOUN
ap-3511	13	11	–	–	PUNCT
ap-3511	13	12	(	(	PUNCT
ap-3511	13	13	s–)functions	s–)function	NOUN
ap-3511	13	14	correspond	correspond	VERB
ap-3511	13	15	to	to	ADP
ap-3511	13	16	the	the	DET
ap-3511	13	17	permanent	permanent	ADJ
ap-3511	13	18	(	(	PUNCT
ap-3511	13	19	determinant	determinant	ADJ
ap-3511	13	20	)	)	PUNCT
ap-3511	13	21	of	of	ADP
ap-3511	13	22	the	the	DET
ap-3511	13	23	matrix	matrix	NOUN
ap-3511	13	24	a	a	PRON
ap-3511	13	25	and	and	CCONJ
ap-3511	13	26	studied	study	VERB
ap-3511	13	27	non	non	ADJ
ap-3511	13	28	-	-	ADJ
ap-3511	13	29	trivial	trivial	ADJ
ap-3511	13	30	immanants	immanant	NOUN
ap-3511	13	31	.	.	PUNCT
ap-3511	14	1	these	these	DET
ap-3511	14	2	new	new	ADJ
ap-3511	14	3	special	special	ADJ
ap-3511	14	4	functions	function	NOUN
ap-3511	14	5	possess	possess	VERB
ap-3511	14	6	some	some	PRON
ap-3511	14	7	of	of	ADP
ap-3511	14	8	the	the	DET
ap-3511	14	9	properties	property	NOUN
ap-3511	14	10	of	of	ADP
ap-3511	14	11	orbit	orbit	NOUN
ap-3511	14	12	functions	function	NOUN
ap-3511	14	13	,	,	PUNCT
ap-3511	14	14	although	although	SCONJ
ap-3511	14	15	they	they	PRON
ap-3511	14	16	are	be	AUX
ap-3511	14	17	not	not	PART
ap-3511	14	18	invariant	invariant	ADJ
ap-3511	14	19	with	with	ADP
ap-3511	14	20	respect	respect	NOUN
ap-3511	14	21	to	to	ADP
ap-3511	14	22	the	the	DET
ap-3511	14	23	weyl	weyl	PROPN
ap-3511	14	24	group	group	NOUN
ap-3511	14	25	an	an	PROPN
ap-3511	14	26	.	.	PUNCT
ap-3511	15	1	another	another	DET
ap-3511	15	2	way	way	NOUN
ap-3511	15	3	to	to	PART
ap-3511	15	4	define	define	VERB
ap-3511	15	5	these	these	DET
ap-3511	15	6	functions	function	NOUN
ap-3511	15	7	is	be	AUX
ap-3511	15	8	to	to	PART
ap-3511	15	9	use	use	VERB
ap-3511	15	10	irreducible	irreducible	ADJ
ap-3511	15	11	characters	character	NOUN
ap-3511	15	12	of	of	ADP
ap-3511	15	13	the	the	DET
ap-3511	15	14	weyl	weyl	VERB
ap-3511	15	15	group	group	NOUN
ap-3511	15	16	of	of	ADP
ap-3511	15	17	an	an	DET
ap-3511	15	18	directly	directly	ADV
ap-3511	15	19	.	.	PUNCT
ap-3511	16	1	this	this	DET
ap-3511	16	2	definition	definition	NOUN
ap-3511	16	3	is	be	AUX
ap-3511	16	4	then	then	ADV
ap-3511	16	5	extended	extend	VERB
ap-3511	16	6	for	for	ADP
ap-3511	16	7	all	all	DET
ap-3511	16	8	weyl	weyl	VERB
ap-3511	16	9	groups	group	NOUN
ap-3511	16	10	of	of	ADP
ap-3511	16	11	simple	simple	ADJ
ap-3511	16	12	lie	lie	NOUN
ap-3511	16	13	algebras	algebra	NOUN
ap-3511	16	14	(	(	PUNCT
ap-3511	16	15	11	11	NUM
ap-3511	16	16	)	)	PUNCT
ap-3511	16	17	.	.	PUNCT
ap-3511	17	1	in	in	ADP
ap-3511	17	2	this	this	DET
ap-3511	17	3	paper	paper	NOUN
ap-3511	17	4	we	we	PRON
ap-3511	17	5	show	show	VERB
ap-3511	17	6	that	that	SCONJ
ap-3511	17	7	we	we	PRON
ap-3511	17	8	can	can	AUX
ap-3511	17	9	describe	describe	VERB
ap-3511	17	10	uniformly	uniformly	ADV
ap-3511	17	11	the	the	DET
ap-3511	17	12	four	four	NUM
ap-3511	17	13	families	family	NOUN
ap-3511	17	14	of	of	ADP
ap-3511	17	15	orbit	orbit	NOUN
ap-3511	17	16	functions	function	NOUN
ap-3511	17	17	,	,	PUNCT
ap-3511	17	18	immanant	immanant	ADJ
ap-3511	17	19	functions	function	NOUN
ap-3511	17	20	and	and	CCONJ
ap-3511	17	21	new	new	ADJ
ap-3511	17	22	families	family	NOUN
ap-3511	17	23	of	of	ADP
ap-3511	17	24	functions	function	NOUN
ap-3511	17	25	related	relate	VERB
ap-3511	17	26	to	to	ADP
ap-3511	17	27	the	the	DET
ap-3511	17	28	corresponding	corresponding	ADJ
ap-3511	17	29	weyl	weyl	VERB
ap-3511	17	30	group	group	NOUN
ap-3511	17	31	using	use	VERB
ap-3511	17	32	its	its	PRON
ap-3511	17	33	irreducible	irreducible	ADJ
ap-3511	17	34	characters	character	NOUN
ap-3511	17	35	via	via	ADP
ap-3511	17	36	the	the	DET
ap-3511	17	37	definition	definition	NOUN
ap-3511	17	38	(	(	PUNCT
ap-3511	17	39	11	11	NUM
ap-3511	17	40	)	)	PUNCT
ap-3511	17	41	.	.	PUNCT
ap-3511	18	1	we	we	PRON
ap-3511	18	2	give	give	VERB
ap-3511	18	3	several	several	ADJ
ap-3511	18	4	examples	example	NOUN
ap-3511	18	5	and	and	CCONJ
ap-3511	18	6	prove	prove	VERB
ap-3511	18	7	some	some	DET
ap-3511	18	8	important	important	ADJ
ap-3511	18	9	properties	property	NOUN
ap-3511	18	10	.	.	PUNCT
ap-3511	19	1	the	the	DET
ap-3511	19	2	paper	paper	NOUN
ap-3511	19	3	is	be	AUX
ap-3511	19	4	organized	organize	VERB
ap-3511	19	5	as	as	SCONJ
ap-3511	19	6	follows	follow	VERB
ap-3511	19	7	:	:	PUNCT
ap-3511	19	8	in	in	ADP
ap-3511	19	9	section	section	NOUN
ap-3511	19	10	2	2	NUM
ap-3511	19	11	we	we	PRON
ap-3511	19	12	review	review	VERB
ap-3511	19	13	some	some	DET
ap-3511	19	14	definitions	definition	NOUN
ap-3511	19	15	and	and	CCONJ
ap-3511	19	16	notions	notion	NOUN
ap-3511	19	17	from	from	ADP
ap-3511	19	18	the	the	DET
ap-3511	19	19	representation	representation	NOUN
ap-3511	19	20	theory	theory	NOUN
ap-3511	19	21	of	of	ADP
ap-3511	19	22	finite	finite	ADJ
ap-3511	19	23	groups	group	NOUN
ap-3511	19	24	and	and	CCONJ
ap-3511	19	25	the	the	DET
ap-3511	19	26	theory	theory	NOUN
ap-3511	19	27	of	of	ADP
ap-3511	19	28	weyl	weyl	VERB
ap-3511	19	29	groups	group	NOUN
ap-3511	19	30	of	of	ADP
ap-3511	19	31	semisimple	semisimple	PROPN
ap-3511	19	32	lie	lie	NOUN
ap-3511	19	33	algebras	algebras	PROPN
ap-3511	19	34	.	.	PUNCT
ap-3511	20	1	section	section	NOUN
ap-3511	20	2	3	3	NUM
ap-3511	20	3	presents	present	VERB
ap-3511	20	4	infinite	infinite	ADJ
ap-3511	20	5	families	family	NOUN
ap-3511	20	6	of	of	ADP
ap-3511	20	7	special	special	ADJ
ap-3511	20	8	functions	function	NOUN
ap-3511	20	9	related	relate	VERB
ap-3511	20	10	to	to	ADP
ap-3511	20	11	the	the	DET
ap-3511	20	12	weyl	weyl	VERB
ap-3511	20	13	groups	group	NOUN
ap-3511	20	14	.	.	PUNCT
ap-3511	21	1	namely	namely	ADV
ap-3511	21	2	,	,	PUNCT
ap-3511	21	3	we	we	PRON
ap-3511	21	4	summarize	summarize	VERB
ap-3511	21	5	some	some	DET
ap-3511	21	6	properties	property	NOUN
ap-3511	21	7	of	of	ADP
ap-3511	21	8	the	the	DET
ap-3511	21	9	families	family	NOUN
ap-3511	21	10	of	of	ADP
ap-3511	21	11	c−	c−	PROPN
ap-3511	21	12	,	,	PUNCT
ap-3511	21	13	s−	s−	PROPN
ap-3511	21	14	,	,	PUNCT
ap-3511	21	15	ss	ss	PROPN
ap-3511	21	16	–	–	PUNCT
ap-3511	21	17	and	and	CCONJ
ap-3511	21	18	sl	sl	NOUN
ap-3511	21	19	–	–	PUNCT
ap-3511	21	20	orbit	orbit	NOUN
ap-3511	21	21	functions	function	NOUN
ap-3511	21	22	and	and	CCONJ
ap-3511	21	23	we	we	PRON
ap-3511	21	24	define	define	VERB
ap-3511	21	25	their	their	PRON
ap-3511	21	26	generalization	generalization	NOUN
ap-3511	21	27	.	.	PUNCT
ap-3511	22	1	in	in	ADP
ap-3511	22	2	section	section	NOUN
ap-3511	22	3	4	4	NUM
ap-3511	22	4	we	we	PRON
ap-3511	22	5	study	study	VERB
ap-3511	22	6	properties	property	NOUN
ap-3511	22	7	of	of	ADP
ap-3511	22	8	these	these	DET
ap-3511	22	9	special	special	ADJ
ap-3511	22	10	functions	function	NOUN
ap-3511	22	11	,	,	PUNCT
ap-3511	22	12	including	include	VERB
ap-3511	22	13	their	their	PRON
ap-3511	22	14	continuous	continuous	ADJ
ap-3511	22	15	and	and	CCONJ
ap-3511	22	16	discrete	discrete	ADJ
ap-3511	22	17	orthogonality	orthogonality	NOUN
ap-3511	22	18	in	in	ADP
ap-3511	22	19	section	section	NOUN
ap-3511	22	20	4.2	4.2	NUM
ap-3511	22	21	and	and	CCONJ
ap-3511	22	22	linear	linear	ADJ
ap-3511	22	23	independence	independence	NOUN
ap-3511	22	24	in	in	ADP
ap-3511	22	25	section	section	NOUN
ap-3511	22	26	4.3	4.3	NUM
ap-3511	22	27	.	.	PUNCT
ap-3511	23	1	section	section	NOUN
ap-3511	23	2	5	5	NUM
ap-3511	23	3	gives	give	VERB
ap-3511	23	4	examples	example	NOUN
ap-3511	23	5	of	of	ADP
ap-3511	23	6	functions	function	NOUN
ap-3511	23	7	related	relate	VERB
ap-3511	23	8	to	to	ADP
ap-3511	23	9	weyl	weyl	VERB
ap-3511	23	10	groups	group	NOUN
ap-3511	23	11	of	of	ADP
ap-3511	23	12	rank	rank	NOUN
ap-3511	23	13	2	2	NUM
ap-3511	23	14	and	and	CCONJ
ap-3511	23	15	3	3	NUM
ap-3511	23	16	.	.	NOUN
ap-3511	23	17	2	2	NUM
ap-3511	23	18	.	.	NUM
ap-3511	23	19	preliminaries	preliminary	NOUN
ap-3511	23	20	2.1	2.1	NUM
ap-3511	23	21	.	.	PUNCT
ap-3511	24	1	irreducible	irreducible	ADJ
ap-3511	24	2	characters	character	NOUN
ap-3511	24	3	of	of	ADP
ap-3511	24	4	symmetric	symmetric	ADJ
ap-3511	24	5	groups	group	NOUN
ap-3511	24	6	for	for	ADP
ap-3511	24	7	the	the	DET
ap-3511	24	8	general	general	ADJ
ap-3511	24	9	definition	definition	NOUN
ap-3511	24	10	of	of	ADP
ap-3511	24	11	character	character	NOUN
ap-3511	24	12	functions	function	NOUN
ap-3511	24	13	we	we	PRON
ap-3511	24	14	need	need	VERB
ap-3511	24	15	to	to	PART
ap-3511	24	16	review	review	VERB
ap-3511	24	17	some	some	DET
ap-3511	24	18	notation	notation	NOUN
ap-3511	24	19	and	and	CCONJ
ap-3511	24	20	facts	fact	NOUN
ap-3511	24	21	from	from	ADP
ap-3511	24	22	the	the	DET
ap-3511	24	23	standard	standard	ADJ
ap-3511	24	24	representation	representation	NOUN
ap-3511	24	25	theory	theory	NOUN
ap-3511	24	26	of	of	ADP
ap-3511	24	27	finite	finite	ADJ
ap-3511	24	28	groups	group	NOUN
ap-3511	24	29	;	;	PUNCT
ap-3511	24	30	see	see	VERB
ap-3511	24	31	for	for	ADP
ap-3511	24	32	example	example	NOUN
ap-3511	24	33	[	[	X
ap-3511	24	34	8	8	NUM
ap-3511	24	35	,	,	PUNCT
ap-3511	24	36	9	9	NUM
ap-3511	24	37	]	]	PUNCT
ap-3511	24	38	.	.	PUNCT
ap-3511	25	1	let	let	VERB
ap-3511	25	2	g	g	PRON
ap-3511	25	3	be	be	AUX
ap-3511	25	4	a	a	DET
ap-3511	25	5	finite	finite	ADJ
ap-3511	25	6	group	group	NOUN
ap-3511	25	7	.	.	PUNCT
ap-3511	26	1	it	it	PRON
ap-3511	26	2	can	can	AUX
ap-3511	26	3	be	be	AUX
ap-3511	26	4	written	write	VERB
ap-3511	26	5	as	as	ADP
ap-3511	26	6	a	a	DET
ap-3511	26	7	union	union	NOUN
ap-3511	26	8	of	of	ADP
ap-3511	26	9	its	its	PRON
ap-3511	26	10	conjugacy	conjugacy	ADJ
ap-3511	26	11	classes	class	NOUN
ap-3511	26	12	.	.	PUNCT
ap-3511	27	1	irreducible	irreducible	ADJ
ap-3511	27	2	characters	character	NOUN
ap-3511	27	3	χ	χ	NOUN
ap-3511	27	4	,	,	PUNCT
ap-3511	27	5	traces	trace	NOUN
ap-3511	27	6	of	of	ADP
ap-3511	27	7	irreducible	irreducible	ADJ
ap-3511	27	8	representations	representation	NOUN
ap-3511	27	9	,	,	PUNCT
ap-3511	27	10	are	be	AUX
ap-3511	27	11	mappings	mapping	NOUN
ap-3511	27	12	of	of	ADP
ap-3511	27	13	conjugacy	conjugacy	ADJ
ap-3511	27	14	classes	class	NOUN
ap-3511	27	15	to	to	ADP
ap-3511	27	16	complex	complex	ADJ
ap-3511	27	17	numbers	number	NOUN
ap-3511	27	18	.	.	PUNCT
ap-3511	28	1	the	the	DET
ap-3511	28	2	number	number	NOUN
ap-3511	28	3	of	of	ADP
ap-3511	28	4	conjugacy	conjugacy	ADJ
ap-3511	28	5	classes	class	NOUN
ap-3511	28	6	equals	equal	VERB
ap-3511	28	7	the	the	DET
ap-3511	28	8	number	number	NOUN
ap-3511	28	9	of	of	ADP
ap-3511	28	10	irreducible	irreducible	ADJ
ap-3511	28	11	characters	character	NOUN
ap-3511	28	12	.	.	PUNCT
ap-3511	29	1	the	the	DET
ap-3511	29	2	values	value	NOUN
ap-3511	29	3	of	of	ADP
ap-3511	29	4	the	the	DET
ap-3511	29	5	characters	character	NOUN
ap-3511	29	6	are	be	AUX
ap-3511	29	7	then	then	ADV
ap-3511	29	8	listed	list	VERB
ap-3511	29	9	in	in	ADP
ap-3511	29	10	so	so	ADV
ap-3511	29	11	-	-	PUNCT
ap-3511	29	12	called	call	VERB
ap-3511	29	13	character	character	NOUN
ap-3511	29	14	tables	table	NOUN
ap-3511	29	15	;	;	PUNCT
ap-3511	29	16	see	see	VERB
ap-3511	29	17	table	table	NOUN
ap-3511	29	18	1	1	NUM
ap-3511	29	19	.	.	PUNCT
ap-3511	29	20	degree	degree	NOUN
ap-3511	29	21	dk	dk	PROPN
ap-3511	29	22	of	of	ADP
ap-3511	29	23	the	the	DET
ap-3511	29	24	character	character	NOUN
ap-3511	29	25	χk	χk	PROPN
ap-3511	29	26	is	be	AUX
ap-3511	29	27	the	the	DET
ap-3511	29	28	dimension	dimension	NOUN
ap-3511	29	29	of	of	ADP
ap-3511	29	30	the	the	DET
ap-3511	29	31	corresponding	corresponding	ADJ
ap-3511	29	32	representation	representation	NOUN
ap-3511	29	33	.	.	PUNCT
ap-3511	30	1	linear	linear	ADJ
ap-3511	30	2	characters	character	NOUN
ap-3511	30	3	are	be	AUX
ap-3511	30	4	the	the	DET
ap-3511	30	5	characters	character	NOUN
ap-3511	30	6	of	of	ADP
ap-3511	30	7	degree	degree	NOUN
ap-3511	30	8	one	one	NUM
ap-3511	30	9	.	.	PUNCT
ap-3511	31	1	they	they	PRON
ap-3511	31	2	are	be	AUX
ap-3511	31	3	homomorphisms	homomorphism	NOUN
ap-3511	31	4	between	between	ADP
ap-3511	31	5	group	group	NOUN
ap-3511	31	6	g	g	PROPN
ap-3511	31	7	and	and	CCONJ
ap-3511	31	8	the	the	DET
ap-3511	31	9	multiplicative	multiplicative	ADJ
ap-3511	31	10	group	group	NOUN
ap-3511	31	11	of	of	ADP
ap-3511	31	12	non	non	ADJ
ap-3511	31	13	-	-	ADJ
ap-3511	31	14	zero	zero	ADJ
ap-3511	31	15	complex	complex	ADJ
ap-3511	31	16	numbers	number	NOUN
ap-3511	31	17	.	.	PUNCT
ap-3511	32	1	characters	character	NOUN
ap-3511	32	2	are	be	AUX
ap-3511	32	3	real	real	ADV
ap-3511	32	4	valued	value	VERB
ap-3511	32	5	if	if	SCONJ
ap-3511	32	6	and	and	CCONJ
ap-3511	32	7	only	only	ADV
ap-3511	32	8	if	if	SCONJ
ap-3511	32	9	every	every	DET
ap-3511	32	10	g	g	PROPN
ap-3511	32	11	∈	∈	PROPN
ap-3511	32	12	g	g	PROPN
ap-3511	32	13	is	be	AUX
ap-3511	32	14	conjugated	conjugate	VERB
ap-3511	32	15	to	to	ADP
ap-3511	32	16	its	its	PRON
ap-3511	32	17	inverse	inverse	NOUN
ap-3511	32	18	.	.	PUNCT
ap-3511	33	1	this	this	PRON
ap-3511	33	2	is	be	AUX
ap-3511	33	3	the	the	DET
ap-3511	33	4	case	case	NOUN
ap-3511	33	5	for	for	ADP
ap-3511	33	6	example	example	NOUN
ap-3511	33	7	for	for	ADP
ap-3511	33	8	all	all	DET
ap-3511	33	9	the	the	DET
ap-3511	33	10	weyl	weyl	VERB
ap-3511	33	11	groups	group	NOUN
ap-3511	33	12	of	of	ADP
ap-3511	33	13	simple	simple	ADJ
ap-3511	33	14	lie	lie	NOUN
ap-3511	33	15	algebras	algebra	NOUN
ap-3511	33	16	[	[	X
ap-3511	33	17	10	10	NUM
ap-3511	33	18	,	,	PUNCT
ap-3511	33	19	corollary	corollary	ADJ
ap-3511	33	20	3.2.14	3.2.14	NOUN
ap-3511	33	21	]	]	X
ap-3511	33	22	.	.	PUNCT
ap-3511	34	1	the	the	DET
ap-3511	34	2	inner	inner	ADJ
ap-3511	34	3	product	product	NOUN
ap-3511	34	4	of	of	ADP
ap-3511	34	5	characters	character	NOUN
ap-3511	34	6	is	be	AUX
ap-3511	34	7	defined	define	VERB
ap-3511	34	8	as	as	ADP
ap-3511	34	9	〈	〈	PROPN
ap-3511	34	10	χk	χk	PROPN
ap-3511	34	11	,	,	PUNCT
ap-3511	34	12	χl	χl	PROPN
ap-3511	34	13	〉	〉	NOUN
ap-3511	34	14	=	=	SYM
ap-3511	34	15	1	1	NUM
ap-3511	34	16	|g|	|g|	PROPN
ap-3511	34	17	∑	∑	PROPN
ap-3511	34	18	g∈g	g∈g	NOUN
ap-3511	34	19	χk(g)χl(g	χk(g)χl(g	NOUN
ap-3511	34	20	)	)	PUNCT
ap-3511	34	21	,	,	PUNCT
ap-3511	34	22	where	where	SCONJ
ap-3511	34	23	|g|	|g|	PROPN
ap-3511	34	24	denotes	denote	VERB
ap-3511	34	25	the	the	DET
ap-3511	34	26	order	order	NOUN
ap-3511	34	27	of	of	ADP
ap-3511	34	28	group	group	NOUN
ap-3511	34	29	g.	g.	PROPN
ap-3511	35	1	the	the	DET
ap-3511	35	2	row	row	NOUN
ap-3511	35	3	orthogonality	orthogonality	NOUN
ap-3511	35	4	relation	relation	NOUN
ap-3511	35	5	states	state	VERB
ap-3511	35	6	that	that	SCONJ
ap-3511	35	7	for	for	ADP
ap-3511	35	8	every	every	DET
ap-3511	35	9	irreducible	irreducible	ADJ
ap-3511	35	10	440	440	NUM
ap-3511	35	11	http://dx.doi.org/10.14311/ap.2016.56.0440	http://dx.doi.org/10.14311/ap.2016.56.0440	X
ap-3511	35	12	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-3511	35	13	vol	vol	NOUN
ap-3511	35	14	.	.	PUNCT
ap-3511	36	1	56	56	NUM
ap-3511	36	2	no	no	NOUN
ap-3511	36	3	.	.	PUNCT
ap-3511	37	1	6/2016	6/2016	NUM
ap-3511	37	2	on	on	ADP
ap-3511	37	3	generalization	generalization	NOUN
ap-3511	37	4	of	of	ADP
ap-3511	37	5	special	special	ADJ
ap-3511	37	6	functions	function	NOUN
ap-3511	37	7	related	relate	VERB
ap-3511	37	8	to	to	ADP
ap-3511	37	9	weyl	weyl	VERB
ap-3511	37	10	groups	group	NOUN
ap-3511	37	11	characters	character	NOUN
ap-3511	37	12	χk	χk	PROPN
ap-3511	37	13	,	,	PUNCT
ap-3511	37	14	χl	χl	PROPN
ap-3511	37	15	,	,	PUNCT
ap-3511	37	16	1	1	NUM
ap-3511	37	17	|g|	|g|	PROPN
ap-3511	37	18	∑	∑	PROPN
ap-3511	37	19	g∈g	g∈g	NOUN
ap-3511	37	20	χk(g)χl(g	χk(g)χl(g	NOUN
ap-3511	37	21	)	)	PUNCT
ap-3511	38	1	=	=	SYM
ap-3511	38	2	δkl	δkl	ADJ
ap-3511	38	3	.	.	PUNCT
ap-3511	39	1	(	(	PUNCT
ap-3511	39	2	1	1	X
ap-3511	39	3	)	)	PUNCT
ap-3511	39	4	the	the	DET
ap-3511	39	5	column	column	NOUN
ap-3511	39	6	orthogonality	orthogonality	NOUN
ap-3511	39	7	relation	relation	NOUN
ap-3511	39	8	is	be	AUX
ap-3511	39	9	the	the	DET
ap-3511	39	10	following	following	NOUN
ap-3511	39	11	:	:	PUNCT
ap-3511	39	12	for	for	ADP
ap-3511	39	13	every	every	DET
ap-3511	39	14	g	g	NOUN
ap-3511	39	15	,	,	PUNCT
ap-3511	39	16	h	h	NOUN
ap-3511	39	17	∈	∈	PROPN
ap-3511	39	18	g	g	PROPN
ap-3511	39	19	,	,	PUNCT
ap-3511	39	20	k∑	k∑	VERB
ap-3511	39	21	r=1	r=1	X
ap-3511	39	22	χk(g)χk(h	χk(g)χk(h	ADV
ap-3511	39	23	)	)	PUNCT
ap-3511	40	1	=	=	SYM
ap-3511	40	2	δgh	δgh	NOUN
ap-3511	40	3	|g|	|g|	PROPN
ap-3511	40	4	|[g]|	|[g]|	NOUN
ap-3511	40	5	,	,	PUNCT
ap-3511	40	6	(	(	PUNCT
ap-3511	40	7	2	2	X
ap-3511	40	8	)	)	PUNCT
ap-3511	40	9	where	where	SCONJ
ap-3511	40	10	|[g]|	|[g]|	NOUN
ap-3511	40	11	is	be	AUX
ap-3511	40	12	the	the	DET
ap-3511	40	13	size	size	NOUN
ap-3511	40	14	of	of	ADP
ap-3511	40	15	the	the	DET
ap-3511	40	16	conjugacy	conjugacy	ADJ
ap-3511	40	17	class	class	NOUN
ap-3511	40	18	of	of	ADP
ap-3511	40	19	g.	g.	PROPN
ap-3511	40	20	moreover	moreover	ADV
ap-3511	40	21	,	,	PUNCT
ap-3511	40	22	another	another	DET
ap-3511	40	23	useful	useful	ADJ
ap-3511	40	24	identity	identity	NOUN
ap-3511	40	25	holds	hold	VERB
ap-3511	40	26	[	[	X
ap-3511	40	27	9	9	NUM
ap-3511	40	28	,	,	PUNCT
ap-3511	40	29	theorem	theorem	ADJ
ap-3511	40	30	iii.2.7	iii.2.7	NOUN
ap-3511	40	31	]	]	PUNCT
ap-3511	40	32	:	:	PUNCT
ap-3511	40	33	∑	∑	PUNCT
ap-3511	40	34	g∈g	g∈g	NOUN
ap-3511	40	35	χk(hg−1)χl(g	χk(hg−1)χl(g	NOUN
ap-3511	40	36	)	)	PUNCT
ap-3511	40	37	=	=	PUNCT
ap-3511	41	1	δkl	δkl	ADJ
ap-3511	41	2	|g|	|g|	PROPN
ap-3511	41	3	dk	dk	PROPN
ap-3511	41	4	χk(h	χk(h	PUNCT
ap-3511	41	5	)	)	PUNCT
ap-3511	41	6	.	.	PUNCT
ap-3511	42	1	(	(	PUNCT
ap-3511	42	2	3	3	X
ap-3511	42	3	)	)	PUNCT
ap-3511	42	4	2.2	2.2	NUM
ap-3511	42	5	.	.	PUNCT
ap-3511	43	1	weyl	weyl	VERB
ap-3511	43	2	groups	group	NOUN
ap-3511	43	3	of	of	ADP
ap-3511	43	4	simple	simple	ADJ
ap-3511	43	5	lie	lie	NOUN
ap-3511	43	6	algebras	algebra	VERB
ap-3511	43	7	details	detail	NOUN
ap-3511	43	8	about	about	ADP
ap-3511	43	9	the	the	DET
ap-3511	43	10	notion	notion	NOUN
ap-3511	43	11	introduced	introduce	VERB
ap-3511	43	12	in	in	ADP
ap-3511	43	13	this	this	DET
ap-3511	43	14	subsection	subsection	NOUN
ap-3511	43	15	are	be	AUX
ap-3511	43	16	to	to	PART
ap-3511	43	17	be	be	AUX
ap-3511	43	18	found	find	VERB
ap-3511	43	19	for	for	ADP
ap-3511	43	20	example	example	NOUN
ap-3511	43	21	in	in	ADP
ap-3511	43	22	[	[	X
ap-3511	43	23	5	5	NUM
ap-3511	43	24	]	]	PUNCT
ap-3511	43	25	.	.	PUNCT
ap-3511	44	1	we	we	PRON
ap-3511	44	2	consider	consider	VERB
ap-3511	44	3	simple	simple	ADJ
ap-3511	44	4	lie	lie	NOUN
ap-3511	44	5	algebras	algebra	NOUN
ap-3511	44	6	of	of	ADP
ap-3511	44	7	rank	rank	NOUN
ap-3511	44	8	n	n	PROPN
ap-3511	44	9	with	with	ADP
ap-3511	44	10	the	the	DET
ap-3511	44	11	set	set	NOUN
ap-3511	44	12	of	of	ADP
ap-3511	44	13	simple	simple	ADJ
ap-3511	44	14	roots	root	NOUN
ap-3511	44	15	∆	∆	X
ap-3511	44	16	=	=	SYM
ap-3511	44	17	{	{	PUNCT
ap-3511	44	18	α1	α1	PROPN
ap-3511	44	19	,	,	PUNCT
ap-3511	44	20	.	.	PUNCT
ap-3511	44	21	.	.	PUNCT
ap-3511	45	1	.	.	PUNCT
ap-3511	46	1	,	,	PUNCT
ap-3511	46	2	αn	αn	NOUN
ap-3511	46	3	}	}	PUNCT
ap-3511	46	4	.	.	PUNCT
ap-3511	47	1	the	the	DET
ap-3511	47	2	roots	root	NOUN
ap-3511	47	3	are	be	AUX
ap-3511	47	4	either	either	PRON
ap-3511	47	5	of	of	ADP
ap-3511	47	6	the	the	DET
ap-3511	47	7	same	same	ADJ
ap-3511	47	8	length	length	NOUN
ap-3511	47	9	or	or	CCONJ
ap-3511	47	10	of	of	ADP
ap-3511	47	11	two	two	NUM
ap-3511	47	12	different	different	ADJ
ap-3511	47	13	lengths	length	NOUN
ap-3511	47	14	,	,	PUNCT
ap-3511	47	15	called	call	VERB
ap-3511	47	16	the	the	DET
ap-3511	47	17	short	short	ADJ
ap-3511	47	18	and	and	CCONJ
ap-3511	47	19	long	long	ADJ
ap-3511	47	20	roots	root	NOUN
ap-3511	47	21	.	.	PUNCT
ap-3511	48	1	in	in	ADP
ap-3511	48	2	the	the	DET
ap-3511	48	3	latter	latter	ADJ
ap-3511	48	4	case	case	NOUN
ap-3511	48	5	we	we	PRON
ap-3511	48	6	can	can	AUX
ap-3511	48	7	write	write	VERB
ap-3511	48	8	∆	∆	X
ap-3511	48	9	=	=	SYM
ap-3511	48	10	∆s	∆s	PROPN
ap-3511	48	11	∪∆l	∪∆l	PROPN
ap-3511	48	12	.	.	PUNCT
ap-3511	49	1	coroots	coroot	NOUN
ap-3511	49	2	are	be	AUX
ap-3511	49	3	a	a	DET
ap-3511	49	4	normalization	normalization	NOUN
ap-3511	49	5	of	of	ADP
ap-3511	49	6	simple	simple	ADJ
ap-3511	49	7	roots	root	NOUN
ap-3511	49	8	,	,	PUNCT
ap-3511	49	9	α∨	α∨	PROPN
ap-3511	49	10	=	=	SYM
ap-3511	49	11	2α	2α	NOUN
ap-3511	49	12	/	/	SYM
ap-3511	49	13	〈α	〈α	NOUN
ap-3511	49	14	,	,	PUNCT
ap-3511	49	15	α	α	NOUN
ap-3511	49	16	〉	〉	PROPN
ap-3511	49	17	.	.	PUNCT
ap-3511	50	1	weights	weight	NOUN
ap-3511	50	2	ω	ω	NUM
ap-3511	50	3	and	and	CCONJ
ap-3511	50	4	coweights	coweight	NOUN
ap-3511	50	5	ω∨	ω∨	PROPN
ap-3511	50	6	are	be	AUX
ap-3511	50	7	dual	dual	ADJ
ap-3511	50	8	to	to	ADP
ap-3511	50	9	coroots	coroot	NOUN
ap-3511	50	10	and	and	CCONJ
ap-3511	50	11	simple	simple	ADJ
ap-3511	50	12	roots	root	NOUN
ap-3511	50	13	,	,	PUNCT
ap-3511	50	14	〈	〈	PROPN
ap-3511	50	15	αi	αi	NOUN
ap-3511	50	16	,	,	PUNCT
ap-3511	50	17	ω∨j	ω∨j	PROPN
ap-3511	50	18	〉	〉	NOUN
ap-3511	50	19	=	=	SYM
ap-3511	50	20	〈	〈	PROPN
ap-3511	50	21	α∨i	α∨i	NOUN
ap-3511	50	22	,	,	PUNCT
ap-3511	50	23	ωj	ωj	ADP
ap-3511	50	24	〉	〉	NOUN
ap-3511	50	25	=	=	SYM
ap-3511	50	26	δij	δij	NOUN
ap-3511	50	27	.	.	PUNCT
ap-3511	51	1	integer	integer	NOUN
ap-3511	51	2	combinations	combination	NOUN
ap-3511	51	3	of	of	ADP
ap-3511	51	4	the	the	DET
ap-3511	51	5	mentioned	mention	VERB
ap-3511	51	6	vectors	vector	NOUN
ap-3511	51	7	are	be	AUX
ap-3511	51	8	an	an	DET
ap-3511	51	9	important	important	ADJ
ap-3511	51	10	tool	tool	NOUN
ap-3511	51	11	when	when	SCONJ
ap-3511	51	12	dealing	deal	VERB
ap-3511	51	13	with	with	ADP
ap-3511	51	14	orbit	orbit	NOUN
ap-3511	51	15	functions	function	NOUN
ap-3511	51	16	.	.	PUNCT
ap-3511	52	1	we	we	PRON
ap-3511	52	2	define	define	VERB
ap-3511	52	3	p	p	NOUN
ap-3511	52	4	=	=	NOUN
ap-3511	52	5	zω1	zω1	NOUN
ap-3511	52	6	+	+	X
ap-3511	52	7	.	.	PUNCT
ap-3511	52	8	.	.	PUNCT
ap-3511	53	1	.+	.+	NOUN
ap-3511	53	2	zωn	zωn	VERB
ap-3511	53	3	(	(	PUNCT
ap-3511	53	4	the	the	DET
ap-3511	53	5	weight	weight	NOUN
ap-3511	53	6	lattice	lattice	PROPN
ap-3511	53	7	)	)	PUNCT
ap-3511	53	8	,	,	PUNCT
ap-3511	53	9	p∨	p∨	NOUN
ap-3511	53	10	=	=	PUNCT
ap-3511	53	11	zω∨1	zω∨1	PUNCT
ap-3511	54	1	+	+	CCONJ
ap-3511	54	2	.	.	PUNCT
ap-3511	54	3	.	.	PUNCT
ap-3511	55	1	.+	.+	NOUN
ap-3511	56	1	zω∨n	zω∨n	PUNCT
ap-3511	57	1	(	(	PUNCT
ap-3511	57	2	the	the	DET
ap-3511	57	3	coweight	coweight	ADJ
ap-3511	57	4	lattice	lattice	NOUN
ap-3511	57	5	)	)	PUNCT
ap-3511	57	6	,	,	PUNCT
ap-3511	57	7	q	q	NOUN
ap-3511	58	1	=	=	PUNCT
ap-3511	58	2	zα1	zα1	NOUN
ap-3511	58	3	+	+	CCONJ
ap-3511	58	4	.	.	PUNCT
ap-3511	58	5	.	.	PUNCT
ap-3511	59	1	.+	.+	NOUN
ap-3511	59	2	zαn	zαn	PROPN
ap-3511	59	3	(	(	PUNCT
ap-3511	59	4	the	the	DET
ap-3511	59	5	root	root	NOUN
ap-3511	59	6	lattice	lattice	PROPN
ap-3511	59	7	)	)	PUNCT
ap-3511	59	8	,	,	PUNCT
ap-3511	59	9	q∨	q∨	PROPN
ap-3511	59	10	=	=	PUNCT
ap-3511	59	11	zα∨1	zα∨1	PROPN
ap-3511	60	1	+	+	CCONJ
ap-3511	60	2	.	.	PUNCT
ap-3511	60	3	.	.	PUNCT
ap-3511	61	1	.+	.+	NOUN
ap-3511	62	1	zα∨n	zα∨n	INTJ
ap-3511	63	1	(	(	PUNCT
ap-3511	63	2	the	the	DET
ap-3511	63	3	coroot	coroot	ADJ
ap-3511	63	4	lattice	lattice	NOUN
ap-3511	63	5	)	)	PUNCT
ap-3511	63	6	.	.	PUNCT
ap-3511	64	1	moreover	moreover	ADV
ap-3511	64	2	,	,	PUNCT
ap-3511	64	3	we	we	PRON
ap-3511	64	4	denote	denote	VERB
ap-3511	64	5	by	by	ADP
ap-3511	64	6	p+	p+	PROPN
ap-3511	64	7	and	and	CCONJ
ap-3511	64	8	p++	p++	VERB
ap-3511	64	9	the	the	DET
ap-3511	64	10	non	non	ADJ
ap-3511	64	11	-	-	ADJ
ap-3511	64	12	negative	negative	ADJ
ap-3511	64	13	and	and	CCONJ
ap-3511	64	14	positive	positive	ADJ
ap-3511	64	15	part	part	NOUN
ap-3511	64	16	of	of	ADP
ap-3511	64	17	p	p	NOUN
ap-3511	64	18	,	,	PUNCT
ap-3511	64	19	respectively	respectively	ADV
ap-3511	64	20	.	.	PUNCT
ap-3511	65	1	weyl	weyl	VERB
ap-3511	65	2	groups	group	NOUN
ap-3511	65	3	w	w	ADP
ap-3511	65	4	are	be	AUX
ap-3511	65	5	generated	generate	VERB
ap-3511	65	6	by	by	ADP
ap-3511	65	7	reflections	reflection	NOUN
ap-3511	65	8	ri	ri	NOUN
ap-3511	65	9	with	with	ADP
ap-3511	65	10	respect	respect	NOUN
ap-3511	65	11	to	to	ADP
ap-3511	65	12	the	the	DET
ap-3511	65	13	hyperplanes	hyperplane	NOUN
ap-3511	65	14	orthogonal	orthogonal	ADJ
ap-3511	65	15	to	to	ADP
ap-3511	65	16	the	the	DET
ap-3511	65	17	simple	simple	ADJ
ap-3511	65	18	roots	root	NOUN
ap-3511	65	19	αi	αi	VERB
ap-3511	65	20	,	,	PUNCT
ap-3511	65	21	i.e.	i.e.	X
ap-3511	65	22	,	,	PUNCT
ap-3511	65	23	rix	rix	PROPN
ap-3511	65	24	=	=	SYM
ap-3511	65	25	x−〈αi	x−〈αi	PROPN
ap-3511	65	26	,	,	PUNCT
ap-3511	65	27	x〉α∨i	x〉α∨i	VERB
ap-3511	65	28	.	.	PUNCT
ap-3511	66	1	their	their	PRON
ap-3511	66	2	action	action	NOUN
ap-3511	66	3	on	on	ADP
ap-3511	66	4	the	the	DET
ap-3511	66	5	set	set	NOUN
ap-3511	66	6	of	of	ADP
ap-3511	66	7	simple	simple	ADJ
ap-3511	66	8	roots	root	NOUN
ap-3511	66	9	gives	give	VERB
ap-3511	66	10	the	the	DET
ap-3511	66	11	root	root	NOUN
ap-3511	66	12	system	system	NOUN
ap-3511	66	13	w	w	X
ap-3511	66	14	(	(	PUNCT
ap-3511	66	15	∆	∆	PROPN
ap-3511	66	16	)	)	PUNCT
ap-3511	66	17	.	.	PUNCT
ap-3511	67	1	since	since	SCONJ
ap-3511	67	2	such	such	DET
ap-3511	67	3	a	a	DET
ap-3511	67	4	root	root	NOUN
ap-3511	67	5	system	system	NOUN
ap-3511	67	6	is	be	AUX
ap-3511	67	7	irreducible	irreducible	ADJ
ap-3511	67	8	,	,	PUNCT
ap-3511	67	9	there	there	PRON
ap-3511	67	10	exists	exist	VERB
ap-3511	67	11	a	a	DET
ap-3511	67	12	unique	unique	ADJ
ap-3511	67	13	highest	high	ADJ
ap-3511	67	14	root	root	NOUN
ap-3511	67	15	ξ	ξ	PROPN
ap-3511	67	16	.	.	PUNCT
ap-3511	67	17	coordinates	coordinate	NOUN
ap-3511	67	18	of	of	ADP
ap-3511	67	19	ξ	ξ	PROPN
ap-3511	67	20	in	in	ADP
ap-3511	67	21	the	the	DET
ap-3511	67	22	basis	basis	NOUN
ap-3511	67	23	of	of	ADP
ap-3511	67	24	simple	simple	ADJ
ap-3511	67	25	roots	root	NOUN
ap-3511	67	26	mi	mi	PROPN
ap-3511	67	27	are	be	AUX
ap-3511	67	28	called	call	VERB
ap-3511	67	29	marks	mark	NOUN
ap-3511	67	30	.	.	PUNCT
ap-3511	68	1	the	the	DET
ap-3511	68	2	affine	affine	NOUN
ap-3511	68	3	weyl	weyl	PROPN
ap-3511	68	4	group	group	NOUN
ap-3511	68	5	is	be	AUX
ap-3511	68	6	an	an	DET
ap-3511	68	7	infinite	infinite	ADJ
ap-3511	68	8	extension	extension	NOUN
ap-3511	68	9	which	which	PRON
ap-3511	68	10	can	can	AUX
ap-3511	68	11	be	be	AUX
ap-3511	68	12	described	describe	VERB
ap-3511	68	13	as	as	ADP
ap-3511	68	14	a	a	DET
ap-3511	68	15	semidirect	semidirect	NOUN
ap-3511	68	16	product	product	NOUN
ap-3511	68	17	of	of	ADP
ap-3511	68	18	shifts	shift	NOUN
ap-3511	68	19	by	by	ADP
ap-3511	68	20	integer	integer	NOUN
ap-3511	68	21	combinations	combination	NOUN
ap-3511	68	22	of	of	ADP
ap-3511	68	23	coroots	coroot	NOUN
ap-3511	68	24	q∨	q∨	PROPN
ap-3511	68	25	,	,	PUNCT
ap-3511	68	26	and	and	CCONJ
ap-3511	68	27	the	the	DET
ap-3511	68	28	weyl	weyl	PROPN
ap-3511	68	29	group	group	NOUN
ap-3511	68	30	w	w	PROPN
ap-3511	68	31	.	.	PUNCT
ap-3511	69	1	its	its	PRON
ap-3511	69	2	fundamental	fundamental	ADJ
ap-3511	69	3	domain	domain	NOUN
ap-3511	69	4	f	f	X
ap-3511	69	5	is	be	AUX
ap-3511	69	6	a	a	DET
ap-3511	69	7	simplex	simplex	NOUN
ap-3511	69	8	with	with	ADP
ap-3511	69	9	vertices	vertex	NOUN
ap-3511	69	10	{	{	PUNCT
ap-3511	69	11	0	0	NUM
ap-3511	69	12	,	,	PUNCT
ap-3511	69	13	ω	ω	X
ap-3511	69	14	∨	∨	X
ap-3511	69	15	1	1	NUM
ap-3511	69	16	m1	m1	PROPN
ap-3511	69	17	,	,	PUNCT
ap-3511	69	18	.	.	PUNCT
ap-3511	69	19	.	.	PUNCT
ap-3511	70	1	.	.	PUNCT
ap-3511	71	1	,	,	PUNCT
ap-3511	71	2	ω∨	ω∨	PROPN
ap-3511	71	3	n	n	PRON
ap-3511	71	4	mn	mn	PROPN
ap-3511	71	5	}	}	PUNCT
ap-3511	71	6	.	.	PUNCT
ap-3511	72	1	the	the	DET
ap-3511	72	2	set	set	NOUN
ap-3511	72	3	of	of	ADP
ap-3511	72	4	coroots	coroot	NOUN
ap-3511	72	5	∆∨	∆∨	NOUN
ap-3511	72	6	generates	generate	VERB
ap-3511	72	7	the	the	DET
ap-3511	72	8	same	same	ADJ
ap-3511	72	9	weyl	weyl	VERB
ap-3511	72	10	group	group	NOUN
ap-3511	72	11	;	;	PUNCT
ap-3511	72	12	its	its	PRON
ap-3511	72	13	action	action	NOUN
ap-3511	72	14	on	on	ADP
ap-3511	72	15	∆∨	∆∨	NOUN
ap-3511	72	16	gives	give	VERB
ap-3511	72	17	a	a	DET
ap-3511	72	18	dual	dual	ADJ
ap-3511	72	19	root	root	NOUN
ap-3511	72	20	system	system	NOUN
ap-3511	72	21	with	with	ADP
ap-3511	72	22	the	the	DET
ap-3511	72	23	highest	high	ADJ
ap-3511	72	24	root	root	NOUN
ap-3511	72	25	η	η	PROPN
ap-3511	72	26	.	.	PUNCT
ap-3511	73	1	the	the	DET
ap-3511	73	2	coordinates	coordinate	NOUN
ap-3511	73	3	of	of	ADP
ap-3511	73	4	η	η	PROPN
ap-3511	73	5	in	in	ADP
ap-3511	73	6	the	the	DET
ap-3511	73	7	basis	basis	NOUN
ap-3511	73	8	of	of	ADP
ap-3511	73	9	coroots	coroot	NOUN
ap-3511	73	10	are	be	AUX
ap-3511	73	11	called	call	VERB
ap-3511	73	12	dual	dual	ADJ
ap-3511	73	13	marks	mark	NOUN
ap-3511	73	14	and	and	CCONJ
ap-3511	73	15	denoted	denote	VERB
ap-3511	73	16	m∨i	m∨i	NOUN
ap-3511	73	17	.	.	PUNCT
ap-3511	74	1	finally	finally	ADV
ap-3511	74	2	,	,	PUNCT
ap-3511	74	3	the	the	DET
ap-3511	74	4	dual	dual	ADJ
ap-3511	74	5	affine	affine	NOUN
ap-3511	74	6	weyl	weyl	PROPN
ap-3511	74	7	group	group	NOUN
ap-3511	74	8	can	can	AUX
ap-3511	74	9	be	be	AUX
ap-3511	74	10	written	write	VERB
ap-3511	74	11	as	as	ADP
ap-3511	74	12	qow	qow	ADV
ap-3511	74	13	and	and	CCONJ
ap-3511	74	14	its	its	PRON
ap-3511	74	15	fundamental	fundamental	ADJ
ap-3511	74	16	domain	domain	NOUN
ap-3511	74	17	f∨	f∨	PROPN
ap-3511	74	18	is	be	AUX
ap-3511	74	19	a	a	DET
ap-3511	74	20	simplex	simplex	NOUN
ap-3511	74	21	with	with	ADP
ap-3511	74	22	vertices	vertex	NOUN
ap-3511	74	23	{	{	PUNCT
ap-3511	74	24	0	0	NUM
ap-3511	74	25	,	,	PUNCT
ap-3511	74	26	ω1	ω1	PROPN
ap-3511	74	27	m∨	m∨	PROPN
ap-3511	74	28	1	1	NUM
ap-3511	74	29	,	,	PUNCT
ap-3511	74	30	.	.	PUNCT
ap-3511	74	31	.	.	PUNCT
ap-3511	74	32	.	.	PUNCT
ap-3511	75	1	,	,	PUNCT
ap-3511	75	2	ωn	ωn	ADP
ap-3511	75	3	m∨	m∨	NOUN
ap-3511	75	4	n	n	PROPN
ap-3511	75	5	}	}	PUNCT
ap-3511	75	6	.	.	PUNCT
ap-3511	76	1	weyl	weyl	VERB
ap-3511	76	2	groups	group	NOUN
ap-3511	76	3	can	can	AUX
ap-3511	76	4	be	be	AUX
ap-3511	76	5	described	describe	VERB
ap-3511	76	6	also	also	ADV
ap-3511	76	7	by	by	ADP
ap-3511	76	8	their	their	PRON
ap-3511	76	9	presentation	presentation	NOUN
ap-3511	76	10	as	as	ADP
ap-3511	76	11	a	a	DET
ap-3511	76	12	finite	finite	NOUN
ap-3511	76	13	coxeter	coxeter	NOUN
ap-3511	76	14	group	group	NOUN
ap-3511	76	15	,	,	PUNCT
ap-3511	76	16	i.e.	i.e.	X
ap-3511	76	17	,	,	PUNCT
ap-3511	76	18	a	a	DET
ap-3511	76	19	group	group	NOUN
ap-3511	76	20	generated	generate	VERB
ap-3511	76	21	by	by	ADP
ap-3511	76	22	elements	element	NOUN
ap-3511	76	23	ri	ri	X
ap-3511	76	24	which	which	PRON
ap-3511	76	25	satisfy	satisfy	VERB
ap-3511	76	26	r2	r2	PROPN
ap-3511	76	27	i	i	NOUN
ap-3511	76	28	=	=	NOUN
ap-3511	76	29	1	1	NUM
ap-3511	76	30	,	,	PUNCT
ap-3511	76	31	(	(	PUNCT
ap-3511	76	32	rirj)sij	rirj)sij	NOUN
ap-3511	76	33	=	=	SYM
ap-3511	76	34	1	1	NUM
ap-3511	76	35	,	,	PUNCT
ap-3511	76	36	i	i	PRON
ap-3511	76	37	,	,	PUNCT
ap-3511	76	38	j	j	PROPN
ap-3511	76	39	∈	∈	PROPN
ap-3511	76	40	{	{	PUNCT
ap-3511	76	41	1	1	NUM
ap-3511	76	42	,	,	PUNCT
ap-3511	76	43	.	.	PUNCT
ap-3511	76	44	.	.	PUNCT
ap-3511	77	1	.	.	PUNCT
ap-3511	78	1	,	,	PUNCT
ap-3511	79	1	n	n	CCONJ
ap-3511	79	2	}	}	PUNCT
ap-3511	80	1	,	,	PUNCT
ap-3511	80	2	(	(	PUNCT
ap-3511	80	3	4	4	X
ap-3511	80	4	)	)	PUNCT
ap-3511	80	5	where	where	SCONJ
ap-3511	80	6	sij	sij	PROPN
ap-3511	80	7	=	=	PUNCT
ap-3511	80	8	sji	sji	PROPN
ap-3511	80	9	are	be	AUX
ap-3511	80	10	integers	integer	NOUN
ap-3511	80	11	greater	great	ADJ
ap-3511	80	12	than	than	ADP
ap-3511	80	13	2	2	NUM
ap-3511	80	14	.	.	NOUN
ap-3511	80	15	3	3	NUM
ap-3511	80	16	.	.	NOUN
ap-3511	80	17	special	special	ADJ
ap-3511	80	18	functions	function	NOUN
ap-3511	80	19	related	relate	VERB
ap-3511	80	20	to	to	ADP
ap-3511	80	21	weyl	weyl	VERB
ap-3511	80	22	groups	group	NOUN
ap-3511	80	23	3.1	3.1	NUM
ap-3511	80	24	.	.	PUNCT
ap-3511	81	1	weyl	weyl	PROPN
ap-3511	81	2	group	group	PROPN
ap-3511	81	3	orbit	orbit	NOUN
ap-3511	81	4	functions	function	VERB
ap-3511	81	5	the	the	DET
ap-3511	81	6	standard	standard	ADJ
ap-3511	81	7	way	way	NOUN
ap-3511	81	8	of	of	ADP
ap-3511	81	9	defining	define	VERB
ap-3511	81	10	four	four	NUM
ap-3511	81	11	families	family	NOUN
ap-3511	81	12	of	of	ADP
ap-3511	81	13	orbit	orbit	NOUN
ap-3511	81	14	functions	function	NOUN
ap-3511	81	15	uses	use	VERB
ap-3511	81	16	the	the	DET
ap-3511	81	17	concept	concept	NOUN
ap-3511	81	18	of	of	ADP
ap-3511	81	19	sign	sign	NOUN
ap-3511	81	20	homomorphisms	homomorphism	NOUN
ap-3511	81	21	,	,	PUNCT
ap-3511	81	22	i.e.	i.e.	X
ap-3511	81	23	,	,	PUNCT
ap-3511	81	24	mappings	mapping	NOUN
ap-3511	81	25	σ	σ	NOUN
ap-3511	81	26	:	:	PUNCT
ap-3511	81	27	w	w	X
ap-3511	81	28	→	→	PUNCT
ap-3511	81	29	{	{	PUNCT
ap-3511	81	30	±1	±1	NOUN
ap-3511	81	31	}	}	PUNCT
ap-3511	81	32	.	.	PUNCT
ap-3511	82	1	a	a	DET
ap-3511	82	2	sign	sign	NOUN
ap-3511	82	3	homomorphism	homomorphism	NOUN
ap-3511	82	4	can	can	AUX
ap-3511	82	5	be	be	AUX
ap-3511	82	6	defined	define	VERB
ap-3511	82	7	by	by	ADP
ap-3511	82	8	prescribing	prescribe	VERB
ap-3511	82	9	its	its	PRON
ap-3511	82	10	values	value	NOUN
ap-3511	82	11	on	on	ADP
ap-3511	82	12	the	the	DET
ap-3511	82	13	generators	generator	NOUN
ap-3511	82	14	of	of	ADP
ap-3511	82	15	w	w	PROPN
ap-3511	82	16	.	.	PUNCT
ap-3511	83	1	they	they	PRON
ap-3511	83	2	have	have	VERB
ap-3511	83	3	to	to	PART
ap-3511	83	4	satisfy	satisfy	VERB
ap-3511	83	5	the	the	DET
ap-3511	83	6	condition	condition	NOUN
ap-3511	83	7	(	(	PUNCT
ap-3511	83	8	4	4	NUM
ap-3511	83	9	)	)	PUNCT
ap-3511	83	10	;	;	PUNCT
ap-3511	83	11	we	we	PRON
ap-3511	83	12	get	get	VERB
ap-3511	83	13	σ(ri)2	σ(ri)2	PROPN
ap-3511	83	14	=	=	SYM
ap-3511	83	15	1	1	NUM
ap-3511	83	16	,	,	PUNCT
ap-3511	83	17	(	(	PUNCT
ap-3511	83	18	σ(ri)σ(rj))sij	σ(ri)σ(rj))sij	X
ap-3511	83	19	=	=	SYM
ap-3511	83	20	1	1	NUM
ap-3511	83	21	,	,	PUNCT
ap-3511	83	22	i	i	PRON
ap-3511	83	23	,	,	PUNCT
ap-3511	83	24	j	j	PROPN
ap-3511	83	25	=	=	PUNCT
ap-3511	83	26	{	{	PUNCT
ap-3511	83	27	1	1	NUM
ap-3511	83	28	,	,	PUNCT
ap-3511	83	29	.	.	PUNCT
ap-3511	83	30	.	.	PUNCT
ap-3511	84	1	.	.	PUNCT
ap-3511	85	1	,	,	PUNCT
ap-3511	86	1	n	n	CCONJ
ap-3511	86	2	}	}	PUNCT
ap-3511	86	3	.	.	PUNCT
ap-3511	87	1	there	there	PRON
ap-3511	87	2	are	be	VERB
ap-3511	87	3	four	four	NUM
ap-3511	87	4	admissible	admissible	ADJ
ap-3511	87	5	mappings	mapping	NOUN
ap-3511	87	6	:	:	PUNCT
ap-3511	87	7	the	the	DET
ap-3511	87	8	identity	identity	NOUN
ap-3511	87	9	,	,	PUNCT
ap-3511	87	10	the	the	DET
ap-3511	87	11	determinant	determinant	ADJ
ap-3511	87	12	and	and	CCONJ
ap-3511	87	13	homomorphisms	homomorphism	NOUN
ap-3511	87	14	σs	σs	ADP
ap-3511	87	15	and	and	CCONJ
ap-3511	87	16	σl	σl	PROPN
ap-3511	87	17	,	,	PUNCT
ap-3511	87	18	defined	define	VERB
ap-3511	87	19	as	as	ADP
ap-3511	87	20	σs(rα	σs(rα	PROPN
ap-3511	87	21	)	)	PUNCT
ap-3511	88	1	=	=	PRON
ap-3511	88	2	{	{	PUNCT
ap-3511	88	3	1	1	NUM
ap-3511	88	4	,	,	PUNCT
ap-3511	88	5	α	α	PROPN
ap-3511	88	6	∈	∈	PROPN
ap-3511	88	7	∆l	∆l	PROPN
ap-3511	88	8	,	,	PUNCT
ap-3511	88	9	−1	−1	NOUN
ap-3511	88	10	,	,	PUNCT
ap-3511	88	11	α	α	PROPN
ap-3511	88	12	∈	∈	PROPN
ap-3511	88	13	∆s	∆s	PROPN
ap-3511	88	14	,	,	PUNCT
ap-3511	88	15	σl(rα	σl(rα	PROPN
ap-3511	88	16	)	)	PUNCT
ap-3511	88	17	=	=	PRON
ap-3511	88	18	{	{	PUNCT
ap-3511	88	19	1	1	NUM
ap-3511	88	20	,	,	PUNCT
ap-3511	88	21	α	α	PROPN
ap-3511	88	22	∈	∈	PROPN
ap-3511	88	23	∆s	∆s	PROPN
ap-3511	88	24	,	,	PUNCT
ap-3511	88	25	−1	−1	NOUN
ap-3511	88	26	,	,	PUNCT
ap-3511	88	27	α	α	PROPN
ap-3511	88	28	∈	∈	PROPN
ap-3511	88	29	∆l	∆l	PROPN
ap-3511	88	30	.	.	PUNCT
ap-3511	89	1	the	the	DET
ap-3511	89	2	general	general	ADJ
ap-3511	89	3	formula	formula	NOUN
ap-3511	89	4	defining	define	VERB
ap-3511	89	5	the	the	DET
ap-3511	89	6	four	four	NUM
ap-3511	89	7	families	family	NOUN
ap-3511	89	8	of	of	ADP
ap-3511	89	9	orbit	orbit	NOUN
ap-3511	89	10	functions	function	NOUN
ap-3511	89	11	is	be	AUX
ap-3511	89	12	for	for	ADP
ap-3511	89	13	every	every	DET
ap-3511	89	14	x	x	SYM
ap-3511	89	15	∈	∈	PROPN
ap-3511	89	16	rn	rn	PROPN
ap-3511	89	17	and	and	CCONJ
ap-3511	89	18	every	every	DET
ap-3511	89	19	λ	λ	PROPN
ap-3511	89	20	∈	∈	PROPN
ap-3511	89	21	p	p	NOUN
ap-3511	89	22	ϕσλ	ϕσλ	PROPN
ap-3511	89	23	=	=	SYM
ap-3511	89	24	∑	∑	ADJ
ap-3511	89	25	w∈w	w∈w	VERB
ap-3511	89	26	σ(w)e2πı〈wλ	σ(w)e2πı〈wλ	ADJ
ap-3511	89	27	,	,	PUNCT
ap-3511	89	28	x	x	NOUN
ap-3511	89	29	〉	〉	NUM
ap-3511	89	30	,	,	PUNCT
ap-3511	89	31	(	(	PUNCT
ap-3511	89	32	5	5	NUM
ap-3511	89	33	)	)	PUNCT
ap-3511	89	34	where	where	SCONJ
ap-3511	89	35	σ	σ	PROPN
ap-3511	89	36	is	be	AUX
ap-3511	89	37	one	one	NUM
ap-3511	89	38	of	of	ADP
ap-3511	89	39	the	the	DET
ap-3511	89	40	four	four	NUM
ap-3511	89	41	sign	sign	NOUN
ap-3511	89	42	homomorphisms	homomorphism	NOUN
ap-3511	89	43	.	.	PUNCT
ap-3511	90	1	for	for	ADP
ap-3511	90	2	the	the	DET
ap-3511	90	3	choice	choice	NOUN
ap-3511	90	4	σ	σ	NOUN
ap-3511	90	5	=	=	PUNCT
ap-3511	90	6	i	i	PROPN
ap-3511	90	7	d	d	PROPN
ap-3511	90	8	,	,	PUNCT
ap-3511	90	9	we	we	PRON
ap-3511	90	10	get	get	VERB
ap-3511	90	11	the	the	DET
ap-3511	90	12	family	family	NOUN
ap-3511	90	13	of	of	ADP
ap-3511	90	14	c	c	PROPN
ap-3511	90	15	–	–	PUNCT
ap-3511	90	16	orbit	orbit	NOUN
ap-3511	90	17	functions	function	NOUN
ap-3511	90	18	,	,	PUNCT
ap-3511	90	19	which	which	PRON
ap-3511	90	20	are	be	AUX
ap-3511	90	21	denoted	denote	VERB
ap-3511	90	22	φλ	φλ	ADP
ap-3511	90	23	.	.	PUNCT
ap-3511	91	1	the	the	DET
ap-3511	91	2	family	family	NOUN
ap-3511	91	3	of	of	ADP
ap-3511	91	4	s	s	PROPN
ap-3511	91	5	–	–	PUNCT
ap-3511	91	6	functions	function	NOUN
ap-3511	91	7	comes	come	VERB
ap-3511	91	8	from	from	ADP
ap-3511	91	9	the	the	DET
ap-3511	91	10	choice	choice	NOUN
ap-3511	91	11	σ	σ	PROPN
ap-3511	91	12	=	=	SYM
ap-3511	91	13	det	det	PROPN
ap-3511	91	14	;	;	PUNCT
ap-3511	91	15	we	we	PRON
ap-3511	91	16	denote	denote	VERB
ap-3511	91	17	ϕλ	ϕλ	NOUN
ap-3511	91	18	.	.	PUNCT
ap-3511	92	1	the	the	DET
ap-3511	92	2	homomorphisms	homomorphisms	PROPN
ap-3511	92	3	σs	σs	ADP
ap-3511	92	4	and	and	CCONJ
ap-3511	92	5	σl	σl	PART
ap-3511	92	6	induce	induce	ADJ
ap-3511	92	7	families	family	NOUN
ap-3511	92	8	of	of	ADP
ap-3511	92	9	ss	ss	NOUN
ap-3511	92	10	–	–	PUNCT
ap-3511	92	11	and	and	CCONJ
ap-3511	92	12	sl	sl	NOUN
ap-3511	92	13	–	–	PUNCT
ap-3511	92	14	functions	function	NOUN
ap-3511	92	15	,	,	PUNCT
ap-3511	92	16	denoted	denote	VERB
ap-3511	92	17	ϕs	ϕs	ADP
ap-3511	92	18	and	and	CCONJ
ap-3511	92	19	ϕl	ϕl	INTJ
ap-3511	92	20	.	.	PUNCT
ap-3511	93	1	these	these	DET
ap-3511	93	2	functions	function	NOUN
ap-3511	93	3	have	have	AUX
ap-3511	93	4	been	be	AUX
ap-3511	93	5	extensively	extensively	ADV
ap-3511	93	6	studied	study	VERB
ap-3511	93	7	;	;	PUNCT
ap-3511	93	8	see	see	VERB
ap-3511	93	9	[	[	X
ap-3511	93	10	1	1	NUM
ap-3511	93	11	,	,	PUNCT
ap-3511	93	12	2	2	NUM
ap-3511	93	13	,	,	PUNCT
ap-3511	93	14	4	4	NUM
ap-3511	93	15	]	]	PUNCT
ap-3511	93	16	and	and	CCONJ
ap-3511	93	17	others	other	NOUN
ap-3511	93	18	.	.	PUNCT
ap-3511	94	1	they	they	PRON
ap-3511	94	2	are	be	AUX
ap-3511	94	3	multivariable	multivariable	ADJ
ap-3511	94	4	complex	complex	ADJ
ap-3511	94	5	functions	function	NOUN
ap-3511	94	6	,	,	PUNCT
ap-3511	94	7	invariant	invariant	ADJ
ap-3511	94	8	or	or	CCONJ
ap-3511	94	9	anti	anti	ADJ
ap-3511	94	10	-	-	ADJ
ap-3511	94	11	invariant	invariant	ADJ
ap-3511	94	12	with	with	ADP
ap-3511	94	13	respect	respect	NOUN
ap-3511	94	14	to	to	ADP
ap-3511	94	15	the	the	DET
ap-3511	94	16	affine	affine	NOUN
ap-3511	94	17	weyl	weyl	VERB
ap-3511	94	18	group	group	NOUN
ap-3511	94	19	.	.	PUNCT
ap-3511	95	1	they	they	PRON
ap-3511	95	2	form	form	VERB
ap-3511	95	3	an	an	DET
ap-3511	95	4	orthogonal	orthogonal	ADJ
ap-3511	95	5	basis	basis	NOUN
ap-3511	95	6	of	of	ADP
ap-3511	95	7	spaces	space	NOUN
ap-3511	95	8	of	of	ADP
ap-3511	95	9	continuous	continuous	ADJ
ap-3511	95	10	functions	function	NOUN
ap-3511	95	11	defined	define	VERB
ap-3511	95	12	on	on	ADP
ap-3511	95	13	the	the	DET
ap-3511	95	14	fundamental	fundamental	ADJ
ap-3511	95	15	domain	domain	NOUN
ap-3511	95	16	f	f	PROPN
ap-3511	95	17	or	or	CCONJ
ap-3511	95	18	of	of	ADP
ap-3511	95	19	discrete	discrete	ADJ
ap-3511	95	20	functions	function	NOUN
ap-3511	95	21	defined	define	VERB
ap-3511	95	22	on	on	ADP
ap-3511	95	23	points	point	NOUN
ap-3511	95	24	of	of	ADP
ap-3511	95	25	a	a	DET
ap-3511	95	26	finite	finite	ADJ
ap-3511	95	27	grid	grid	NOUN
ap-3511	95	28	in	in	ADP
ap-3511	95	29	f	f	PROPN
ap-3511	95	30	.	.	PUNCT
ap-3511	96	1	details	detail	NOUN
ap-3511	96	2	are	be	AUX
ap-3511	96	3	found	find	VERB
ap-3511	96	4	in	in	ADP
ap-3511	96	5	[	[	X
ap-3511	96	6	3	3	NUM
ap-3511	96	7	,	,	PUNCT
ap-3511	96	8	5	5	NUM
ap-3511	96	9	,	,	PUNCT
ap-3511	96	10	11	11	NUM
ap-3511	96	11	]	]	PUNCT
ap-3511	96	12	.	.	PUNCT
ap-3511	97	1	in	in	ADP
ap-3511	97	2	this	this	DET
ap-3511	97	3	paper	paper	NOUN
ap-3511	97	4	we	we	PRON
ap-3511	97	5	prove	prove	VERB
ap-3511	97	6	the	the	DET
ap-3511	97	7	orthogonality	orthogonality	NOUN
ap-3511	97	8	of	of	ADP
ap-3511	97	9	generalized	generalized	ADJ
ap-3511	97	10	orbit	orbit	NOUN
ap-3511	97	11	functions	function	NOUN
ap-3511	97	12	using	use	VERB
ap-3511	97	13	their	their	PRON
ap-3511	97	14	relations	relation	NOUN
ap-3511	97	15	with	with	ADP
ap-3511	97	16	the	the	DET
ap-3511	97	17	family	family	NOUN
ap-3511	97	18	of	of	ADP
ap-3511	97	19	c	c	PROPN
ap-3511	97	20	–	–	PUNCT
ap-3511	97	21	functions	function	NOUN
ap-3511	97	22	;	;	PUNCT
ap-3511	97	23	see	see	VERB
ap-3511	97	24	lemma	lemma	PROPN
ap-3511	97	25	2	2	X
ap-3511	97	26	.	.	PUNCT
ap-3511	98	1	we	we	PRON
ap-3511	98	2	will	will	AUX
ap-3511	98	3	use	use	VERB
ap-3511	98	4	the	the	DET
ap-3511	98	5	following	follow	VERB
ap-3511	98	6	properties	property	NOUN
ap-3511	98	7	of	of	ADP
ap-3511	98	8	c	c	NOUN
ap-3511	98	9	–	–	PUNCT
ap-3511	98	10	functions	function	NOUN
ap-3511	98	11	:	:	PUNCT
ap-3511	98	12	continuous	continuous	ADJ
ap-3511	98	13	orthogonality	orthogonality	NOUN
ap-3511	98	14	—	—	PUNCT
ap-3511	98	15	for	for	ADP
ap-3511	98	16	every	every	DET
ap-3511	98	17	λ	λ	PROPN
ap-3511	98	18	,	,	PUNCT
ap-3511	98	19	µ	µ	PROPN
ap-3511	98	20	∈	∈	NOUN
ap-3511	98	21	p+	p+	VERB
ap-3511	98	22	it	it	PRON
ap-3511	98	23	holds	hold	VERB
ap-3511	98	24	that∫	that∫	NOUN
ap-3511	98	25	f	f	PROPN
ap-3511	98	26	φλ(x)φµ(x)dx	φλ(x)φµ(x)dx	PROPN
ap-3511	98	27	=	=	SYM
ap-3511	99	1	|f	|f	PROPN
ap-3511	99	2	||w	||w	PROPN
ap-3511	99	3	||stabw	||stabw	ADV
ap-3511	99	4	(	(	PUNCT
ap-3511	99	5	λ)|δλµ	λ)|δλµ	PROPN
ap-3511	99	6	,	,	PUNCT
ap-3511	99	7	(	(	PUNCT
ap-3511	99	8	6	6	NUM
ap-3511	99	9	)	)	PUNCT
ap-3511	100	1	where	where	SCONJ
ap-3511	100	2	|f	|f	PROPN
ap-3511	101	1	|	|	ADV
ap-3511	101	2	denotes	denote	VERB
ap-3511	101	3	the	the	DET
ap-3511	101	4	volume	volume	NOUN
ap-3511	101	5	of	of	ADP
ap-3511	101	6	the	the	DET
ap-3511	101	7	fundamental	fundamental	ADJ
ap-3511	101	8	domain	domain	NOUN
ap-3511	101	9	f	f	PROPN
ap-3511	101	10	,	,	PUNCT
ap-3511	101	11	|w	|w	NOUN
ap-3511	101	12	|	|	ADV
ap-3511	101	13	is	be	AUX
ap-3511	101	14	the	the	DET
ap-3511	101	15	order	order	NOUN
ap-3511	101	16	of	of	ADP
ap-3511	101	17	the	the	DET
ap-3511	101	18	weyl	weyl	PROPN
ap-3511	101	19	group	group	NOUN
ap-3511	101	20	w	w	PROPN
ap-3511	101	21	441	441	NUM
ap-3511	101	22	lenka	lenka	PROPN
ap-3511	101	23	háková	háková	PROPN
ap-3511	101	24	,	,	PUNCT
ap-3511	101	25	agnieszka	agnieszka	PROPN
ap-3511	101	26	tereszkiewicz	tereszkiewicz	PROPN
ap-3511	101	27	acta	acta	PROPN
ap-3511	101	28	polytechnica	polytechnica	PROPN
ap-3511	101	29	and	and	CCONJ
ap-3511	101	30	stabw	stabw	NOUN
ap-3511	101	31	(	(	PUNCT
ap-3511	101	32	λ	λ	X
ap-3511	101	33	)	)	PUNCT
ap-3511	101	34	is	be	AUX
ap-3511	101	35	the	the	DET
ap-3511	101	36	stabilizer	stabilizer	NOUN
ap-3511	101	37	of	of	ADP
ap-3511	101	38	the	the	DET
ap-3511	101	39	action	action	NOUN
ap-3511	101	40	of	of	ADP
ap-3511	101	41	w	w	PROPN
ap-3511	101	42	on	on	ADP
ap-3511	101	43	λ	λ	PROPN
ap-3511	101	44	.	.	PROPN
ap-3511	101	45	in	in	ADP
ap-3511	101	46	particular	particular	ADJ
ap-3511	101	47	,	,	PUNCT
ap-3511	101	48	for	for	ADP
ap-3511	101	49	the	the	DET
ap-3511	101	50	choice	choice	NOUN
ap-3511	101	51	µ	µ	X
ap-3511	101	52	=	=	SYM
ap-3511	101	53	0	0	NUM
ap-3511	101	54	,	,	PUNCT
ap-3511	101	55	the	the	DET
ap-3511	101	56	c	c	NOUN
ap-3511	101	57	–	–	PUNCT
ap-3511	101	58	function	function	NOUN
ap-3511	101	59	becomes	become	VERB
ap-3511	101	60	a	a	DET
ap-3511	101	61	constant	constant	ADJ
ap-3511	101	62	equal	equal	ADJ
ap-3511	101	63	to	to	ADP
ap-3511	101	64	|w	|w	ADJ
ap-3511	101	65	|	|	NOUN
ap-3511	101	66	and	and	CCONJ
ap-3511	101	67	equation	equation	NOUN
ap-3511	101	68	(	(	PUNCT
ap-3511	101	69	6	6	NUM
ap-3511	101	70	)	)	PUNCT
ap-3511	101	71	gives∫	gives∫	NOUN
ap-3511	101	72	f	f	NOUN
ap-3511	101	73	φλ(x)φ0(x)dx	φλ(x)φ0(x)dx	NUM
ap-3511	101	74	=	=	PUNCT
ap-3511	101	75	|w	|w	NOUN
ap-3511	102	1	|	|	ADV
ap-3511	102	2	∫	∫	PROPN
ap-3511	103	1	f	f	PROPN
ap-3511	103	2	φλ(x)dx	φλ(x)dx	PROPN
ap-3511	103	3	=	=	PUNCT
ap-3511	103	4	|f	|f	PROPN
ap-3511	103	5	||w	||w	PROPN
ap-3511	103	6	|2δλ0	|2δλ0	NOUN
ap-3511	103	7	.	.	PUNCT
ap-3511	104	1	(	(	PUNCT
ap-3511	104	2	7	7	X
ap-3511	104	3	)	)	PUNCT
ap-3511	104	4	discrete	discrete	ADJ
ap-3511	104	5	orthogonality	orthogonality	NOUN
ap-3511	104	6	—	—	PUNCT
ap-3511	104	7	let	let	VERB
ap-3511	104	8	m	m	PRON
ap-3511	104	9	be	be	AUX
ap-3511	104	10	a	a	DET
ap-3511	104	11	positive	positive	ADJ
ap-3511	104	12	integer	integer	NOUN
ap-3511	104	13	of	of	ADP
ap-3511	104	14	our	our	PRON
ap-3511	104	15	choice	choice	NOUN
ap-3511	104	16	.	.	PUNCT
ap-3511	105	1	we	we	PRON
ap-3511	105	2	define	define	VERB
ap-3511	105	3	a	a	DET
ap-3511	105	4	w	w	PROPN
ap-3511	105	5	–	–	PUNCT
ap-3511	105	6	invariant	invariant	ADJ
ap-3511	105	7	lattice	lattice	NOUN
ap-3511	105	8	grid	grid	PROPN
ap-3511	105	9	fm	fm	PROPN
ap-3511	105	10	as	as	ADP
ap-3511	105	11	1	1	NUM
ap-3511	105	12	m	m	PROPN
ap-3511	105	13	p∨/q∨	p∨/q∨	NOUN
ap-3511	105	14	∩	∩	PROPN
ap-3511	105	15	f.	f.	PROPN
ap-3511	105	16	we	we	PRON
ap-3511	105	17	consider	consider	VERB
ap-3511	105	18	a	a	DET
ap-3511	105	19	space	space	NOUN
ap-3511	105	20	of	of	ADP
ap-3511	105	21	functions	function	NOUN
ap-3511	105	22	sampled	sample	VERB
ap-3511	105	23	on	on	ADP
ap-3511	105	24	the	the	DET
ap-3511	105	25	points	point	NOUN
ap-3511	105	26	of	of	ADP
ap-3511	105	27	fm	fm	PROPN
ap-3511	105	28	with	with	ADP
ap-3511	105	29	a	a	DET
ap-3511	105	30	scalar	scalar	ADJ
ap-3511	105	31	product	product	NOUN
ap-3511	105	32	defined	define	VERB
ap-3511	105	33	for	for	ADP
ap-3511	105	34	each	each	DET
ap-3511	105	35	pair	pair	NOUN
ap-3511	105	36	of	of	ADP
ap-3511	105	37	functions	function	NOUN
ap-3511	105	38	f	f	X
ap-3511	105	39	,	,	PUNCT
ap-3511	105	40	g	g	PROPN
ap-3511	105	41	as	as	ADP
ap-3511	105	42	〈	〈	PROPN
ap-3511	105	43	f	f	PROPN
ap-3511	105	44	,	,	PUNCT
ap-3511	105	45	g〉fm	g〉fm	NOUN
ap-3511	105	46	=	=	PUNCT
ap-3511	105	47	∑	∑	PUNCT
ap-3511	105	48	x∈fm	x∈fm	PROPN
ap-3511	105	49	ε(x)f(x)g(x	ε(x)f(x)g(x	NOUN
ap-3511	105	50	)	)	PUNCT
ap-3511	105	51	.	.	PUNCT
ap-3511	106	1	(	(	PUNCT
ap-3511	106	2	8)	8)	NUM
ap-3511	106	3	the	the	DET
ap-3511	106	4	weight	weight	NOUN
ap-3511	106	5	function	function	NOUN
ap-3511	106	6	ε(x	ε(x	VERB
ap-3511	106	7	)	)	PUNCT
ap-3511	106	8	is	be	AUX
ap-3511	106	9	given	give	VERB
ap-3511	106	10	by	by	ADP
ap-3511	106	11	the	the	DET
ap-3511	106	12	order	order	NOUN
ap-3511	106	13	of	of	ADP
ap-3511	106	14	the	the	DET
ap-3511	106	15	weyl	weyl	VERB
ap-3511	106	16	orbit	orbit	NOUN
ap-3511	106	17	of	of	ADP
ap-3511	106	18	x	x	PROPN
ap-3511	106	19	,	,	PUNCT
ap-3511	106	20	ε(x	ε(x	NOUN
ap-3511	106	21	)	)	PUNCT
ap-3511	107	1	=	=	SYM
ap-3511	107	2	|w	|w	NOUN
ap-3511	108	1	|	|	ADV
ap-3511	108	2	|stabw	|stabw	PROPN
ap-3511	108	3	(	(	PUNCT
ap-3511	108	4	x)|	x)|	PROPN
ap-3511	108	5	.	.	PUNCT
ap-3511	109	1	the	the	DET
ap-3511	109	2	set	set	NOUN
ap-3511	109	3	of	of	ADP
ap-3511	109	4	parameters	parameter	NOUN
ap-3511	109	5	λm	λm	ADP
ap-3511	109	6	is	be	AUX
ap-3511	109	7	defined	define	VERB
ap-3511	109	8	as	as	ADP
ap-3511	109	9	λm	λm	ADP
ap-3511	109	10	=	=	SYM
ap-3511	109	11	p	p	X
ap-3511	109	12	/	/	SYM
ap-3511	109	13	mq∩mf∨.	mq∩mf∨.	PROPN
ap-3511	109	14	it	it	PRON
ap-3511	109	15	gives	give	VERB
ap-3511	109	16	us	we	PRON
ap-3511	109	17	a	a	DET
ap-3511	109	18	finite	finite	ADJ
ap-3511	109	19	family	family	NOUN
ap-3511	109	20	of	of	ADP
ap-3511	109	21	orbit	orbit	NOUN
ap-3511	109	22	functions	function	NOUN
ap-3511	109	23	which	which	PRON
ap-3511	109	24	are	be	AUX
ap-3511	109	25	pairwise	pairwise	NOUN
ap-3511	109	26	orthogonal	orthogonal	NOUN
ap-3511	109	27	with	with	ADP
ap-3511	109	28	respect	respect	NOUN
ap-3511	109	29	to	to	ADP
ap-3511	109	30	the	the	DET
ap-3511	109	31	scalar	scalar	ADJ
ap-3511	109	32	product	product	NOUN
ap-3511	109	33	(	(	PUNCT
ap-3511	109	34	8)	8)	NUM
ap-3511	109	35	.	.	PUNCT
ap-3511	110	1	for	for	ADP
ap-3511	110	2	every	every	DET
ap-3511	110	3	λ	λ	PROPN
ap-3511	110	4	,	,	PUNCT
ap-3511	110	5	µ	µ	X
ap-3511	110	6	∈	∈	NOUN
ap-3511	110	7	λm	λm	SCONJ
ap-3511	110	8	it	it	PRON
ap-3511	110	9	holds	hold	VERB
ap-3511	110	10	that	that	SCONJ
ap-3511	110	11	〈	〈	PROPN
ap-3511	110	12	φλ	φλ	ADV
ap-3511	110	13	,	,	PUNCT
ap-3511	110	14	φµ〉fm	φµ〉fm	NOUN
ap-3511	110	15	=	=	SYM
ap-3511	110	16	c|w	c|w	NOUN
ap-3511	111	1	|mnh∨λδλµ	|mnh∨λδλµ	PROPN
ap-3511	111	2	,	,	PUNCT
ap-3511	111	3	(	(	PUNCT
ap-3511	111	4	9	9	NUM
ap-3511	111	5	)	)	PUNCT
ap-3511	111	6	where	where	SCONJ
ap-3511	111	7	the	the	DET
ap-3511	111	8	coefficient	coefficient	NOUN
ap-3511	111	9	h∨λ	h∨λ	NOUN
ap-3511	111	10	is	be	AUX
ap-3511	111	11	the	the	DET
ap-3511	111	12	order	order	NOUN
ap-3511	111	13	of	of	ADP
ap-3511	111	14	the	the	DET
ap-3511	111	15	stabilizer	stabilizer	NOUN
ap-3511	111	16	of	of	ADP
ap-3511	111	17	λ	λ	PROPN
ap-3511	111	18	and	and	CCONJ
ap-3511	111	19	c	c	PROPN
ap-3511	111	20	is	be	AUX
ap-3511	111	21	the	the	DET
ap-3511	111	22	determinant	determinant	NOUN
ap-3511	111	23	of	of	ADP
ap-3511	111	24	the	the	DET
ap-3511	111	25	cartan	cartan	ADJ
ap-3511	111	26	matrix	matrix	NOUN
ap-3511	111	27	of	of	ADP
ap-3511	111	28	the	the	DET
ap-3511	111	29	corresponding	corresponding	ADJ
ap-3511	111	30	weyl	weyl	VERB
ap-3511	111	31	group	group	NOUN
ap-3511	111	32	.	.	PUNCT
ap-3511	112	1	the	the	DET
ap-3511	112	2	values	value	NOUN
ap-3511	112	3	of	of	ADP
ap-3511	112	4	|w	|w	ADJ
ap-3511	112	5	|	|	NOUN
ap-3511	112	6	,	,	PUNCT
ap-3511	112	7	c	c	NOUN
ap-3511	112	8	,	,	PUNCT
ap-3511	112	9	ε(x	ε(x	NOUN
ap-3511	112	10	)	)	PUNCT
ap-3511	112	11	and	and	CCONJ
ap-3511	112	12	h∨λ	h∨λ	NOUN
ap-3511	112	13	can	can	AUX
ap-3511	112	14	be	be	AUX
ap-3511	112	15	found	find	VERB
ap-3511	112	16	in	in	ADP
ap-3511	112	17	several	several	ADJ
ap-3511	112	18	papers	paper	NOUN
ap-3511	112	19	,	,	PUNCT
ap-3511	112	20	e.g.	e.g.	ADV
ap-3511	112	21	,	,	PUNCT
ap-3511	112	22	[	[	X
ap-3511	112	23	5	5	NUM
ap-3511	112	24	]	]	PUNCT
ap-3511	112	25	.	.	PUNCT
ap-3511	113	1	with	with	ADP
ap-3511	113	2	the	the	DET
ap-3511	113	3	choice	choice	NOUN
ap-3511	113	4	µ	µ	X
ap-3511	113	5	=	=	SYM
ap-3511	113	6	0	0	NUM
ap-3511	113	7	we	we	PRON
ap-3511	113	8	can	can	AUX
ap-3511	113	9	rewrite	rewrite	VERB
ap-3511	113	10	the	the	DET
ap-3511	113	11	orthogonality	orthogonality	NOUN
ap-3511	113	12	relation	relation	NOUN
ap-3511	113	13	(	(	PUNCT
ap-3511	113	14	9	9	NUM
ap-3511	113	15	)	)	PUNCT
ap-3511	113	16	as∑	as∑	PROPN
ap-3511	113	17	x∈fm	x∈fm	PROPN
ap-3511	113	18	ε(x)φλ(x	ε(x)φλ(x	NOUN
ap-3511	113	19	)	)	PUNCT
ap-3511	114	1	=	=	SYM
ap-3511	114	2	c|w	c|w	NOUN
ap-3511	114	3	|mnδλ0	|mnδλ0	VERB
ap-3511	114	4	,	,	PUNCT
ap-3511	114	5	(	(	PUNCT
ap-3511	114	6	10	10	NUM
ap-3511	114	7	)	)	PUNCT
ap-3511	114	8	3.2	3.2	NUM
ap-3511	114	9	.	.	PUNCT
ap-3511	115	1	character	character	NOUN
ap-3511	115	2	functions	function	NOUN
ap-3511	115	3	let	let	VERB
ap-3511	115	4	w	w	NOUN
ap-3511	115	5	be	be	AUX
ap-3511	115	6	a	a	DET
ap-3511	115	7	weyl	weyl	VERB
ap-3511	115	8	group	group	NOUN
ap-3511	115	9	of	of	ADP
ap-3511	115	10	rank	rank	NOUN
ap-3511	115	11	n	n	PROPN
ap-3511	115	12	with	with	ADP
ap-3511	115	13	irreducible	irreducible	ADJ
ap-3511	115	14	characters	character	NOUN
ap-3511	115	15	χ1	χ1	NOUN
ap-3511	115	16	,	,	PUNCT
ap-3511	115	17	.	.	PUNCT
ap-3511	115	18	.	.	PUNCT
ap-3511	116	1	.	.	PUNCT
ap-3511	117	1	,	,	PUNCT
ap-3511	117	2	χr	χr	PROPN
ap-3511	117	3	.	.	PROPN
ap-3511	118	1	for	for	ADP
ap-3511	118	2	every	every	DET
ap-3511	118	3	x	x	NOUN
ap-3511	118	4	,	,	PUNCT
ap-3511	118	5	λ	λ	PROPN
ap-3511	118	6	∈	∈	PROPN
ap-3511	118	7	rn	rn	PROPN
ap-3511	118	8	and	and	CCONJ
ap-3511	118	9	k	k	PROPN
ap-3511	118	10	=	=	SYM
ap-3511	118	11	1	1	NUM
ap-3511	118	12	,	,	PUNCT
ap-3511	118	13	.	.	PUNCT
ap-3511	118	14	.	.	PUNCT
ap-3511	118	15	.	.	PUNCT
ap-3511	119	1	,	,	PUNCT
ap-3511	119	2	r	r	NOUN
ap-3511	119	3	we	we	PRON
ap-3511	119	4	define	define	VERB
ap-3511	119	5	φkλ(x	φkλ(x	NOUN
ap-3511	119	6	)	)	PUNCT
ap-3511	119	7	=	=	SYM
ap-3511	119	8	∑	∑	ADV
ap-3511	119	9	w∈w	w∈w	VERB
ap-3511	119	10	χk(w)e2πı〈wλ	χk(w)e2πı〈wλ	PROPN
ap-3511	119	11	,	,	PUNCT
ap-3511	119	12	x	x	NOUN
ap-3511	119	13	〉	〉	NUM
ap-3511	119	14	.	.	PUNCT
ap-3511	120	1	(	(	PUNCT
ap-3511	120	2	11	11	NUM
ap-3511	120	3	)	)	PUNCT
ap-3511	120	4	we	we	PRON
ap-3511	120	5	obtain	obtain	VERB
ap-3511	120	6	several	several	ADJ
ap-3511	120	7	infinite	infinite	ADJ
ap-3511	120	8	families	family	NOUN
ap-3511	120	9	of	of	ADP
ap-3511	120	10	functions	function	NOUN
ap-3511	120	11	related	relate	VERB
ap-3511	120	12	to	to	ADP
ap-3511	120	13	the	the	DET
ap-3511	120	14	irreducible	irreducible	ADJ
ap-3511	120	15	characters	character	NOUN
ap-3511	120	16	of	of	ADP
ap-3511	120	17	w	w	PROPN
ap-3511	120	18	.	.	PUNCT
ap-3511	121	1	for	for	ADP
ap-3511	121	2	shortness	shortness	NOUN
ap-3511	121	3	we	we	PRON
ap-3511	121	4	will	will	AUX
ap-3511	121	5	refer	refer	VERB
ap-3511	121	6	to	to	ADP
ap-3511	121	7	them	they	PRON
ap-3511	121	8	within	within	ADP
ap-3511	121	9	this	this	DET
ap-3511	121	10	paper	paper	NOUN
ap-3511	121	11	as	as	ADP
ap-3511	121	12	to	to	ADP
ap-3511	121	13	character	character	NOUN
ap-3511	121	14	functions	function	NOUN
ap-3511	121	15	.	.	PUNCT
ap-3511	122	1	the	the	DET
ap-3511	122	2	first	first	ADJ
ap-3511	122	3	two	two	NUM
ap-3511	122	4	irreducible	irreducible	ADJ
ap-3511	122	5	characters	character	NOUN
ap-3511	122	6	are	be	AUX
ap-3511	122	7	the	the	DET
ap-3511	122	8	trivial	trivial	ADJ
ap-3511	122	9	and	and	CCONJ
ap-3511	122	10	alternating	alternate	VERB
ap-3511	122	11	character	character	NOUN
ap-3511	122	12	.	.	PUNCT
ap-3511	123	1	their	their	PRON
ap-3511	123	2	values	value	NOUN
ap-3511	123	3	correspond	correspond	VERB
ap-3511	123	4	to	to	ADP
ap-3511	123	5	the	the	DET
ap-3511	123	6	values	value	NOUN
ap-3511	123	7	of	of	ADP
ap-3511	123	8	the	the	DET
ap-3511	123	9	first	first	ADJ
ap-3511	123	10	two	two	NUM
ap-3511	123	11	sign	sign	NOUN
ap-3511	123	12	homomorphisms	homomorphism	NOUN
ap-3511	123	13	,	,	PUNCT
ap-3511	123	14	the	the	DET
ap-3511	123	15	identity	identity	NOUN
ap-3511	123	16	and	and	CCONJ
ap-3511	123	17	determinant	determinant	ADJ
ap-3511	123	18	.	.	PUNCT
ap-3511	124	1	in	in	ADP
ap-3511	124	2	the	the	DET
ap-3511	124	3	case	case	NOUN
ap-3511	124	4	of	of	ADP
ap-3511	124	5	the	the	DET
ap-3511	124	6	weyl	weyl	VERB
ap-3511	124	7	groups	group	NOUN
ap-3511	124	8	of	of	ADP
ap-3511	124	9	bn	bn	NOUN
ap-3511	124	10	,	,	PUNCT
ap-3511	124	11	cn	cn	PROPN
ap-3511	124	12	,	,	PUNCT
ap-3511	124	13	f4	f4	PROPN
ap-3511	124	14	and	and	CCONJ
ap-3511	124	15	g2	g2	PROPN
ap-3511	124	16	,	,	PUNCT
ap-3511	124	17	the	the	DET
ap-3511	124	18	sign	sign	NOUN
ap-3511	124	19	homomorphisms	homomorphism	VERB
ap-3511	124	20	σs	σs	ADP
ap-3511	124	21	and	and	CCONJ
ap-3511	124	22	σl	σl	INTJ
ap-3511	124	23	are	be	AUX
ap-3511	124	24	the	the	DET
ap-3511	124	25	only	only	ADV
ap-3511	124	26	two	two	NUM
ap-3511	124	27	other	other	ADJ
ap-3511	124	28	possible	possible	ADJ
ap-3511	124	29	linear	linear	NOUN
ap-3511	124	30	characters	character	NOUN
ap-3511	124	31	.	.	PUNCT
ap-3511	125	1	therefore	therefore	ADV
ap-3511	125	2	,	,	PUNCT
ap-3511	125	3	the	the	DET
ap-3511	125	4	definition	definition	NOUN
ap-3511	125	5	(	(	PUNCT
ap-3511	125	6	11	11	NUM
ap-3511	125	7	)	)	PUNCT
ap-3511	125	8	includes	include	VERB
ap-3511	125	9	the	the	DET
ap-3511	125	10	families	family	NOUN
ap-3511	125	11	of	of	ADP
ap-3511	125	12	c	c	PROPN
ap-3511	125	13	–	–	PUNCT
ap-3511	125	14	and	and	CCONJ
ap-3511	125	15	s	s	PROPN
ap-3511	125	16	–	–	PUNCT
ap-3511	125	17	functions	function	NOUN
ap-3511	125	18	for	for	ADP
ap-3511	125	19	all	all	DET
ap-3511	125	20	the	the	DET
ap-3511	125	21	weyl	weyl	VERB
ap-3511	125	22	groups	group	NOUN
ap-3511	125	23	and	and	CCONJ
ap-3511	125	24	the	the	DET
ap-3511	125	25	families	family	NOUN
ap-3511	125	26	of	of	ADP
ap-3511	125	27	ss	ss	NOUN
ap-3511	125	28	–	–	PUNCT
ap-3511	125	29	and	and	CCONJ
ap-3511	125	30	sl	sl	NOUN
ap-3511	125	31	–	–	PUNCT
ap-3511	125	32	functions	function	NOUN
ap-3511	125	33	for	for	ADP
ap-3511	125	34	bn	bn	NOUN
ap-3511	125	35	,	,	PUNCT
ap-3511	125	36	cn	cn	PROPN
ap-3511	125	37	,	,	PUNCT
ap-3511	125	38	f4	f4	PROPN
ap-3511	125	39	and	and	CCONJ
ap-3511	125	40	g2	g2	PROPN
ap-3511	125	41	.	.	PUNCT
ap-3511	126	1	the	the	DET
ap-3511	126	2	rest	rest	NOUN
ap-3511	126	3	of	of	ADP
ap-3511	126	4	the	the	DET
ap-3511	126	5	paper	paper	NOUN
ap-3511	126	6	studies	study	NOUN
ap-3511	126	7	the	the	DET
ap-3511	126	8	properties	property	NOUN
ap-3511	126	9	of	of	ADP
ap-3511	126	10	functions	function	NOUN
ap-3511	126	11	related	relate	VERB
ap-3511	126	12	to	to	ADP
ap-3511	126	13	irreducible	irreducible	ADJ
ap-3511	126	14	characters	character	NOUN
ap-3511	126	15	of	of	ADP
ap-3511	126	16	degree	degree	NOUN
ap-3511	126	17	≥	≥	NOUN
ap-3511	126	18	2	2	NUM
ap-3511	126	19	.	.	NOUN
ap-3511	126	20	4	4	NUM
ap-3511	126	21	.	.	PUNCT
ap-3511	126	22	properties	property	NOUN
ap-3511	126	23	of	of	ADP
ap-3511	126	24	character	character	NOUN
ap-3511	126	25	functions	function	NOUN
ap-3511	126	26	4.1	4.1	NUM
ap-3511	126	27	.	.	PUNCT
ap-3511	127	1	general	general	ADJ
ap-3511	127	2	properties	property	NOUN
ap-3511	127	3	character	character	NOUN
ap-3511	127	4	functions	function	NOUN
ap-3511	127	5	are	be	AUX
ap-3511	127	6	trivial	trivial	ADJ
ap-3511	127	7	in	in	ADP
ap-3511	127	8	the	the	DET
ap-3511	127	9	case	case	NOUN
ap-3511	127	10	when	when	SCONJ
ap-3511	127	11	λ	λ	X
ap-3511	127	12	=	=	SYM
ap-3511	127	13	0	0	X
ap-3511	127	14	.	.	PUNCT
ap-3511	128	1	indeed	indeed	ADV
ap-3511	128	2	,	,	PUNCT
ap-3511	128	3	from	from	ADP
ap-3511	128	4	the	the	DET
ap-3511	128	5	orthogonality	orthogonality	NOUN
ap-3511	128	6	relation	relation	NOUN
ap-3511	128	7	(	(	PUNCT
ap-3511	128	8	1	1	X
ap-3511	128	9	)	)	PUNCT
ap-3511	128	10	applied	apply	VERB
ap-3511	128	11	to	to	ADP
ap-3511	128	12	the	the	DET
ap-3511	128	13	trivial	trivial	ADJ
ap-3511	128	14	character	character	NOUN
ap-3511	128	15	,	,	PUNCT
ap-3511	128	16	we	we	PRON
ap-3511	128	17	get	get	VERB
ap-3511	128	18	〈	〈	PROPN
ap-3511	128	19	χk	χk	NOUN
ap-3511	128	20	,	,	PUNCT
ap-3511	128	21	χ1	χ1	NOUN
ap-3511	128	22	〉	〉	NOUN
ap-3511	128	23	=	=	SYM
ap-3511	128	24	1	1	NUM
ap-3511	128	25	|w	|w	NOUN
ap-3511	129	1	|	|	ADV
ap-3511	129	2	∑	∑	ADV
ap-3511	129	3	w∈w	w∈w	VERB
ap-3511	129	4	χk(w	χk(w	PUNCT
ap-3511	129	5	)	)	PUNCT
ap-3511	129	6	=	=	PUNCT
ap-3511	129	7	δk1	δk1	X
ap-3511	129	8	.	.	PUNCT
ap-3511	130	1	it	it	PRON
ap-3511	130	2	implies	imply	VERB
ap-3511	130	3	that	that	SCONJ
ap-3511	130	4	the	the	DET
ap-3511	130	5	c	c	PROPN
ap-3511	130	6	–	–	PUNCT
ap-3511	130	7	function	function	NOUN
ap-3511	130	8	φ0	φ0	NOUN
ap-3511	130	9	=	=	PUNCT
ap-3511	130	10	φ1	φ1	PROPN
ap-3511	130	11	0	0	PUNCT
ap-3511	130	12	equals	equal	VERB
ap-3511	130	13	the	the	DET
ap-3511	130	14	order	order	NOUN
ap-3511	130	15	of	of	ADP
ap-3511	130	16	the	the	DET
ap-3511	130	17	weyl	weyl	VERB
ap-3511	130	18	group	group	NOUN
ap-3511	130	19	and	and	CCONJ
ap-3511	130	20	all	all	DET
ap-3511	130	21	the	the	DET
ap-3511	130	22	others	other	NOUN
ap-3511	130	23	are	be	AUX
ap-3511	130	24	identically	identically	ADV
ap-3511	130	25	zero	zero	NUM
ap-3511	130	26	.	.	PUNCT
ap-3511	131	1	therefore	therefore	ADV
ap-3511	131	2	,	,	PUNCT
ap-3511	131	3	we	we	PRON
ap-3511	131	4	now	now	ADV
ap-3511	131	5	consider	consider	VERB
ap-3511	131	6	only	only	ADV
ap-3511	131	7	λ	λ	PROPN
ap-3511	131	8	6=	6=	ADP
ap-3511	131	9	0	0	NUM
ap-3511	131	10	.	.	PUNCT
ap-3511	132	1	character	character	NOUN
ap-3511	132	2	function	function	NOUN
ap-3511	132	3	are	be	AUX
ap-3511	132	4	not	not	PART
ap-3511	132	5	,	,	PUNCT
ap-3511	132	6	in	in	ADP
ap-3511	132	7	general	general	ADJ
ap-3511	132	8	,	,	PUNCT
ap-3511	132	9	invariant	invariant	ADJ
ap-3511	132	10	with	with	ADP
ap-3511	132	11	respect	respect	NOUN
ap-3511	132	12	to	to	ADP
ap-3511	132	13	the	the	DET
ap-3511	132	14	weyl	weyl	VERB
ap-3511	132	15	group	group	NOUN
ap-3511	132	16	.	.	PUNCT
ap-3511	133	1	nevertheless	nevertheless	ADV
ap-3511	133	2	,	,	PUNCT
ap-3511	133	3	we	we	PRON
ap-3511	133	4	can	can	AUX
ap-3511	133	5	describe	describe	VERB
ap-3511	133	6	several	several	ADJ
ap-3511	133	7	symmetries	symmetry	NOUN
ap-3511	133	8	and	and	CCONJ
ap-3511	133	9	identities	identity	NOUN
ap-3511	133	10	.	.	PUNCT
ap-3511	134	1	let	let	VERB
ap-3511	134	2	χk	χk	PROPN
ap-3511	134	3	,	,	PUNCT
ap-3511	134	4	χl	χl	X
ap-3511	134	5	be	be	AUX
ap-3511	134	6	any	any	DET
ap-3511	134	7	irreducible	irreducible	ADJ
ap-3511	134	8	characters	character	NOUN
ap-3511	134	9	,	,	PUNCT
ap-3511	134	10	c	c	PROPN
ap-3511	134	11	∈	∈	PROPN
ap-3511	134	12	r	r	NOUN
ap-3511	134	13	and	and	CCONJ
ap-3511	134	14	x	x	PROPN
ap-3511	134	15	∈	∈	PROPN
ap-3511	134	16	rn	rn	PROPN
ap-3511	134	17	.	.	PROPN
ap-3511	135	1	then	then	ADV
ap-3511	135	2	φkλ(x	φkλ(x	X
ap-3511	135	3	)	)	PUNCT
ap-3511	135	4	=	=	SYM
ap-3511	135	5	φkx(λ	φkx(λ	PROPN
ap-3511	135	6	)	)	PUNCT
ap-3511	135	7	φkcλ(x	φkcλ(x	PROPN
ap-3511	135	8	)	)	PUNCT
ap-3511	135	9	=	=	SYM
ap-3511	135	10	φkλ(cx	φkλ(cx	NOUN
ap-3511	135	11	)	)	PUNCT
ap-3511	135	12	moreover	moreover	ADV
ap-3511	135	13	,	,	PUNCT
ap-3511	135	14	for	for	ADP
ap-3511	135	15	each	each	DET
ap-3511	135	16	w	w	NOUN
ap-3511	135	17	∈w	∈w	NOUN
ap-3511	135	18	and	and	CCONJ
ap-3511	135	19	x	x	SYM
ap-3511	135	20	∈	∈	PROPN
ap-3511	135	21	rn	rn	NOUN
ap-3511	135	22	we	we	PRON
ap-3511	135	23	have	have	AUX
ap-3511	135	24	φkwλ(x	φkwλ(x	VERB
ap-3511	135	25	)	)	PUNCT
ap-3511	135	26	=	=	SYM
ap-3511	136	1	φkλ(w−1x	φkλ(w−1x	NOUN
ap-3511	136	2	)	)	PUNCT
ap-3511	136	3	,	,	PUNCT
ap-3511	136	4	φkwλ(wx	φkwλ(wx	NOUN
ap-3511	136	5	)	)	PUNCT
ap-3511	136	6	=	=	SYM
ap-3511	136	7	φkλ(x	φkλ(x	PROPN
ap-3511	136	8	)	)	PUNCT
ap-3511	136	9	(	(	PUNCT
ap-3511	136	10	12	12	NUM
ap-3511	136	11	)	)	PUNCT
ap-3511	136	12	and	and	CCONJ
ap-3511	136	13	for	for	ADP
ap-3511	136	14	linear	linear	PROPN
ap-3511	136	15	characters	character	NOUN
ap-3511	136	16	φkwλ(x	φkwλ(x	ADJ
ap-3511	136	17	)	)	PUNCT
ap-3511	136	18	=	=	SYM
ap-3511	136	19	χk(w)φkλ(x	χk(w)φkλ(x	PROPN
ap-3511	136	20	)	)	PUNCT
ap-3511	136	21	.	.	PUNCT
ap-3511	137	1	let	let	VERB
ap-3511	137	2	λ	λ	PROPN
ap-3511	137	3	,	,	PUNCT
ap-3511	137	4	µ	µ	PROPN
ap-3511	137	5	∈	∈	PROPN
ap-3511	137	6	rn	rn	PROPN
ap-3511	137	7	.	.	PUNCT
ap-3511	138	1	we	we	PRON
ap-3511	138	2	get	get	VERB
ap-3511	138	3	the	the	DET
ap-3511	138	4	following	follow	VERB
ap-3511	138	5	formula	formula	NOUN
ap-3511	138	6	for	for	ADP
ap-3511	138	7	a	a	DET
ap-3511	138	8	product	product	NOUN
ap-3511	138	9	of	of	ADP
ap-3511	138	10	two	two	NUM
ap-3511	138	11	character	character	NOUN
ap-3511	138	12	functions	function	NOUN
ap-3511	138	13	φkλ(x)φlµ(x	φkλ(x)φlµ(x	ADJ
ap-3511	138	14	)	)	PUNCT
ap-3511	139	1	=	=	SYM
ap-3511	139	2	∑	∑	PROPN
ap-3511	139	3	w	w	PROPN
ap-3511	139	4	,	,	PUNCT
ap-3511	139	5	w̃∈w	w̃∈w	PROPN
ap-3511	139	6	χk(w)χl(w̃)e2πi〈wλ+w̃µ,x	χk(w)χl(w̃)e2πi〈wλ+w̃µ,x	PROPN
ap-3511	139	7	〉	〉	PROPN
ap-3511	139	8	.	.	PUNCT
ap-3511	140	1	(	(	PUNCT
ap-3511	140	2	13	13	NUM
ap-3511	140	3	)	)	PUNCT
ap-3511	140	4	two	two	NUM
ap-3511	140	5	particular	particular	ADJ
ap-3511	140	6	cases	case	NOUN
ap-3511	140	7	are	be	AUX
ap-3511	140	8	of	of	ADP
ap-3511	140	9	interest	interest	NOUN
ap-3511	140	10	,	,	PUNCT
ap-3511	140	11	when	when	SCONJ
ap-3511	140	12	l	l	NOUN
ap-3511	140	13	=	=	SYM
ap-3511	140	14	1	1	NUM
ap-3511	140	15	,	,	PUNCT
ap-3511	140	16	i.e.	i.e.	X
ap-3511	140	17	,	,	PUNCT
ap-3511	140	18	product	product	NOUN
ap-3511	140	19	of	of	ADP
ap-3511	140	20	a	a	DET
ap-3511	140	21	general	general	ADJ
ap-3511	140	22	character	character	NOUN
ap-3511	140	23	functions	function	NOUN
ap-3511	140	24	with	with	ADP
ap-3511	140	25	a	a	DET
ap-3511	140	26	c	c	NOUN
ap-3511	140	27	–	–	PUNCT
ap-3511	140	28	function	function	NOUN
ap-3511	140	29	,	,	PUNCT
ap-3511	140	30	it	it	PRON
ap-3511	140	31	holds	hold	VERB
ap-3511	140	32	that	that	SCONJ
ap-3511	140	33	φkλ(x)φ1	φkλ(x)φ1	ADP
ap-3511	140	34	µ(x	µ(x	NOUN
ap-3511	140	35	)	)	PUNCT
ap-3511	140	36	=	=	SYM
ap-3511	141	1	∑	∑	PROPN
ap-3511	141	2	w∈w	w∈w	VERB
ap-3511	141	3	φkλ+wµ(x	φkλ+wµ(x	ADJ
ap-3511	141	4	)	)	PUNCT
ap-3511	141	5	,	,	PUNCT
ap-3511	141	6	and	and	CCONJ
ap-3511	141	7	in	in	ADP
ap-3511	141	8	the	the	DET
ap-3511	141	9	case	case	NOUN
ap-3511	141	10	of	of	ADP
ap-3511	141	11	χk	χk	PROPN
ap-3511	141	12	being	be	AUX
ap-3511	141	13	a	a	DET
ap-3511	141	14	linear	linear	ADJ
ap-3511	141	15	character	character	NOUN
ap-3511	141	16	,	,	PUNCT
ap-3511	141	17	we	we	PRON
ap-3511	141	18	get	get	VERB
ap-3511	141	19	φkλ(x)φ1	φkλ(x)φ1	ADP
ap-3511	141	20	µ(x	µ(x	NOUN
ap-3511	141	21	)	)	PUNCT
ap-3511	141	22	=	=	SYM
ap-3511	141	23	∑	∑	ADP
ap-3511	141	24	w∈w	w∈w	VERB
ap-3511	141	25	χk(w)φkwλ+µ(x	χk(w)φkwλ+µ(x	NOUN
ap-3511	141	26	)	)	PUNCT
ap-3511	141	27	,	,	PUNCT
ap-3511	141	28	φkλ(x)φkµ(x	φkλ(x)φkµ(x	NOUN
ap-3511	141	29	)	)	PUNCT
ap-3511	141	30	=	=	SYM
ap-3511	141	31	∑	∑	ADP
ap-3511	141	32	w∈w	w∈w	VERB
ap-3511	141	33	χk(w)φkλ+wµ(x	χk(w)φkλ+wµ(x	NOUN
ap-3511	141	34	)	)	PUNCT
ap-3511	141	35	.	.	PUNCT
ap-3511	142	1	the	the	DET
ap-3511	142	2	formula	formula	NOUN
ap-3511	142	3	for	for	ADP
ap-3511	142	4	the	the	DET
ap-3511	142	5	product	product	NOUN
ap-3511	142	6	of	of	ADP
ap-3511	142	7	two	two	NUM
ap-3511	142	8	character	character	NOUN
ap-3511	142	9	functions	function	NOUN
ap-3511	142	10	can	can	AUX
ap-3511	142	11	be	be	AUX
ap-3511	142	12	rewritten	rewrite	VERB
ap-3511	142	13	using	use	VERB
ap-3511	142	14	the	the	DET
ap-3511	142	15	following	follow	VERB
ap-3511	142	16	lemma	lemma	PROPN
ap-3511	142	17	.	.	PUNCT
ap-3511	143	1	lemma	lemma	PROPN
ap-3511	143	2	1	1	X
ap-3511	143	3	.	.	PUNCT
ap-3511	144	1	let	let	VERB
ap-3511	144	2	w	w	NOUN
ap-3511	144	3	be	be	AUX
ap-3511	144	4	any	any	DET
ap-3511	144	5	element	element	NOUN
ap-3511	144	6	of	of	ADP
ap-3511	144	7	a	a	DET
ap-3511	144	8	weyl	weyl	VERB
ap-3511	144	9	group	group	NOUN
ap-3511	144	10	w	w	PROPN
ap-3511	144	11	and	and	CCONJ
ap-3511	144	12	x	x	SYM
ap-3511	144	13	,	,	PUNCT
ap-3511	144	14	ν	ν	PROPN
ap-3511	144	15	∈	∈	PROPN
ap-3511	144	16	rn	rn	PROPN
ap-3511	144	17	.	.	PROPN
ap-3511	145	1	then	then	ADV
ap-3511	145	2	e2πı〈wν	e2πı〈wν	VERB
ap-3511	145	3	,	,	PUNCT
ap-3511	145	4	x	x	NOUN
ap-3511	145	5	〉	〉	NUM
ap-3511	145	6	=	=	SYM
ap-3511	145	7	|[w]|	|[w]|	NUM
ap-3511	145	8	|w	|w	NOUN
ap-3511	146	1	|	|	NOUN
ap-3511	146	2	r∑	r∑	AUX
ap-3511	146	3	j=1	j=1	PROPN
ap-3511	146	4	χj(w)φjν(x	χj(w)φjν(x	NOUN
ap-3511	146	5	)	)	PUNCT
ap-3511	146	6	.	.	PUNCT
ap-3511	147	1	(	(	PUNCT
ap-3511	147	2	14	14	NUM
ap-3511	147	3	)	)	PUNCT
ap-3511	147	4	442	442	NUM
ap-3511	147	5	vol	vol	NOUN
ap-3511	147	6	.	.	PUNCT
ap-3511	148	1	56	56	NUM
ap-3511	148	2	no	no	NOUN
ap-3511	148	3	.	.	PUNCT
ap-3511	149	1	6/2016	6/2016	NUM
ap-3511	149	2	on	on	ADP
ap-3511	149	3	generalization	generalization	NOUN
ap-3511	149	4	of	of	ADP
ap-3511	149	5	special	special	ADJ
ap-3511	149	6	functions	function	NOUN
ap-3511	149	7	related	relate	VERB
ap-3511	149	8	to	to	ADP
ap-3511	149	9	weyl	weyl	VERB
ap-3511	149	10	groups	group	NOUN
ap-3511	149	11	proof	proof	NOUN
ap-3511	149	12	.	.	PUNCT
ap-3511	150	1	we	we	PRON
ap-3511	150	2	consider	consider	VERB
ap-3511	150	3	the	the	DET
ap-3511	150	4	sum	sum	NOUN
ap-3511	150	5	from	from	ADP
ap-3511	150	6	the	the	DET
ap-3511	150	7	right	right	ADJ
ap-3511	150	8	hand	hand	NOUN
ap-3511	150	9	side	side	NOUN
ap-3511	150	10	of	of	ADP
ap-3511	150	11	(	(	PUNCT
ap-3511	150	12	14	14	NUM
ap-3511	150	13	)	)	PUNCT
ap-3511	150	14	and	and	CCONJ
ap-3511	150	15	we	we	PRON
ap-3511	150	16	use	use	VERB
ap-3511	150	17	formulas	formula	NOUN
ap-3511	150	18	(	(	PUNCT
ap-3511	150	19	2	2	NUM
ap-3511	150	20	)	)	PUNCT
ap-3511	150	21	and	and	CCONJ
ap-3511	150	22	(	(	PUNCT
ap-3511	150	23	11	11	NUM
ap-3511	150	24	)	)	PUNCT
ap-3511	150	25	.	.	PUNCT
ap-3511	151	1	r∑	r∑	NOUN
ap-3511	151	2	j=1	j=1	PROPN
ap-3511	151	3	χj(w)φjν(x	χj(w)φjν(x	PROPN
ap-3511	151	4	)	)	PUNCT
ap-3511	151	5	=	=	SYM
ap-3511	152	1	r∑	r∑	NOUN
ap-3511	152	2	j=1	j=1	NOUN
ap-3511	152	3	χj(w	χj(w	PUNCT
ap-3511	152	4	)	)	PUNCT
ap-3511	152	5	∑	∑	PUNCT
ap-3511	152	6	w̃∈w	w̃∈w	PROPN
ap-3511	152	7	χj(w̃)e2πı〈w̃ν	χj(w̃)e2πı〈w̃ν	NOUN
ap-3511	152	8	,	,	PUNCT
ap-3511	152	9	x	x	NOUN
ap-3511	152	10	〉	〉	NUM
ap-3511	152	11	=	=	SYM
ap-3511	152	12	∑	∑	PUNCT
ap-3511	152	13	w̃∈w	w̃∈w	PROPN
ap-3511	152	14	e2πı〈w̃ν	e2πı〈w̃ν	NOUN
ap-3511	152	15	,	,	PUNCT
ap-3511	152	16	x	x	NOUN
ap-3511	152	17	〉	〉	NUM
ap-3511	152	18	r∑	r∑	NOUN
ap-3511	152	19	j=1	j=1	NOUN
ap-3511	152	20	χj(w)χj(w̃	χj(w)χj(w̃	NOUN
ap-3511	152	21	)	)	PUNCT
ap-3511	152	22	=	=	SYM
ap-3511	152	23	∑	∑	PUNCT
ap-3511	152	24	w̃∈w	w̃∈w	PROPN
ap-3511	152	25	e2πı〈w̃ν	e2πı〈w̃ν	NOUN
ap-3511	152	26	,	,	PUNCT
ap-3511	152	27	x〉δww̃	x〉δww̃	PROPN
ap-3511	152	28	|w	|w	NOUN
ap-3511	152	29	|	|	NOUN
ap-3511	152	30	|[w]|	|[w]|	NUM
ap-3511	152	31	=	=	NOUN
ap-3511	152	32	|w	|w	ADJ
ap-3511	152	33	|	|	ADV
ap-3511	152	34	|[w]|e	|[w]|e	NOUN
ap-3511	152	35	2πı〈wν	2πı〈wν	NUM
ap-3511	152	36	,	,	PUNCT
ap-3511	152	37	x	x	NOUN
ap-3511	152	38	〉	〉	NOUN
ap-3511	152	39	.	.	PUNCT
ap-3511	153	1	now	now	ADV
ap-3511	153	2	,	,	PUNCT
ap-3511	153	3	putting	put	VERB
ap-3511	153	4	in	in	ADP
ap-3511	153	5	lemma	lemma	PROPN
ap-3511	153	6	1	1	NUM
ap-3511	153	7	:	:	PUNCT
ap-3511	153	8	w	w	NOUN
ap-3511	153	9	=	=	PUNCT
ap-3511	153	10	i	i	PROPN
ap-3511	153	11	d	d	PROPN
ap-3511	153	12	and	and	CCONJ
ap-3511	153	13	ν	ν	X
ap-3511	153	14	=	=	PUNCT
ap-3511	153	15	wλ+w̃µ	wλ+w̃µ	SCONJ
ap-3511	153	16	we	we	PRON
ap-3511	153	17	could	could	AUX
ap-3511	153	18	rewrite	rewrite	VERB
ap-3511	153	19	(	(	PUNCT
ap-3511	153	20	13	13	NUM
ap-3511	153	21	)	)	PUNCT
ap-3511	153	22	in	in	ADP
ap-3511	153	23	the	the	DET
ap-3511	153	24	form	form	NOUN
ap-3511	153	25	φkλ(x)φlµ(x	φkλ(x)φlµ(x	ADJ
ap-3511	153	26	)	)	PUNCT
ap-3511	154	1	=	=	SYM
ap-3511	154	2	1	1	NUM
ap-3511	154	3	|w	|w	NOUN
ap-3511	155	1	|	|	ADV
ap-3511	156	1	r∑	r∑	NOUN
ap-3511	156	2	j=1	j=1	NOUN
ap-3511	156	3	dj	dj	X
ap-3511	156	4	∑	∑	PROPN
ap-3511	156	5	w	w	PROPN
ap-3511	156	6	,	,	PUNCT
ap-3511	156	7	w̃∈w	w̃∈w	PROPN
ap-3511	156	8	χk(w)χl(w̃)φj	χk(w)χl(w̃)φj	ADJ
ap-3511	156	9	wλ+w̃µ	wλ+w̃µ	PROPN
ap-3511	156	10	(	(	PUNCT
ap-3511	156	11	x	x	NOUN
ap-3511	156	12	)	)	PUNCT
ap-3511	156	13	.	.	PUNCT
ap-3511	157	1	another	another	DET
ap-3511	157	2	remarkable	remarkable	ADJ
ap-3511	157	3	property	property	NOUN
ap-3511	157	4	of	of	ADP
ap-3511	157	5	orbit	orbit	NOUN
ap-3511	157	6	functions	function	NOUN
ap-3511	157	7	is	be	AUX
ap-3511	157	8	the	the	DET
ap-3511	157	9	fact	fact	NOUN
ap-3511	157	10	that	that	SCONJ
ap-3511	157	11	they	they	PRON
ap-3511	157	12	are	be	AUX
ap-3511	157	13	eigenfunctions	eigenfunction	NOUN
ap-3511	157	14	of	of	ADP
ap-3511	157	15	laplace	laplace	NOUN
ap-3511	157	16	operator	operator	NOUN
ap-3511	157	17	in	in	ADP
ap-3511	157	18	rn	rn	PROPN
ap-3511	157	19	.	.	PUNCT
ap-3511	158	1	by	by	ADP
ap-3511	158	2	an	an	DET
ap-3511	158	3	analogy	analogy	NOUN
ap-3511	158	4	to	to	ADP
ap-3511	158	5	[	[	X
ap-3511	158	6	1	1	X
ap-3511	158	7	]	]	PUNCT
ap-3511	158	8	we	we	PRON
ap-3511	158	9	calculate	calculate	VERB
ap-3511	158	10	the	the	DET
ap-3511	158	11	laplace	laplace	NOUN
ap-3511	158	12	operator	operator	NOUN
ap-3511	158	13	in	in	ADP
ap-3511	158	14	rn	rn	PROPN
ap-3511	158	15	and	and	CCONJ
ap-3511	158	16	we	we	PRON
ap-3511	158	17	get	get	VERB
ap-3511	158	18	that	that	PRON
ap-3511	158	19	φkλ(x	φkλ(x	NOUN
ap-3511	158	20	)	)	PUNCT
ap-3511	158	21	fulfills	fulfill	VERB
ap-3511	158	22	the	the	DET
ap-3511	158	23	helmholtz	helmholtz	NOUN
ap-3511	158	24	equation	equation	NOUN
ap-3511	158	25	4φkλ(x	4φkλ(x	NUM
ap-3511	158	26	)	)	PUNCT
ap-3511	158	27	=	=	SYM
ap-3511	158	28	−4π2〈λ	−4π2〈λ	NOUN
ap-3511	158	29	,	,	PUNCT
ap-3511	158	30	λ〉φkλ(x	λ〉φkλ(x	NUM
ap-3511	158	31	)	)	PUNCT
ap-3511	158	32	.	.	PUNCT
ap-3511	159	1	finally	finally	ADV
ap-3511	159	2	,	,	PUNCT
ap-3511	159	3	the	the	DET
ap-3511	159	4	following	follow	VERB
ap-3511	159	5	lemma	lemma	PROPN
ap-3511	159	6	is	be	AUX
ap-3511	159	7	crucial	crucial	ADJ
ap-3511	159	8	for	for	ADP
ap-3511	159	9	the	the	DET
ap-3511	159	10	continuous	continuous	ADJ
ap-3511	159	11	and	and	CCONJ
ap-3511	159	12	discrete	discrete	ADJ
ap-3511	159	13	orthogonality	orthogonality	NOUN
ap-3511	159	14	.	.	PUNCT
ap-3511	160	1	its	its	PRON
ap-3511	160	2	proof	proof	NOUN
ap-3511	160	3	is	be	AUX
ap-3511	160	4	straightforward	straightforward	ADJ
ap-3511	160	5	and	and	CCONJ
ap-3511	160	6	it	it	PRON
ap-3511	160	7	is	be	AUX
ap-3511	160	8	analogous	analogous	ADJ
ap-3511	160	9	to	to	ADP
ap-3511	160	10	the	the	DET
ap-3511	160	11	proof	proof	NOUN
ap-3511	160	12	of	of	ADP
ap-3511	160	13	the	the	DET
ap-3511	160	14	similar	similar	ADJ
ap-3511	160	15	proposition	proposition	NOUN
ap-3511	160	16	for	for	ADP
ap-3511	160	17	the	the	DET
ap-3511	160	18	immanant	immanant	ADJ
ap-3511	160	19	functions	function	NOUN
ap-3511	160	20	in	in	ADP
ap-3511	160	21	[	[	X
ap-3511	160	22	7	7	NUM
ap-3511	160	23	]	]	PUNCT
ap-3511	160	24	.	.	PUNCT
ap-3511	161	1	lemma	lemma	PROPN
ap-3511	161	2	2	2	X
ap-3511	161	3	.	.	PUNCT
ap-3511	162	1	let	let	VERB
ap-3511	162	2	0	0	NUM
ap-3511	162	3	6=	6=	NUM
ap-3511	162	4	λ	λ	PROPN
ap-3511	162	5	,	,	PUNCT
ap-3511	162	6	µ	µ	PROPN
ap-3511	162	7	∈	∈	PROPN
ap-3511	162	8	p+	p+	X
ap-3511	162	9	and	and	CCONJ
ap-3511	162	10	χk	χk	PROPN
ap-3511	162	11	,	,	PUNCT
ap-3511	162	12	χl	χl	NOUN
ap-3511	162	13	irreducible	irreducible	ADJ
ap-3511	162	14	characters	character	NOUN
ap-3511	162	15	.	.	PUNCT
ap-3511	163	1	then∑	then∑	NOUN
ap-3511	163	2	w∈w	w∈w	VERB
ap-3511	163	3	φkwλ(x)φlwµ(x	φkwλ(x)φlwµ(x	NOUN
ap-3511	163	4	)	)	PUNCT
ap-3511	163	5	=	=	PUNCT
ap-3511	164	1	∑	∑	PUNCT
ap-3511	165	1	w̃,ŵ∈w	w̃,ŵ∈w	PROPN
ap-3511	165	2	χk(w̃)χl(ŵ)φ1	χk(w̃)χl(ŵ)φ1	NUM
ap-3511	165	3	λ+w̃ŵµ(x	λ+w̃ŵµ(x	NOUN
ap-3511	165	4	)	)	PUNCT
ap-3511	165	5	,	,	PUNCT
ap-3511	165	6	∑	∑	ADV
ap-3511	165	7	w∈w	w∈w	VERB
ap-3511	165	8	φkwλ(x)φlwµ(x	φkwλ(x)φlwµ(x	NOUN
ap-3511	165	9	)	)	PUNCT
ap-3511	165	10	=	=	PUNCT
ap-3511	165	11	∑	∑	PUNCT
ap-3511	165	12	w̃,ŵ∈w	w̃,ŵ∈w	VERB
ap-3511	165	13	χk(w̃)χl(ŵ)φ1	χk(w̃)χl(ŵ)φ1	NUM
ap-3511	165	14	λ−w̃ŵµ(x	λ−w̃ŵµ(x	NOUN
ap-3511	165	15	)	)	PUNCT
ap-3511	165	16	.	.	PUNCT
ap-3511	166	1	4.2	4.2	NUM
ap-3511	166	2	.	.	PUNCT
ap-3511	167	1	continuous	continuous	ADJ
ap-3511	167	2	and	and	CCONJ
ap-3511	167	3	discrete	discrete	ADJ
ap-3511	167	4	orthogonality	orthogonality	NOUN
ap-3511	167	5	the	the	DET
ap-3511	167	6	following	follow	VERB
ap-3511	167	7	theorem	theorem	NOUN
ap-3511	167	8	is	be	AUX
ap-3511	167	9	analogous	analogous	ADJ
ap-3511	167	10	to	to	PART
ap-3511	167	11	theorem	theorem	VERB
ap-3511	167	12	3	3	NUM
ap-3511	167	13	in	in	ADP
ap-3511	167	14	[	[	X
ap-3511	167	15	7	7	NUM
ap-3511	167	16	]	]	PUNCT
ap-3511	167	17	.	.	PUNCT
ap-3511	168	1	it	it	PRON
ap-3511	168	2	describes	describe	VERB
ap-3511	168	3	the	the	DET
ap-3511	168	4	continuous	continuous	ADJ
ap-3511	168	5	orthogonality	orthogonality	NOUN
ap-3511	168	6	of	of	ADP
ap-3511	168	7	character	character	NOUN
ap-3511	168	8	functions	function	NOUN
ap-3511	168	9	over	over	ADP
ap-3511	168	10	the	the	DET
ap-3511	168	11	domain	domain	NOUN
ap-3511	168	12	f̃	f̃	PROPN
ap-3511	168	13	=	=	PUNCT
ap-3511	168	14	⋃	⋃	NOUN
ap-3511	168	15	w∈w	w∈w	VERB
ap-3511	168	16	wf	wf	NOUN
ap-3511	168	17	,	,	PUNCT
ap-3511	168	18	where	where	SCONJ
ap-3511	168	19	w	w	NOUN
ap-3511	168	20	is	be	AUX
ap-3511	168	21	any	any	DET
ap-3511	168	22	weyl	weyl	VERB
ap-3511	168	23	group	group	NOUN
ap-3511	168	24	and	and	CCONJ
ap-3511	168	25	f	f	PROPN
ap-3511	168	26	the	the	DET
ap-3511	168	27	fundamental	fundamental	ADJ
ap-3511	168	28	domain	domain	NOUN
ap-3511	168	29	of	of	ADP
ap-3511	168	30	the	the	DET
ap-3511	168	31	corresponding	corresponding	ADJ
ap-3511	168	32	affine	affine	NOUN
ap-3511	168	33	weyl	weyl	PROPN
ap-3511	168	34	group	group	NOUN
ap-3511	168	35	.	.	PUNCT
ap-3511	169	1	theorem	theorem	VERB
ap-3511	169	2	3	3	NUM
ap-3511	169	3	.	.	PUNCT
ap-3511	169	4	for	for	ADP
ap-3511	169	5	every	every	DET
ap-3511	169	6	0	0	NUM
ap-3511	169	7	6=	6=	ADP
ap-3511	169	8	λ	λ	PROPN
ap-3511	169	9	,	,	PUNCT
ap-3511	169	10	µ	µ	PROPN
ap-3511	169	11	∈	∈	PROPN
ap-3511	169	12	p+	p+	NOUN
ap-3511	169	13	and	and	CCONJ
ap-3511	169	14	every	every	DET
ap-3511	169	15	pair	pair	NOUN
ap-3511	169	16	of	of	ADP
ap-3511	169	17	characters	character	NOUN
ap-3511	169	18	χk	χk	PROPN
ap-3511	169	19	,	,	PUNCT
ap-3511	169	20	χl	χl	VERB
ap-3511	169	21	the	the	DET
ap-3511	169	22	following	follow	VERB
ap-3511	169	23	relation	relation	NOUN
ap-3511	169	24	holds.∫	holds.∫	PRON
ap-3511	169	25	f̃	f̃	PROPN
ap-3511	169	26	φkλ(x)φlµ(x)dx	φkλ(x)φlµ(x)dx	ADJ
ap-3511	169	27	=	=	SYM
ap-3511	169	28	|w	|w	NOUN
ap-3511	170	1	|	|	ADV
ap-3511	170	2	2|f	2|f	NUM
ap-3511	171	1	|	|	ADV
ap-3511	171	2	dk	dk	INTJ
ap-3511	171	3	δλµδkl	δλµδkl	NOUN
ap-3511	171	4	∑	∑	PROPN
ap-3511	171	5	w∈stabw	w∈stabw	PROPN
ap-3511	171	6	(	(	PUNCT
ap-3511	171	7	λ	λ	NOUN
ap-3511	171	8	)	)	PUNCT
ap-3511	171	9	χk(w	χk(w	PUNCT
ap-3511	171	10	)	)	PUNCT
ap-3511	171	11	,	,	PUNCT
ap-3511	171	12	where	where	SCONJ
ap-3511	171	13	dk	dk	PROPN
ap-3511	171	14	is	be	AUX
ap-3511	171	15	the	the	DET
ap-3511	171	16	degree	degree	NOUN
ap-3511	171	17	of	of	ADP
ap-3511	171	18	the	the	DET
ap-3511	171	19	character	character	NOUN
ap-3511	171	20	χk	χk	PROPN
ap-3511	171	21	.	.	PUNCT
ap-3511	172	1	in	in	ADP
ap-3511	172	2	particular	particular	ADJ
ap-3511	172	3	,	,	PUNCT
ap-3511	172	4	for	for	ADP
ap-3511	172	5	λ	λ	PROPN
ap-3511	172	6	,	,	PUNCT
ap-3511	172	7	µ	µ	DET
ap-3511	172	8	∈	∈	PROPN
ap-3511	172	9	p++	p++	NOUN
ap-3511	172	10	it	it	PRON
ap-3511	172	11	holds	hold	VERB
ap-3511	172	12	that∫	that∫	PROPN
ap-3511	172	13	f̃	f̃	PROPN
ap-3511	172	14	φkλ(x)φlµ(x)dx	φkλ(x)φlµ(x)dx	VERB
ap-3511	172	15	=	=	PUNCT
ap-3511	172	16	|f	|f	PROPN
ap-3511	172	17	||w	||w	PROPN
ap-3511	172	18	|2δklδλµ	|2δklδλµ	PROPN
ap-3511	172	19	.	.	PUNCT
ap-3511	173	1	proof	proof	NOUN
ap-3511	173	2	.	.	PUNCT
ap-3511	174	1	using	use	VERB
ap-3511	174	2	the	the	DET
ap-3511	174	3	symmetries	symmetry	NOUN
ap-3511	174	4	of	of	ADP
ap-3511	174	5	character	character	NOUN
ap-3511	174	6	functions	function	NOUN
ap-3511	174	7	given	give	VERB
ap-3511	174	8	by	by	ADP
ap-3511	174	9	(	(	PUNCT
ap-3511	174	10	12	12	NUM
ap-3511	174	11	)	)	PUNCT
ap-3511	174	12	we	we	PRON
ap-3511	174	13	write⋃	write⋃	AUX
ap-3511	174	14	w∈w	w∈w	VERB
ap-3511	174	15	∫	∫	PROPN
ap-3511	174	16	f	f	PROPN
ap-3511	174	17	φkλ(x)φlµ(x)dx	φkλ(x)φlµ(x)dx	VERB
ap-3511	174	18	=	=	SYM
ap-3511	174	19	∑	∑	ADP
ap-3511	174	20	w∈w	w∈w	VERB
ap-3511	174	21	∫	∫	PROPN
ap-3511	174	22	f	f	PROPN
ap-3511	174	23	φkwλ(x)φlwµ(x)dx	φkwλ(x)φlwµ(x)dx	PROPN
ap-3511	174	24	=	=	SYM
ap-3511	174	25	∫	∫	PROPN
ap-3511	174	26	f	f	PROPN
ap-3511	174	27	∑	∑	ADV
ap-3511	174	28	w∈w	w∈w	VERB
ap-3511	174	29	φkwλ(x)φlwµ(x)dx	φkwλ(x)φlwµ(x)dx	NOUN
ap-3511	174	30	.	.	PUNCT
ap-3511	175	1	from	from	ADP
ap-3511	175	2	lemma	lemma	PROPN
ap-3511	175	3	2	2	NUM
ap-3511	175	4	we	we	PRON
ap-3511	175	5	get∫	get∫	PROPN
ap-3511	175	6	f	f	PROPN
ap-3511	175	7	∑	∑	ADV
ap-3511	175	8	w∈w	w∈w	VERB
ap-3511	175	9	φkwλ(x)φlwµ(x)dx	φkwλ(x)φlwµ(x)dx	NOUN
ap-3511	175	10	=	=	PUNCT
ap-3511	176	1	=	=	SYM
ap-3511	176	2	∫	∫	PROPN
ap-3511	176	3	f	f	PROPN
ap-3511	176	4	∑	∑	PUNCT
ap-3511	176	5	w̃,ŵ∈w	w̃,ŵ∈w	VERB
ap-3511	176	6	χk(w̃)χl(ŵ)φ1	χk(w̃)χl(ŵ)φ1	NUM
ap-3511	176	7	λ−w̃ŵµ(x)dx	λ−w̃ŵµ(x)dx	NUM
ap-3511	176	8	=	=	SYM
ap-3511	176	9	∑	∑	PROPN
ap-3511	176	10	w	w	PROPN
ap-3511	176	11	,	,	PUNCT
ap-3511	176	12	ŵ∈w	ŵ∈w	ADJ
ap-3511	176	13	χk(wŵ−1)χl(ŵ	χk(wŵ−1)χl(ŵ	NOUN
ap-3511	176	14	)	)	PUNCT
ap-3511	176	15	∫	∫	PROPN
ap-3511	177	1	f	f	PROPN
ap-3511	177	2	φ1	φ1	PROPN
ap-3511	177	3	λ−wµ(x)dx	λ−wµ(x)dx	PROPN
ap-3511	177	4	.	.	PUNCT
ap-3511	178	1	in	in	ADP
ap-3511	178	2	the	the	DET
ap-3511	178	3	last	last	ADJ
ap-3511	178	4	equation	equation	NOUN
ap-3511	178	5	we	we	PRON
ap-3511	178	6	substituted	substitute	VERB
ap-3511	178	7	w	w	PROPN
ap-3511	178	8	=	=	PUNCT
ap-3511	178	9	w̃ŵ.	w̃ŵ.	PROPN
ap-3511	178	10	since	since	SCONJ
ap-3511	178	11	λ	λ	PROPN
ap-3511	178	12	,	,	PUNCT
ap-3511	178	13	µ	µ	PRON
ap-3511	178	14	∈	∈	PROPN
ap-3511	178	15	p+	p+	NOUN
ap-3511	178	16	,	,	PUNCT
ap-3511	178	17	the	the	DET
ap-3511	178	18	expression	expression	NOUN
ap-3511	178	19	λ−wµ	λ−wµ	ADJ
ap-3511	178	20	equals	equal	VERB
ap-3511	178	21	zero	zero	NUM
ap-3511	178	22	only	only	ADV
ap-3511	178	23	for	for	ADP
ap-3511	178	24	λ	λ	PROPN
ap-3511	178	25	=	=	SYM
ap-3511	178	26	µ	µ	X
ap-3511	178	27	and	and	CCONJ
ap-3511	178	28	w	w	PROPN
ap-3511	178	29	∈	∈	PROPN
ap-3511	178	30	stabw	stabw	NOUN
ap-3511	178	31	(	(	PUNCT
ap-3511	178	32	λ	λ	NOUN
ap-3511	178	33	)	)	PUNCT
ap-3511	178	34	.	.	PUNCT
ap-3511	179	1	then	then	ADV
ap-3511	179	2	,	,	PUNCT
ap-3511	179	3	using	use	VERB
ap-3511	179	4	(	(	PUNCT
ap-3511	179	5	3	3	NUM
ap-3511	179	6	)	)	PUNCT
ap-3511	179	7	and	and	CCONJ
ap-3511	179	8	(	(	PUNCT
ap-3511	179	9	7	7	X
ap-3511	179	10	)	)	PUNCT
ap-3511	179	11	we	we	PRON
ap-3511	179	12	get	get	VERB
ap-3511	179	13	∑	∑	PROPN
ap-3511	179	14	w	w	PROPN
ap-3511	179	15	,	,	PUNCT
ap-3511	179	16	ŵ∈w	ŵ∈w	ADJ
ap-3511	179	17	χk(wŵ−1)χl(ŵ	χk(wŵ−1)χl(ŵ	NOUN
ap-3511	179	18	)	)	PUNCT
ap-3511	180	1	∫	∫	PROPN
ap-3511	180	2	f	f	PROPN
ap-3511	180	3	φ1	φ1	PROPN
ap-3511	180	4	λ−wµ(x)dx	λ−wµ(x)dx	ADV
ap-3511	180	5	=	=	PUNCT
ap-3511	180	6	|w	|w	ADJ
ap-3511	180	7	||f	||f	NOUN
ap-3511	180	8	|δλµ	|δλµ	PROPN
ap-3511	180	9	∑	∑	PUNCT
ap-3511	180	10	w∈stabw	w∈stabw	PROPN
ap-3511	180	11	(	(	PUNCT
ap-3511	180	12	λ	λ	X
ap-3511	180	13	)	)	PUNCT
ap-3511	180	14	∑	∑	PUNCT
ap-3511	180	15	ŵ∈w	ŵ∈w	ADJ
ap-3511	180	16	χk(wŵ−1)χl(ŵ	χk(wŵ−1)χl(ŵ	NOUN
ap-3511	180	17	)	)	PUNCT
ap-3511	180	18	=	=	SYM
ap-3511	181	1	|w	|w	PROPN
ap-3511	181	2	|2|f	|2|f	PROPN
ap-3511	181	3	|δλµδkl	|δλµδkl	NUM
ap-3511	181	4	1	1	NUM
ap-3511	181	5	dk	dk	INTJ
ap-3511	181	6	∑	∑	PUNCT
ap-3511	181	7	w∈stabw	w∈stabw	PROPN
ap-3511	181	8	(	(	PUNCT
ap-3511	181	9	λ	λ	NOUN
ap-3511	181	10	)	)	PUNCT
ap-3511	181	11	χk(w	χk(w	PUNCT
ap-3511	181	12	)	)	PUNCT
ap-3511	181	13	.	.	PUNCT
ap-3511	182	1	for	for	ADP
ap-3511	182	2	λ	λ	PROPN
ap-3511	182	3	,	,	PUNCT
ap-3511	182	4	µ	µ	PRON
ap-3511	182	5	∈	∈	PROPN
ap-3511	182	6	p++	p++	NOUN
ap-3511	182	7	the	the	DET
ap-3511	182	8	stabilizer	stabilizer	NOUN
ap-3511	182	9	is	be	AUX
ap-3511	182	10	trivial	trivial	ADJ
ap-3511	182	11	and	and	CCONJ
ap-3511	182	12	the	the	DET
ap-3511	182	13	sum	sum	NOUN
ap-3511	182	14	in	in	ADP
ap-3511	182	15	the	the	DET
ap-3511	182	16	above	above	ADJ
ap-3511	182	17	expression	expression	NOUN
ap-3511	182	18	equals	equal	VERB
ap-3511	182	19	dk	dk	PROPN
ap-3511	182	20	.	.	PUNCT
ap-3511	183	1	an	an	DET
ap-3511	183	2	analogous	analogous	ADJ
ap-3511	183	3	method	method	NOUN
ap-3511	183	4	is	be	AUX
ap-3511	183	5	used	use	VERB
ap-3511	183	6	in	in	ADP
ap-3511	183	7	the	the	DET
ap-3511	183	8	proof	proof	NOUN
ap-3511	183	9	of	of	ADP
ap-3511	183	10	discrete	discrete	ADJ
ap-3511	183	11	orthogonality	orthogonality	NOUN
ap-3511	183	12	.	.	PUNCT
ap-3511	184	1	let	let	VERB
ap-3511	184	2	f̃m	f̃m	NOUN
ap-3511	184	3	=	=	SYM
ap-3511	184	4	∪w∈wwfm	∪w∈wwfm	NOUN
ap-3511	184	5	=	=	SYM
ap-3511	184	6	1	1	NUM
ap-3511	184	7	m	m	NOUN
ap-3511	184	8	p∨/q∨∩f̃	p∨/q∨∩f̃	ADJ
ap-3511	184	9	.	.	PUNCT
ap-3511	185	1	using	use	VERB
ap-3511	185	2	the	the	DET
ap-3511	185	3	orthogonality	orthogonality	NOUN
ap-3511	185	4	of	of	ADP
ap-3511	185	5	c	c	NOUN
ap-3511	185	6	–	–	PUNCT
ap-3511	185	7	functions	function	NOUN
ap-3511	185	8	(	(	PUNCT
ap-3511	185	9	10	10	NUM
ap-3511	185	10	)	)	PUNCT
ap-3511	185	11	we	we	PRON
ap-3511	185	12	get	get	VERB
ap-3511	185	13	the	the	DET
ap-3511	185	14	following	follow	VERB
ap-3511	185	15	theorem	theorem	VERB
ap-3511	185	16	.	.	PUNCT
ap-3511	185	17	theorem	theorem	NOUN
ap-3511	185	18	4	4	NUM
ap-3511	185	19	.	.	PUNCT
ap-3511	185	20	for	for	ADP
ap-3511	185	21	every	every	DET
ap-3511	185	22	0	0	NUM
ap-3511	185	23	6=	6=	ADP
ap-3511	185	24	λ	λ	PROPN
ap-3511	185	25	,	,	PUNCT
ap-3511	186	1	µ	µ	X
ap-3511	186	2	∈	∈	NOUN
ap-3511	186	3	λm	λm	ADP
ap-3511	186	4	and	and	CCONJ
ap-3511	186	5	every	every	DET
ap-3511	186	6	pair	pair	NOUN
ap-3511	186	7	of	of	ADP
ap-3511	186	8	characters	character	NOUN
ap-3511	186	9	χk	χk	PROPN
ap-3511	186	10	,	,	PUNCT
ap-3511	186	11	χl	χl	VERB
ap-3511	186	12	the	the	DET
ap-3511	186	13	following	follow	VERB
ap-3511	186	14	relation	relation	NOUN
ap-3511	186	15	holds.∑	holds.∑	PROPN
ap-3511	186	16	x∈f̃m	x∈f̃m	PROPN
ap-3511	186	17	φkλ(x)φlµ(x	φkλ(x)φlµ(x	PROPN
ap-3511	186	18	)	)	PUNCT
ap-3511	187	1	=	=	SYM
ap-3511	187	2	c|w	c|w	NOUN
ap-3511	188	1	|2mnδλµδkl	|2mnδλµδkl	NOUN
ap-3511	188	2	1	1	NUM
ap-3511	188	3	dk	dk	INTJ
ap-3511	188	4	∑	∑	PUNCT
ap-3511	188	5	w∈stabw	w∈stabw	PROPN
ap-3511	188	6	(	(	PUNCT
ap-3511	188	7	λ	λ	NOUN
ap-3511	188	8	)	)	PUNCT
ap-3511	188	9	χk(w	χk(w	PUNCT
ap-3511	188	10	)	)	PUNCT
ap-3511	188	11	.	.	PUNCT
ap-3511	189	1	in	in	ADP
ap-3511	189	2	particular	particular	ADJ
ap-3511	189	3	,	,	PUNCT
ap-3511	189	4	for	for	ADP
ap-3511	189	5	λ	λ	PROPN
ap-3511	189	6	,	,	PUNCT
ap-3511	189	7	µ	µ	PRON
ap-3511	189	8	∈	∈	NOUN
ap-3511	189	9	λm	λm	ADP
ap-3511	189	10	∩	∩	NOUN
ap-3511	189	11	p++	p++	NOUN
ap-3511	189	12	it	it	PRON
ap-3511	189	13	holds	hold	VERB
ap-3511	189	14	that∑	that∑	NOUN
ap-3511	189	15	x∈f̃m	x∈f̃m	NOUN
ap-3511	189	16	φkλ(x)φlµ(x	φkλ(x)φlµ(x	ADJ
ap-3511	189	17	)	)	PUNCT
ap-3511	190	1	=	=	SYM
ap-3511	190	2	c|w	c|w	PROPN
ap-3511	190	3	|2mnδklδλµ	|2mnδklδλµ	PROPN
ap-3511	190	4	.	.	PUNCT
ap-3511	191	1	4.3	4.3	NUM
ap-3511	191	2	.	.	PUNCT
ap-3511	192	1	linear	linear	ADJ
ap-3511	192	2	independency	independency	NOUN
ap-3511	192	3	of	of	ADP
ap-3511	192	4	character	character	NOUN
ap-3511	192	5	functions	function	NOUN
ap-3511	192	6	the	the	DET
ap-3511	192	7	orthogonality	orthogonality	NOUN
ap-3511	192	8	relations	relation	NOUN
ap-3511	192	9	described	describe	VERB
ap-3511	192	10	in	in	ADP
ap-3511	192	11	the	the	DET
ap-3511	192	12	previous	previous	ADJ
ap-3511	192	13	section	section	NOUN
ap-3511	192	14	show	show	VERB
ap-3511	192	15	that	that	SCONJ
ap-3511	192	16	functions	function	NOUN
ap-3511	192	17	corresponding	correspond	VERB
ap-3511	192	18	to	to	ADP
ap-3511	192	19	different	different	ADJ
ap-3511	192	20	443	443	NUM
ap-3511	192	21	lenka	lenka	PROPN
ap-3511	192	22	háková	háková	PROPN
ap-3511	192	23	,	,	PUNCT
ap-3511	192	24	agnieszka	agnieszka	PROPN
ap-3511	192	25	tereszkiewicz	tereszkiewicz	PROPN
ap-3511	192	26	acta	acta	PROPN
ap-3511	192	27	polytechnica	polytechnica	PROPN
ap-3511	192	28	c1	c1	PROPN
ap-3511	192	29	c2	c2	PROPN
ap-3511	192	30	c3	c3	PROPN
ap-3511	192	31	χ1	χ1	PROPN
ap-3511	192	32	1	1	NUM
ap-3511	192	33	1	1	NUM
ap-3511	192	34	1	1	NUM
ap-3511	192	35	χ2	χ2	NOUN
ap-3511	192	36	1	1	NUM
ap-3511	192	37	1	1	NUM
ap-3511	192	38	−1	−1	NOUN
ap-3511	192	39	χ3	χ3	NOUN
ap-3511	192	40	2	2	NUM
ap-3511	192	41	−1	−1	NOUN
ap-3511	192	42	0	0	NUM
ap-3511	192	43	c1	c1	PROPN
ap-3511	192	44	c2	c2	PROPN
ap-3511	192	45	c3	c3	PROPN
ap-3511	192	46	c4	c4	PROPN
ap-3511	192	47	c5	c5	PROPN
ap-3511	192	48	χ1	χ1	PROPN
ap-3511	192	49	1	1	NUM
ap-3511	192	50	1	1	NUM
ap-3511	192	51	1	1	NUM
ap-3511	192	52	1	1	NUM
ap-3511	192	53	1	1	NUM
ap-3511	192	54	χ2	χ2	NOUN
ap-3511	192	55	1	1	NUM
ap-3511	192	56	1	1	NUM
ap-3511	192	57	1	1	NUM
ap-3511	192	58	−1	−1	NOUN
ap-3511	192	59	−1	−1	NOUN
ap-3511	192	60	χ3	χ3	NOUN
ap-3511	192	61	1	1	NUM
ap-3511	192	62	1	1	NUM
ap-3511	192	63	−1	−1	NOUN
ap-3511	192	64	1	1	NUM
ap-3511	192	65	−1	−1	NOUN
ap-3511	192	66	χ4	χ4	NOUN
ap-3511	192	67	1	1	NUM
ap-3511	192	68	1	1	NUM
ap-3511	192	69	−1	−1	NOUN
ap-3511	192	70	−1	−1	NOUN
ap-3511	192	71	1	1	NUM
ap-3511	192	72	χ5	χ5	NOUN
ap-3511	192	73	2	2	NUM
ap-3511	192	74	−2	−2	NOUN
ap-3511	192	75	0	0	NUM
ap-3511	192	76	0	0	SYM
ap-3511	192	77	0	0	NUM
ap-3511	192	78	c1	c1	PROPN
ap-3511	192	79	c2	c2	PROPN
ap-3511	192	80	c3	c3	PROPN
ap-3511	192	81	c4	c4	PROPN
ap-3511	192	82	c5	c5	PROPN
ap-3511	192	83	c6	c6	PROPN
ap-3511	192	84	χ1	χ1	PROPN
ap-3511	192	85	1	1	NUM
ap-3511	192	86	1	1	NUM
ap-3511	192	87	1	1	NUM
ap-3511	192	88	1	1	NUM
ap-3511	192	89	1	1	NUM
ap-3511	192	90	1	1	NUM
ap-3511	192	91	χ2	χ2	NOUN
ap-3511	192	92	1	1	NUM
ap-3511	192	93	1	1	NUM
ap-3511	192	94	1	1	NUM
ap-3511	192	95	1	1	NUM
ap-3511	192	96	−1	−1	NOUN
ap-3511	192	97	−1	−1	NOUN
ap-3511	192	98	χ3	χ3	NOUN
ap-3511	192	99	1	1	NUM
ap-3511	192	100	−1	−1	NOUN
ap-3511	192	101	1	1	NUM
ap-3511	192	102	−1	−1	NOUN
ap-3511	192	103	1	1	NUM
ap-3511	192	104	−1	−1	NOUN
ap-3511	192	105	χ4	χ4	NOUN
ap-3511	192	106	1	1	NUM
ap-3511	192	107	−1	−1	NOUN
ap-3511	192	108	1	1	NUM
ap-3511	192	109	−1	−1	NOUN
ap-3511	192	110	−1	−1	NOUN
ap-3511	192	111	1	1	NUM
ap-3511	192	112	χ5	χ5	NOUN
ap-3511	192	113	2	2	NUM
ap-3511	192	114	2	2	NUM
ap-3511	192	115	−1	−1	NOUN
ap-3511	192	116	−1	−1	NOUN
ap-3511	192	117	0	0	NUM
ap-3511	192	118	0	0	NUM
ap-3511	192	119	χ6	χ6	ADJ
ap-3511	192	120	2	2	NUM
ap-3511	192	121	−2	−2	NOUN
ap-3511	192	122	−1	−1	NOUN
ap-3511	192	123	1	1	NUM
ap-3511	192	124	0	0	NUM
ap-3511	192	125	0	0	NUM
ap-3511	192	126	table	table	NOUN
ap-3511	192	127	1	1	NUM
ap-3511	192	128	.	.	PUNCT
ap-3511	193	1	character	character	NOUN
ap-3511	193	2	tables	table	NOUN
ap-3511	193	3	of	of	ADP
ap-3511	193	4	weyl	weyl	VERB
ap-3511	193	5	groups	group	NOUN
ap-3511	193	6	of	of	ADP
ap-3511	193	7	a2	a2	PROPN
ap-3511	193	8	,	,	PUNCT
ap-3511	193	9	c2	c2	PROPN
ap-3511	193	10	and	and	CCONJ
ap-3511	193	11	g2	g2	PROPN
ap-3511	193	12	.	.	PUNCT
ap-3511	194	1	irreducible	irreducible	ADJ
ap-3511	194	2	characters	character	NOUN
ap-3511	194	3	are	be	AUX
ap-3511	194	4	linearly	linearly	ADV
ap-3511	194	5	independent	independent	ADJ
ap-3511	194	6	,	,	PUNCT
ap-3511	194	7	as	as	ADV
ap-3511	194	8	well	well	ADV
ap-3511	194	9	as	as	ADP
ap-3511	194	10	functions	function	NOUN
ap-3511	194	11	related	relate	VERB
ap-3511	194	12	to	to	ADP
ap-3511	194	13	the	the	DET
ap-3511	194	14	same	same	ADJ
ap-3511	194	15	character	character	NOUN
ap-3511	194	16	but	but	CCONJ
ap-3511	194	17	labelled	label	VERB
ap-3511	194	18	by	by	ADP
ap-3511	194	19	points	point	NOUN
ap-3511	194	20	of	of	ADP
ap-3511	194	21	two	two	NUM
ap-3511	194	22	different	different	ADJ
ap-3511	194	23	orbits	orbit	NOUN
ap-3511	194	24	.	.	PUNCT
ap-3511	195	1	this	this	DET
ap-3511	195	2	subsection	subsection	NOUN
ap-3511	195	3	describes	describe	VERB
ap-3511	195	4	in	in	ADP
ap-3511	195	5	detail	detail	NOUN
ap-3511	195	6	the	the	DET
ap-3511	195	7	relations	relation	NOUN
ap-3511	195	8	between	between	ADP
ap-3511	195	9	functions	function	NOUN
ap-3511	195	10	corresponding	correspond	VERB
ap-3511	195	11	to	to	ADP
ap-3511	195	12	the	the	DET
ap-3511	195	13	same	same	ADJ
ap-3511	195	14	character	character	NOUN
ap-3511	195	15	and	and	CCONJ
ap-3511	195	16	labelled	label	VERB
ap-3511	195	17	by	by	ADP
ap-3511	195	18	points	point	NOUN
ap-3511	195	19	from	from	ADP
ap-3511	195	20	the	the	DET
ap-3511	195	21	same	same	ADJ
ap-3511	195	22	w	w	NOUN
ap-3511	195	23	–	–	PUNCT
ap-3511	195	24	orbit	orbit	NOUN
ap-3511	195	25	.	.	PUNCT
ap-3511	196	1	theorem	theorem	NOUN
ap-3511	196	2	5	5	NUM
ap-3511	196	3	.	.	PUNCT
ap-3511	197	1	let	let	VERB
ap-3511	197	2	χk	χk	PROPN
ap-3511	197	3	and	and	CCONJ
ap-3511	197	4	χl	χl	NOUN
ap-3511	197	5	be	be	AUX
ap-3511	197	6	any	any	DET
ap-3511	197	7	irreducible	irreducible	ADJ
ap-3511	197	8	characters	character	NOUN
ap-3511	197	9	of	of	ADP
ap-3511	197	10	a	a	DET
ap-3511	197	11	weyl	weyl	VERB
ap-3511	197	12	group	group	NOUN
ap-3511	197	13	w	w	PROPN
ap-3511	197	14	and	and	CCONJ
ap-3511	197	15	λ	λ	PROPN
ap-3511	197	16	∈	∈	PROPN
ap-3511	197	17	rn	rn	PROPN
ap-3511	197	18	.	.	PROPN
ap-3511	197	19	then∑	then∑	NOUN
ap-3511	197	20	w∈w	w∈w	VERB
ap-3511	198	1	χk(w)φlwλ(x	χk(w)φlwλ(x	PROPN
ap-3511	198	2	)	)	PUNCT
ap-3511	198	3	=	=	SYM
ap-3511	198	4	|w	|w	NOUN
ap-3511	199	1	|	|	ADV
ap-3511	199	2	dk	dk	PROPN
ap-3511	199	3	φkλ(x)δkl	φkλ(x)δkl	NOUN
ap-3511	199	4	.	.	PUNCT
ap-3511	200	1	proof	proof	NOUN
ap-3511	200	2	.	.	PUNCT
ap-3511	201	1	we	we	PRON
ap-3511	201	2	write∑	write∑	VERB
ap-3511	201	3	w∈w	w∈w	VERB
ap-3511	201	4	χk(w)φlwλ(x	χk(w)φlwλ(x	PROPN
ap-3511	201	5	)	)	PUNCT
ap-3511	201	6	=	=	PUNCT
ap-3511	202	1	∑	∑	PUNCT
ap-3511	202	2	w∈w	w∈w	VERB
ap-3511	202	3	∑	∑	PROPN
ap-3511	202	4	w̃∈w	w̃∈w	PROPN
ap-3511	202	5	χk(w)χl(w̃)e2πı〈w̃wλ	χk(w)χl(w̃)e2πı〈w̃wλ	PROPN
ap-3511	202	6	,	,	PUNCT
ap-3511	202	7	x	x	NOUN
ap-3511	202	8	〉	〉	NOUN
ap-3511	202	9	=	=	PUNCT
ap-3511	202	10	∑	∑	PUNCT
ap-3511	202	11	w∈w	w∈w	VERB
ap-3511	202	12	∑	∑	PROPN
ap-3511	202	13	w̄∈w	w̄∈w	PROPN
ap-3511	202	14	χk(w)χl(w̄w−1)e2πı〈w̄λ	χk(w)χl(w̄w−1)e2πı〈w̄λ	PROPN
ap-3511	202	15	,	,	PUNCT
ap-3511	202	16	x	x	NOUN
ap-3511	202	17	〉	〉	NUM
ap-3511	202	18	=	=	SYM
ap-3511	202	19	∑	∑	PUNCT
ap-3511	202	20	w̄∈w	w̄∈w	PART
ap-3511	202	21	e2πı〈w̄λ	e2πı〈w̄λ	NOUN
ap-3511	202	22	,	,	PUNCT
ap-3511	202	23	x	x	PUNCT
ap-3511	202	24	〉	〉	NOUN
ap-3511	202	25	∑	∑	ADV
ap-3511	202	26	w∈w	w∈w	VERB
ap-3511	202	27	χl(w̄w−1)χk(w	χl(w̄w−1)χk(w	NOUN
ap-3511	202	28	)	)	PUNCT
ap-3511	202	29	=	=	NOUN
ap-3511	203	1	|w	|w	NOUN
ap-3511	203	2	|	|	ADV
ap-3511	203	3	dk	dk	PROPN
ap-3511	203	4	φkλ(x)δkl	φkλ(x)δkl	NOUN
ap-3511	203	5	.	.	PUNCT
ap-3511	204	1	we	we	PRON
ap-3511	204	2	used	use	VERB
ap-3511	204	3	the	the	DET
ap-3511	204	4	substitution	substitution	NOUN
ap-3511	204	5	w̄	w̄	NOUN
ap-3511	204	6	=	=	SYM
ap-3511	204	7	w̃w	w̃w	PROPN
ap-3511	204	8	,	,	PUNCT
ap-3511	204	9	which	which	PRON
ap-3511	204	10	does	do	AUX
ap-3511	204	11	not	not	PART
ap-3511	204	12	change	change	VERB
ap-3511	204	13	the	the	DET
ap-3511	204	14	summation	summation	NOUN
ap-3511	204	15	limits	limit	NOUN
ap-3511	204	16	.	.	PUNCT
ap-3511	205	1	finally	finally	ADV
ap-3511	205	2	,	,	PUNCT
ap-3511	205	3	we	we	PRON
ap-3511	205	4	applied	apply	VERB
ap-3511	205	5	the	the	DET
ap-3511	205	6	formula	formula	NOUN
ap-3511	205	7	(	(	PUNCT
ap-3511	205	8	3	3	NUM
ap-3511	205	9	)	)	PUNCT
ap-3511	205	10	.	.	PUNCT
ap-3511	206	1	the	the	DET
ap-3511	206	2	theorem	theorem	NOUN
ap-3511	206	3	can	can	AUX
ap-3511	206	4	be	be	AUX
ap-3511	206	5	reformulated	reformulate	VERB
ap-3511	206	6	as	as	SCONJ
ap-3511	206	7	follows	follow	VERB
ap-3511	206	8	.	.	PUNCT
ap-3511	207	1	corollary	corollary	ADJ
ap-3511	207	2	6	6	NUM
ap-3511	207	3	.	.	PUNCT
ap-3511	208	1	letw	letw	NOUN
ap-3511	208	2	be	be	AUX
ap-3511	208	3	a	a	DET
ap-3511	208	4	weyl	weyl	VERB
ap-3511	208	5	group	group	NOUN
ap-3511	208	6	with	with	ADP
ap-3511	208	7	irreducible	irreducible	ADJ
ap-3511	208	8	characters	character	NOUN
ap-3511	208	9	χ1	χ1	NOUN
ap-3511	208	10	,	,	PUNCT
ap-3511	208	11	.	.	PUNCT
ap-3511	208	12	.	.	PUNCT
ap-3511	209	1	.	.	PUNCT
ap-3511	210	1	,	,	PUNCT
ap-3511	210	2	χr	χr	PROPN
ap-3511	210	3	.	.	PUNCT
ap-3511	211	1	we	we	PRON
ap-3511	211	2	fix	fix	VERB
ap-3511	211	3	a	a	DET
ap-3511	211	4	character	character	NOUN
ap-3511	211	5	χl	χl	NOUN
ap-3511	211	6	and	and	CCONJ
ap-3511	211	7	we	we	PRON
ap-3511	211	8	consider	consider	VERB
ap-3511	211	9	the	the	DET
ap-3511	211	10	corresponding	correspond	VERB
ap-3511	211	11	character	character	NOUN
ap-3511	211	12	function	function	NOUN
ap-3511	211	13	φlλ	φlλ	VERB
ap-3511	211	14	as	as	ADP
ap-3511	211	15	a	a	DET
ap-3511	211	16	function	function	NOUN
ap-3511	211	17	of	of	ADP
ap-3511	211	18	x	x	PROPN
ap-3511	211	19	∈	∈	PROPN
ap-3511	211	20	rn	rn	PROPN
ap-3511	211	21	.	.	PUNCT
ap-3511	212	1	the	the	DET
ap-3511	212	2	functions	function	NOUN
ap-3511	212	3	φlwλ	φlwλ	NOUN
ap-3511	212	4	,	,	PUNCT
ap-3511	212	5	where	where	SCONJ
ap-3511	212	6	w	w	NOUN
ap-3511	212	7	∈w	∈w	NOUN
ap-3511	212	8	,	,	PUNCT
ap-3511	212	9	fulfills	fulfill	VERB
ap-3511	212	10	r	r	NOUN
ap-3511	212	11	−	−	PROPN
ap-3511	212	12	1	1	NUM
ap-3511	212	13	linearly	linearly	ADV
ap-3511	212	14	independent	independent	ADJ
ap-3511	212	15	relations	relation	NOUN
ap-3511	212	16	,	,	PUNCT
ap-3511	212	17	namely	namely	ADV
ap-3511	212	18	,	,	PUNCT
ap-3511	212	19	for	for	ADP
ap-3511	212	20	each	each	DET
ap-3511	212	21	k	k	PROPN
ap-3511	212	22	6=	6=	PROPN
ap-3511	212	23	l	l	PROPN
ap-3511	212	24	,	,	PUNCT
ap-3511	212	25	∑	∑	ADP
ap-3511	212	26	w∈w	w∈w	VERB
ap-3511	212	27	χk(w)φlwλ(x	χk(w)φlwλ(x	PROPN
ap-3511	212	28	)	)	PUNCT
ap-3511	212	29	=	=	SYM
ap-3511	212	30	0	0	NUM
ap-3511	212	31	.	.	NOUN
ap-3511	212	32	5	5	NUM
ap-3511	212	33	.	.	X
ap-3511	212	34	character	character	NOUN
ap-3511	212	35	functions	function	NOUN
ap-3511	212	36	related	relate	VERB
ap-3511	212	37	to	to	ADP
ap-3511	212	38	weyl	weyl	VERB
ap-3511	212	39	groups	group	NOUN
ap-3511	212	40	of	of	ADP
ap-3511	212	41	rank	rank	NOUN
ap-3511	212	42	2	2	NUM
ap-3511	212	43	and	and	CCONJ
ap-3511	212	44	3	3	NUM
ap-3511	212	45	character	character	NOUN
ap-3511	212	46	tables	table	NOUN
ap-3511	212	47	of	of	ADP
ap-3511	212	48	all	all	DET
ap-3511	212	49	the	the	DET
ap-3511	212	50	weyl	weyl	VERB
ap-3511	212	51	groups	group	NOUN
ap-3511	212	52	of	of	ADP
ap-3511	212	53	rank	rank	NOUN
ap-3511	212	54	≤	≤	NUM
ap-3511	212	55	4	4	NUM
ap-3511	212	56	can	can	AUX
ap-3511	212	57	be	be	AUX
ap-3511	212	58	found	find	VERB
ap-3511	212	59	for	for	ADP
ap-3511	212	60	example	example	NOUN
ap-3511	212	61	in	in	ADP
ap-3511	212	62	[	[	X
ap-3511	212	63	12	12	NUM
ap-3511	212	64	]	]	PUNCT
ap-3511	212	65	.	.	PUNCT
ap-3511	213	1	some	some	PRON
ap-3511	213	2	of	of	ADP
ap-3511	213	3	them	they	PRON
ap-3511	213	4	are	be	AUX
ap-3511	213	5	quite	quite	ADV
ap-3511	213	6	extensive	extensive	ADJ
ap-3511	213	7	,	,	PUNCT
ap-3511	213	8	therefore	therefore	ADV
ap-3511	213	9	,	,	PUNCT
ap-3511	213	10	we	we	PRON
ap-3511	213	11	give	give	VERB
ap-3511	213	12	here	here	ADV
ap-3511	213	13	examples	example	NOUN
ap-3511	213	14	of	of	ADP
ap-3511	213	15	groups	group	NOUN
ap-3511	213	16	of	of	ADP
ap-3511	213	17	rank	rank	NOUN
ap-3511	213	18	2	2	NUM
ap-3511	213	19	and	and	CCONJ
ap-3511	213	20	3	3	NUM
ap-3511	213	21	.	.	NOUN
ap-3511	213	22	5.1	5.1	NUM
ap-3511	213	23	.	.	PUNCT
ap-3511	214	1	weyl	weyl	VERB
ap-3511	214	2	groups	group	NOUN
ap-3511	214	3	of	of	ADP
ap-3511	214	4	rank	rank	NOUN
ap-3511	214	5	2	2	NUM
ap-3511	214	6	let	let	VERB
ap-3511	214	7	us	we	PRON
ap-3511	214	8	consider	consider	VERB
ap-3511	214	9	the	the	DET
ap-3511	214	10	irreducible	irreducible	ADJ
ap-3511	214	11	weyl	weyl	VERB
ap-3511	214	12	groups	group	NOUN
ap-3511	214	13	of	of	ADP
ap-3511	214	14	rank	rank	NOUN
ap-3511	214	15	two	two	NUM
ap-3511	214	16	,	,	PUNCT
ap-3511	214	17	namely	namely	ADV
ap-3511	214	18	a2	a2	PROPN
ap-3511	214	19	,	,	PUNCT
ap-3511	214	20	c2	c2	PROPN
ap-3511	214	21	and	and	CCONJ
ap-3511	214	22	g2	g2	PROPN
ap-3511	214	23	.	.	PUNCT
ap-3511	215	1	their	their	PRON
ap-3511	215	2	conjugacy	conjugacy	ADJ
ap-3511	215	3	classes	class	NOUN
ap-3511	215	4	are	be	AUX
ap-3511	215	5	the	the	DET
ap-3511	215	6	following	follow	VERB
ap-3511	215	7	:	:	PUNCT
ap-3511	215	8	a2	a2	PROPN
ap-3511	215	9	:	:	PUNCT
ap-3511	215	10	c1	c1	PROPN
ap-3511	215	11	=	=	PUNCT
ap-3511	215	12	{	{	PUNCT
ap-3511	215	13	i	i	PROPN
ap-3511	215	14	d	d	PROPN
ap-3511	215	15	}	}	PUNCT
ap-3511	215	16	,	,	PUNCT
ap-3511	215	17	c2	c2	PROPN
ap-3511	215	18	=	=	SYM
ap-3511	215	19	{	{	PUNCT
ap-3511	215	20	r1r2	r1r2	NOUN
ap-3511	215	21	,	,	PUNCT
ap-3511	215	22	r2r1	r2r1	ADJ
ap-3511	215	23	}	}	PUNCT
ap-3511	215	24	,	,	PUNCT
ap-3511	215	25	c3	c3	PROPN
ap-3511	215	26	=	=	PUNCT
ap-3511	215	27	{	{	PUNCT
ap-3511	215	28	r1	r1	PROPN
ap-3511	215	29	,	,	PUNCT
ap-3511	215	30	r2	r2	PROPN
ap-3511	215	31	,	,	PUNCT
ap-3511	215	32	r1r2r1	r1r2r1	NOUN
ap-3511	215	33	}	}	PUNCT
ap-3511	215	34	,	,	PUNCT
ap-3511	215	35	c2	c2	PROPN
ap-3511	215	36	:	:	PUNCT
ap-3511	215	37	c1	c1	PROPN
ap-3511	215	38	=	=	PUNCT
ap-3511	215	39	{	{	PUNCT
ap-3511	215	40	i	i	PROPN
ap-3511	215	41	d	d	PROPN
ap-3511	215	42	}	}	PUNCT
ap-3511	215	43	,	,	PUNCT
ap-3511	215	44	c2	c2	PROPN
ap-3511	215	45	=	=	SYM
ap-3511	215	46	{	{	PUNCT
ap-3511	215	47	(	(	PUNCT
ap-3511	215	48	r1r2)2	r1r2)2	NOUN
ap-3511	215	49	}	}	PUNCT
ap-3511	215	50	,	,	PUNCT
ap-3511	215	51	c3	c3	PROPN
ap-3511	215	52	=	=	PRON
ap-3511	215	53	{	{	PUNCT
ap-3511	215	54	r1r2	r1r2	NOUN
ap-3511	215	55	,	,	PUNCT
ap-3511	215	56	r2r1	r2r1	ADJ
ap-3511	215	57	}	}	PUNCT
ap-3511	215	58	,	,	PUNCT
ap-3511	215	59	c4	c4	NOUN
ap-3511	215	60	=	=	SYM
ap-3511	215	61	{	{	PUNCT
ap-3511	215	62	r1	r1	PROPN
ap-3511	215	63	,	,	PUNCT
ap-3511	215	64	r1r2r1	r1r2r1	NOUN
ap-3511	215	65	}	}	PUNCT
ap-3511	215	66	,	,	PUNCT
ap-3511	215	67	c5	c5	PROPN
ap-3511	215	68	=	=	PUNCT
ap-3511	215	69	{	{	PUNCT
ap-3511	215	70	r2	r2	PROPN
ap-3511	215	71	,	,	PUNCT
ap-3511	215	72	r2r1r2	r2r1r2	NOUN
ap-3511	215	73	}	}	PUNCT
ap-3511	215	74	,	,	PUNCT
ap-3511	215	75	g2	g2	PROPN
ap-3511	215	76	:	:	PUNCT
ap-3511	215	77	c1	c1	PROPN
ap-3511	215	78	=	=	PUNCT
ap-3511	215	79	{	{	PUNCT
ap-3511	215	80	i	i	PROPN
ap-3511	215	81	d	d	PROPN
ap-3511	215	82	}	}	PUNCT
ap-3511	215	83	,	,	PUNCT
ap-3511	215	84	c2	c2	PROPN
ap-3511	215	85	=	=	SYM
ap-3511	215	86	{	{	PUNCT
ap-3511	215	87	(	(	PUNCT
ap-3511	215	88	r1r2)3	r1r2)3	NUM
ap-3511	215	89	}	}	PUNCT
ap-3511	215	90	,	,	PUNCT
ap-3511	215	91	c3	c3	PROPN
ap-3511	215	92	=	=	PRON
ap-3511	215	93	{	{	PUNCT
ap-3511	215	94	(	(	PUNCT
ap-3511	215	95	r1r2)2	r1r2)2	NOUN
ap-3511	215	96	,	,	PUNCT
ap-3511	215	97	(	(	PUNCT
ap-3511	215	98	r2r1)2	r2r1)2	ADJ
ap-3511	215	99	}	}	PUNCT
ap-3511	215	100	,	,	PUNCT
ap-3511	215	101	c4	c4	NOUN
ap-3511	215	102	=	=	SYM
ap-3511	215	103	{	{	PUNCT
ap-3511	215	104	r1r2	r1r2	NOUN
ap-3511	215	105	,	,	PUNCT
ap-3511	215	106	r2r1	r2r1	ADJ
ap-3511	215	107	}	}	PUNCT
ap-3511	215	108	,	,	PUNCT
ap-3511	215	109	c5	c5	PROPN
ap-3511	215	110	=	=	PROPN
ap-3511	215	111	{	{	PUNCT
ap-3511	215	112	r1	r1	PROPN
ap-3511	215	113	,	,	PUNCT
ap-3511	215	114	r2r1r2	r2r1r2	VERB
ap-3511	215	115	,	,	PUNCT
ap-3511	215	116	(	(	PUNCT
ap-3511	215	117	r1r2)4r1	r1r2)4r1	NOUN
ap-3511	215	118	}	}	PUNCT
ap-3511	215	119	,	,	PUNCT
ap-3511	215	120	c6	c6	PROPN
ap-3511	215	121	=	=	PUNCT
ap-3511	215	122	{	{	PUNCT
ap-3511	215	123	r2	r2	PROPN
ap-3511	215	124	,	,	PUNCT
ap-3511	215	125	r1r2r1	r1r2r1	NOUN
ap-3511	215	126	,	,	PUNCT
ap-3511	215	127	(	(	PUNCT
ap-3511	215	128	r2r1)4r2	r2r1)4r2	NOUN
ap-3511	215	129	}	}	PUNCT
ap-3511	215	130	.	.	PUNCT
ap-3511	216	1	the	the	DET
ap-3511	216	2	irreducible	irreducible	ADJ
ap-3511	216	3	characters	character	NOUN
ap-3511	216	4	of	of	ADP
ap-3511	216	5	weyl	weyl	VERB
ap-3511	216	6	groups	group	NOUN
ap-3511	216	7	of	of	ADP
ap-3511	216	8	rank	rank	NOUN
ap-3511	216	9	two	two	NUM
ap-3511	216	10	are	be	AUX
ap-3511	216	11	listed	list	VERB
ap-3511	216	12	in	in	ADP
ap-3511	216	13	table	table	NOUN
ap-3511	216	14	1	1	NUM
ap-3511	216	15	.	.	PUNCT
ap-3511	217	1	the	the	DET
ap-3511	217	2	trivial	trivial	ADJ
ap-3511	217	3	and	and	CCONJ
ap-3511	217	4	the	the	DET
ap-3511	217	5	alternating	alternate	VERB
ap-3511	217	6	characters	character	NOUN
ap-3511	217	7	correspond	correspond	VERB
ap-3511	217	8	to	to	ADP
ap-3511	217	9	c	c	NOUN
ap-3511	217	10	–	–	PUNCT
ap-3511	217	11	and	and	CCONJ
ap-3511	217	12	s	s	PROPN
ap-3511	217	13	–	–	PUNCT
ap-3511	217	14	orbit	orbit	NOUN
ap-3511	217	15	functions	function	NOUN
ap-3511	217	16	.	.	PUNCT
ap-3511	218	1	for	for	ADP
ap-3511	218	2	the	the	DET
ap-3511	218	3	case	case	NOUN
ap-3511	218	4	of	of	ADP
ap-3511	218	5	c2	c2	PROPN
ap-3511	218	6	and	and	CCONJ
ap-3511	218	7	g2	g2	PROPN
ap-3511	218	8	,	,	PUNCT
ap-3511	218	9	character	character	NOUN
ap-3511	218	10	χ3	χ3	PROPN
ap-3511	218	11	gives	give	VERB
ap-3511	218	12	the	the	DET
ap-3511	218	13	ss	ss	NOUN
ap-3511	218	14	–	–	PUNCT
ap-3511	218	15	function	function	NOUN
ap-3511	218	16	and	and	CCONJ
ap-3511	218	17	χ4	χ4	NOUN
ap-3511	218	18	the	the	DET
ap-3511	218	19	sl	sl	PROPN
ap-3511	218	20	–	–	PUNCT
ap-3511	218	21	function	function	NOUN
ap-3511	218	22	.	.	PUNCT
ap-3511	219	1	therefore	therefore	ADV
ap-3511	219	2	,	,	PUNCT
ap-3511	219	3	the	the	DET
ap-3511	219	4	weyl	weyl	VERB
ap-3511	219	5	groups	group	NOUN
ap-3511	219	6	of	of	ADP
ap-3511	219	7	rank	rank	NOUN
ap-3511	219	8	two	two	NUM
ap-3511	219	9	give	give	VERB
ap-3511	219	10	four	four	NUM
ap-3511	219	11	new	new	ADJ
ap-3511	219	12	families	family	NOUN
ap-3511	219	13	of	of	ADP
ap-3511	219	14	functions	function	NOUN
ap-3511	219	15	.	.	PUNCT
ap-3511	220	1	their	their	PRON
ap-3511	220	2	explicit	explicit	ADJ
ap-3511	220	3	formulas	formula	NOUN
ap-3511	220	4	are	be	AUX
ap-3511	220	5	the	the	DET
ap-3511	220	6	following	follow	VERB
ap-3511	220	7	:	:	PUNCT
ap-3511	220	8	a2	a2	NOUN
ap-3511	220	9	:	:	PUNCT
ap-3511	220	10	φ3	φ3	PROPN
ap-3511	220	11	λ(x	λ(x	PROPN
ap-3511	220	12	)	)	PUNCT
ap-3511	221	1	=	=	SYM
ap-3511	221	2	2e2πı〈λ	2e2πı〈λ	NUM
ap-3511	221	3	,	,	PUNCT
ap-3511	221	4	x	x	NOUN
ap-3511	221	5	〉	〉	NOUN
ap-3511	221	6	−	−	PROPN
ap-3511	221	7	e2πı〈r2r1λ	e2πı〈r2r1λ	PROPN
ap-3511	221	8	,	,	PUNCT
ap-3511	221	9	x	x	NOUN
ap-3511	221	10	〉	〉	NOUN
ap-3511	221	11	−	−	NOUN
ap-3511	221	12	e2πı〈r1r2λ	e2πı〈r1r2λ	NOUN
ap-3511	221	13	,	,	PUNCT
ap-3511	221	14	x	x	NOUN
ap-3511	221	15	〉	〉	NUM
ap-3511	221	16	,	,	PUNCT
ap-3511	221	17	c2	c2	PROPN
ap-3511	221	18	:	:	PUNCT
ap-3511	221	19	φ5	φ5	PROPN
ap-3511	221	20	λ(x	λ(x	PROPN
ap-3511	221	21	)	)	PUNCT
ap-3511	221	22	=	=	SYM
ap-3511	222	1	2e2πı〈λ	2e2πı〈λ	NUM
ap-3511	222	2	,	,	PUNCT
ap-3511	222	3	x	x	NOUN
ap-3511	222	4	〉	〉	NOUN
ap-3511	222	5	−	−	NOUN
ap-3511	222	6	2e2πı〈(r1r2)2λ	2e2πı〈(r1r2)2λ	NUM
ap-3511	222	7	,	,	PUNCT
ap-3511	222	8	x	x	NOUN
ap-3511	222	9	〉	〉	PROPN
ap-3511	222	10	,	,	PUNCT
ap-3511	222	11	g2	g2	PROPN
ap-3511	222	12	:	:	PUNCT
ap-3511	222	13	φ5	φ5	PROPN
ap-3511	222	14	λ(x	λ(x	PROPN
ap-3511	222	15	)	)	PUNCT
ap-3511	222	16	=	=	SYM
ap-3511	222	17	2e2πı〈λ	2e2πı〈λ	NUM
ap-3511	222	18	,	,	PUNCT
ap-3511	222	19	x	x	NOUN
ap-3511	222	20	〉	〉	NOUN
ap-3511	222	21	+	+	CCONJ
ap-3511	222	22	2e2πı〈(r1r2)3λ	2e2πı〈(r1r2)3λ	NUM
ap-3511	222	23	,	,	PUNCT
ap-3511	222	24	x	x	NOUN
ap-3511	222	25	〉	〉	NOUN
ap-3511	222	26	−	−	NOUN
ap-3511	222	27	e2πı〈(r1r2)2λ	e2πı〈(r1r2)2λ	NOUN
ap-3511	222	28	,	,	PUNCT
ap-3511	222	29	x	x	NOUN
ap-3511	222	30	〉	〉	NOUN
ap-3511	222	31	−	−	PROPN
ap-3511	222	32	e2πı〈(r2r1)2λ	e2πı〈(r2r1)2λ	NOUN
ap-3511	222	33	,	,	PUNCT
ap-3511	222	34	x	x	NOUN
ap-3511	222	35	〉	〉	NOUN
ap-3511	222	36	−	−	NOUN
ap-3511	222	37	e2πı〈r1r2λ	e2πı〈r1r2λ	NOUN
ap-3511	222	38	,	,	PUNCT
ap-3511	222	39	x	x	NOUN
ap-3511	222	40	〉	〉	NOUN
ap-3511	222	41	−	−	PROPN
ap-3511	222	42	e2πı〈r2r1λ	e2πı〈r2r1λ	PROPN
ap-3511	222	43	,	,	PUNCT
ap-3511	222	44	x	x	PROPN
ap-3511	222	45	〉	〉	NOUN
ap-3511	222	46	,	,	PUNCT
ap-3511	222	47	φ6	φ6	NOUN
ap-3511	222	48	λ(x	λ(x	PROPN
ap-3511	222	49	)	)	PUNCT
ap-3511	222	50	=	=	SYM
ap-3511	223	1	2e2πı〈λ	2e2πı〈λ	NUM
ap-3511	223	2	,	,	PUNCT
ap-3511	223	3	x	x	NOUN
ap-3511	223	4	〉	〉	NOUN
ap-3511	223	5	−	−	NOUN
ap-3511	223	6	2e2πı〈(r1r2)3λ	2e2πı〈(r1r2)3λ	NUM
ap-3511	223	7	,	,	PUNCT
ap-3511	223	8	x	x	NOUN
ap-3511	223	9	〉	〉	NOUN
ap-3511	223	10	−	−	NOUN
ap-3511	223	11	e2πı〈(r1r2)2λ	e2πı〈(r1r2)2λ	NOUN
ap-3511	223	12	,	,	PUNCT
ap-3511	223	13	x	x	NOUN
ap-3511	223	14	〉	〉	NOUN
ap-3511	223	15	−	−	PROPN
ap-3511	223	16	e2πı〈(r2r1)2λ	e2πı〈(r2r1)2λ	NOUN
ap-3511	223	17	,	,	PUNCT
ap-3511	223	18	x	x	NOUN
ap-3511	223	19	〉	〉	NOUN
ap-3511	223	20	+	+	CCONJ
ap-3511	223	21	e2πı〈r1r2λ	e2πı〈r1r2λ	NOUN
ap-3511	223	22	,	,	PUNCT
ap-3511	223	23	x	x	NOUN
ap-3511	223	24	〉	〉	NOUN
ap-3511	223	25	+	+	PROPN
ap-3511	223	26	e2πı〈r2r1λ	e2πı〈r2r1λ	PROPN
ap-3511	223	27	,	,	PUNCT
ap-3511	223	28	x	x	PROPN
ap-3511	223	29	〉	〉	NOUN
ap-3511	223	30	.	.	NOUN
ap-3511	223	31	444	444	NUM
ap-3511	223	32	vol	vol	NOUN
ap-3511	223	33	.	.	PUNCT
ap-3511	224	1	56	56	NUM
ap-3511	224	2	no	no	NOUN
ap-3511	224	3	.	.	PUNCT
ap-3511	225	1	6/2016	6/2016	NUM
ap-3511	225	2	on	on	ADP
ap-3511	225	3	generalization	generalization	NOUN
ap-3511	225	4	of	of	ADP
ap-3511	225	5	special	special	ADJ
ap-3511	225	6	functions	function	NOUN
ap-3511	225	7	related	relate	VERB
ap-3511	225	8	to	to	ADP
ap-3511	225	9	weyl	weyl	VERB
ap-3511	225	10	groups	group	NOUN
ap-3511	225	11	figure	figure	VERB
ap-3511	225	12	1	1	NUM
ap-3511	225	13	.	.	PUNCT
ap-3511	226	1	the	the	DET
ap-3511	226	2	contour	contour	NOUN
ap-3511	226	3	plot	plot	NOUN
ap-3511	226	4	of	of	ADP
ap-3511	226	5	the	the	DET
ap-3511	226	6	real	real	ADJ
ap-3511	226	7	part	part	NOUN
ap-3511	226	8	(	(	PUNCT
ap-3511	226	9	left	left	ADJ
ap-3511	226	10	)	)	PUNCT
ap-3511	226	11	and	and	CCONJ
ap-3511	226	12	the	the	DET
ap-3511	226	13	imaginary	imaginary	ADJ
ap-3511	226	14	part	part	NOUN
ap-3511	226	15	(	(	PUNCT
ap-3511	226	16	right	right	NOUN
ap-3511	226	17	)	)	PUNCT
ap-3511	226	18	of	of	ADP
ap-3511	226	19	the	the	DET
ap-3511	226	20	function	function	NOUN
ap-3511	226	21	φ3((1	φ3((1	NOUN
ap-3511	226	22	,	,	PUNCT
ap-3511	226	23	2	2	NUM
ap-3511	226	24	)	)	PUNCT
ap-3511	226	25	,	,	PUNCT
ap-3511	226	26	x	x	X
ap-3511	226	27	)	)	PUNCT
ap-3511	226	28	of	of	ADP
ap-3511	226	29	the	the	DET
ap-3511	226	30	weyl	weyl	PROPN
ap-3511	226	31	group	group	NOUN
ap-3511	226	32	w	w	PROPN
ap-3511	226	33	(	(	PUNCT
ap-3511	226	34	a2	a2	PROPN
ap-3511	226	35	)	)	PUNCT
ap-3511	226	36	.	.	PUNCT
ap-3511	227	1	the	the	DET
ap-3511	227	2	triangle	triangle	NOUN
ap-3511	227	3	denotes	denote	VERB
ap-3511	227	4	the	the	DET
ap-3511	227	5	fundamental	fundamental	ADJ
ap-3511	227	6	domain	domain	NOUN
ap-3511	227	7	f	f	PROPN
ap-3511	227	8	of	of	ADP
ap-3511	227	9	the	the	DET
ap-3511	227	10	affine	affine	NOUN
ap-3511	227	11	weyl	weyl	PROPN
ap-3511	227	12	group	group	NOUN
ap-3511	227	13	.	.	PUNCT
ap-3511	228	1	figure	figure	NOUN
ap-3511	228	2	2	2	NUM
ap-3511	228	3	.	.	PUNCT
ap-3511	229	1	the	the	DET
ap-3511	229	2	contour	contour	NOUN
ap-3511	229	3	plot	plot	NOUN
ap-3511	229	4	(	(	PUNCT
ap-3511	229	5	real	real	ADJ
ap-3511	229	6	)	)	PUNCT
ap-3511	229	7	of	of	ADP
ap-3511	229	8	the	the	DET
ap-3511	229	9	function	function	NOUN
ap-3511	229	10	φ5((2	φ5((2	PROPN
ap-3511	229	11	,	,	PUNCT
ap-3511	229	12	1	1	NUM
ap-3511	229	13	)	)	PUNCT
ap-3511	229	14	,	,	PUNCT
ap-3511	229	15	x	x	X
ap-3511	229	16	)	)	PUNCT
ap-3511	229	17	(	(	PUNCT
ap-3511	229	18	left	leave	VERB
ap-3511	229	19	)	)	PUNCT
ap-3511	229	20	and	and	CCONJ
ap-3511	229	21	contour	contour	NOUN
ap-3511	229	22	plot	plot	NOUN
ap-3511	229	23	(	(	PUNCT
ap-3511	229	24	pure	pure	ADJ
ap-3511	229	25	imaginary	imaginary	ADJ
ap-3511	229	26	)	)	PUNCT
ap-3511	229	27	of	of	ADP
ap-3511	229	28	the	the	DET
ap-3511	229	29	function	function	NOUN
ap-3511	229	30	φ5((2	φ5((2	PROPN
ap-3511	229	31	,	,	PUNCT
ap-3511	229	32	1	1	NUM
ap-3511	229	33	)	)	PUNCT
ap-3511	229	34	,	,	PUNCT
ap-3511	229	35	x	x	X
ap-3511	229	36	)	)	PUNCT
ap-3511	229	37	(	(	PUNCT
ap-3511	229	38	right	right	NOUN
ap-3511	229	39	)	)	PUNCT
ap-3511	229	40	of	of	ADP
ap-3511	229	41	the	the	DET
ap-3511	229	42	weyl	weyl	PROPN
ap-3511	229	43	group	group	NOUN
ap-3511	229	44	w	w	PROPN
ap-3511	229	45	(	(	PUNCT
ap-3511	229	46	g2	g2	PROPN
ap-3511	229	47	)	)	PUNCT
ap-3511	229	48	.	.	PUNCT
ap-3511	230	1	the	the	DET
ap-3511	230	2	triangle	triangle	NOUN
ap-3511	230	3	denotes	denote	VERB
ap-3511	230	4	the	the	DET
ap-3511	230	5	fundamental	fundamental	ADJ
ap-3511	230	6	domain	domain	NOUN
ap-3511	230	7	f	f	PROPN
ap-3511	230	8	of	of	ADP
ap-3511	230	9	the	the	DET
ap-3511	230	10	affine	affine	NOUN
ap-3511	230	11	weyl	weyl	VERB
ap-3511	230	12	group	group	NOUN
ap-3511	230	13	.	.	PUNCT
ap-3511	231	1	from	from	ADP
ap-3511	231	2	the	the	DET
ap-3511	231	3	properties	property	NOUN
ap-3511	231	4	of	of	ADP
ap-3511	231	5	orbits	orbit	NOUN
ap-3511	231	6	we	we	PRON
ap-3511	231	7	have	have	VERB
ap-3511	231	8	also	also	ADV
ap-3511	231	9	c2	c2	PROPN
ap-3511	231	10	:	:	PUNCT
ap-3511	231	11	φkλ(x	φkλ(x	X
ap-3511	231	12	)	)	PUNCT
ap-3511	232	1	=	=	PRON
ap-3511	232	2	{	{	PUNCT
ap-3511	232	3	real	real	ADJ
ap-3511	232	4	,	,	PUNCT
ap-3511	232	5	k	k	PROPN
ap-3511	232	6	=	=	SYM
ap-3511	232	7	1	1	NUM
ap-3511	232	8	,	,	PUNCT
ap-3511	232	9	2	2	NUM
ap-3511	232	10	,	,	PUNCT
ap-3511	232	11	3	3	NUM
ap-3511	232	12	,	,	PUNCT
ap-3511	232	13	4	4	NUM
ap-3511	232	14	,	,	PUNCT
ap-3511	232	15	pure	pure	ADJ
ap-3511	232	16	imaginary	imaginary	ADJ
ap-3511	232	17	,	,	PUNCT
ap-3511	232	18	k	k	PROPN
ap-3511	232	19	=	=	SYM
ap-3511	232	20	5	5	NUM
ap-3511	232	21	,	,	PUNCT
ap-3511	232	22	g2	g2	PROPN
ap-3511	232	23	:	:	PUNCT
ap-3511	232	24	φkλ(x	φkλ(x	X
ap-3511	232	25	)	)	PUNCT
ap-3511	232	26	=	=	PRON
ap-3511	233	1	{	{	PUNCT
ap-3511	233	2	real	real	ADJ
ap-3511	233	3	,	,	PUNCT
ap-3511	233	4	k	k	PROPN
ap-3511	233	5	=	=	SYM
ap-3511	233	6	1	1	NUM
ap-3511	233	7	,	,	PUNCT
ap-3511	233	8	2	2	NUM
ap-3511	233	9	,	,	PUNCT
ap-3511	233	10	5	5	NUM
ap-3511	233	11	,	,	PUNCT
ap-3511	233	12	pure	pure	ADJ
ap-3511	233	13	imaginary	imaginary	ADJ
ap-3511	233	14	,	,	PUNCT
ap-3511	233	15	k	k	PROPN
ap-3511	233	16	=	=	SYM
ap-3511	233	17	3	3	NUM
ap-3511	233	18	,	,	PUNCT
ap-3511	233	19	4	4	NUM
ap-3511	233	20	,	,	PUNCT
ap-3511	233	21	6	6	NUM
ap-3511	233	22	.	.	PUNCT
ap-3511	233	23	linear	linear	ADJ
ap-3511	233	24	dependence	dependence	NOUN
ap-3511	233	25	:	:	PUNCT
ap-3511	233	26	a2	a2	NOUN
ap-3511	233	27	:	:	PUNCT
ap-3511	233	28	φ3	φ3	PROPN
ap-3511	233	29	λ(x	λ(x	PROPN
ap-3511	233	30	)	)	PUNCT
ap-3511	234	1	+	+	CCONJ
ap-3511	234	2	φ3	φ3	PROPN
ap-3511	234	3	r1r2λ(x	r1r2λ(x	PROPN
ap-3511	234	4	)	)	PUNCT
ap-3511	235	1	+	+	NUM
ap-3511	235	2	φ3	φ3	PROPN
ap-3511	235	3	r2r1λ(x	r2r1λ(x	PROPN
ap-3511	235	4	)	)	PUNCT
ap-3511	235	5	=	=	SYM
ap-3511	235	6	0	0	NUM
ap-3511	235	7	,	,	PUNCT
ap-3511	235	8	φ3	φ3	PROPN
ap-3511	235	9	r1λ(x	r1λ(x	PROPN
ap-3511	235	10	)	)	PUNCT
ap-3511	236	1	+	+	NUM
ap-3511	236	2	φ3	φ3	PROPN
ap-3511	236	3	r2λ(x	r2λ(x	PROPN
ap-3511	236	4	)	)	PUNCT
ap-3511	237	1	+	+	CCONJ
ap-3511	237	2	φ3	φ3	PROPN
ap-3511	237	3	r1r2r1λ(x	r1r2r1λ(x	NUM
ap-3511	237	4	)	)	PUNCT
ap-3511	238	1	=	=	SYM
ap-3511	238	2	0	0	NUM
ap-3511	238	3	,	,	PUNCT
ap-3511	238	4	c2	c2	PROPN
ap-3511	238	5	:	:	PUNCT
ap-3511	238	6	φ3	φ3	PROPN
ap-3511	238	7	λ(x	λ(x	PROPN
ap-3511	238	8	)	)	PUNCT
ap-3511	239	1	+	+	NUM
ap-3511	239	2	φ3	φ3	NOUN
ap-3511	239	3	(	(	PUNCT
ap-3511	239	4	r1r2)2λ(x	r1r2)2λ(x	NOUN
ap-3511	239	5	)	)	PUNCT
ap-3511	239	6	=	=	SYM
ap-3511	239	7	0	0	NUM
ap-3511	239	8	,	,	PUNCT
ap-3511	239	9	φ3	φ3	PROPN
ap-3511	239	10	r1λ(x	r1λ(x	PROPN
ap-3511	239	11	)	)	PUNCT
ap-3511	240	1	+	+	CCONJ
ap-3511	240	2	φ3	φ3	PROPN
ap-3511	240	3	r2r1r2λ(x	r2r1r2λ(x	NUM
ap-3511	240	4	)	)	PUNCT
ap-3511	240	5	=	=	SYM
ap-3511	240	6	0	0	NUM
ap-3511	240	7	,	,	PUNCT
ap-3511	240	8	φ3	φ3	PROPN
ap-3511	240	9	r2λ(x	r2λ(x	PROPN
ap-3511	240	10	)	)	PUNCT
ap-3511	241	1	+	+	CCONJ
ap-3511	241	2	φ3	φ3	PROPN
ap-3511	241	3	r1r2r1λ(x	r1r2r1λ(x	NUM
ap-3511	241	4	)	)	PUNCT
ap-3511	242	1	=	=	SYM
ap-3511	242	2	0	0	NUM
ap-3511	242	3	,	,	PUNCT
ap-3511	242	4	φ3	φ3	PROPN
ap-3511	242	5	r1λ(x	r1λ(x	PROPN
ap-3511	242	6	)	)	PUNCT
ap-3511	243	1	+	+	CCONJ
ap-3511	243	2	φ3	φ3	PROPN
ap-3511	243	3	r2r1λ(x	r2r1λ(x	PROPN
ap-3511	243	4	)	)	PUNCT
ap-3511	243	5	=	=	SYM
ap-3511	244	1	0	0	X
ap-3511	244	2	.	.	PUNCT
ap-3511	245	1	contour	contour	NOUN
ap-3511	245	2	plots	plot	NOUN
ap-3511	245	3	of	of	ADP
ap-3511	245	4	some	some	DET
ap-3511	245	5	character	character	NOUN
ap-3511	245	6	functions	function	NOUN
ap-3511	245	7	related	relate	VERB
ap-3511	245	8	to	to	ADP
ap-3511	245	9	weyl	weyl	VERB
ap-3511	245	10	groups	group	NOUN
ap-3511	245	11	of	of	ADP
ap-3511	245	12	rank	rank	NOUN
ap-3511	245	13	two	two	NUM
ap-3511	245	14	are	be	AUX
ap-3511	245	15	depicted	depict	VERB
ap-3511	245	16	in	in	ADP
ap-3511	245	17	figures	figure	NOUN
ap-3511	245	18	1	1	NUM
ap-3511	245	19	and	and	CCONJ
ap-3511	245	20	2	2	NUM
ap-3511	245	21	.	.	X
ap-3511	245	22	5.2	5.2	NUM
ap-3511	245	23	.	.	PUNCT
ap-3511	246	1	weyl	weyl	VERB
ap-3511	246	2	groups	group	NOUN
ap-3511	246	3	of	of	ADP
ap-3511	246	4	rank	rank	NOUN
ap-3511	246	5	3	3	NUM
ap-3511	246	6	now	now	ADV
ap-3511	246	7	we	we	PRON
ap-3511	246	8	consider	consider	VERB
ap-3511	246	9	the	the	DET
ap-3511	246	10	irreducible	irreducible	ADJ
ap-3511	246	11	weyl	weyl	VERB
ap-3511	246	12	groups	group	NOUN
ap-3511	246	13	of	of	ADP
ap-3511	246	14	rank	rank	PROPN
ap-3511	246	15	three	three	NUM
ap-3511	246	16	,	,	PUNCT
ap-3511	246	17	namely	namely	ADV
ap-3511	246	18	a3	a3	NOUN
ap-3511	246	19	,	,	PUNCT
ap-3511	246	20	c3	c3	PROPN
ap-3511	246	21	.	.	PUNCT
ap-3511	247	1	their	their	PRON
ap-3511	247	2	character	character	NOUN
ap-3511	247	3	tables	table	NOUN
ap-3511	247	4	are	be	AUX
ap-3511	247	5	to	to	PART
ap-3511	247	6	be	be	AUX
ap-3511	247	7	found	find	VERB
ap-3511	247	8	in	in	ADP
ap-3511	247	9	table	table	NOUN
ap-3511	247	10	2	2	NUM
ap-3511	247	11	.	.	PUNCT
ap-3511	248	1	the	the	DET
ap-3511	248	2	conjugacy	conjugacy	PROPN
ap-3511	248	3	classes	class	NOUN
ap-3511	248	4	of	of	ADP
ap-3511	248	5	the	the	DET
ap-3511	248	6	weyl	weyl	VERB
ap-3511	248	7	group	group	NOUN
ap-3511	248	8	of	of	ADP
ap-3511	248	9	a3	a3	NOUN
ap-3511	248	10	are	be	AUX
ap-3511	248	11	the	the	DET
ap-3511	248	12	following	following	NOUN
ap-3511	248	13	:	:	PUNCT
ap-3511	248	14	a3	a3	NOUN
ap-3511	248	15	:	:	PUNCT
ap-3511	248	16	c1	c1	PROPN
ap-3511	248	17	=	=	PUNCT
ap-3511	248	18	{	{	PUNCT
ap-3511	248	19	i	i	PROPN
ap-3511	248	20	d	d	PROPN
ap-3511	248	21	}	}	PUNCT
ap-3511	248	22	,	,	PUNCT
ap-3511	248	23	c2	c2	PROPN
ap-3511	248	24	=	=	SYM
ap-3511	248	25	{	{	PUNCT
ap-3511	248	26	r1	r1	PROPN
ap-3511	248	27	,	,	PUNCT
ap-3511	248	28	r2	r2	PROPN
ap-3511	248	29	,	,	PUNCT
ap-3511	248	30	r3	r3	PROPN
ap-3511	248	31	,	,	PUNCT
ap-3511	248	32	r1r2r1	r1r2r1	NOUN
ap-3511	248	33	,	,	PUNCT
ap-3511	248	34	r2r3r2	r2r3r2	NOUN
ap-3511	248	35	,	,	PUNCT
ap-3511	248	36	r1r2r3r2r1	r1r2r3r2r1	NOUN
ap-3511	248	37	}	}	PUNCT
ap-3511	248	38	,	,	PUNCT
ap-3511	248	39	c3	c3	PROPN
ap-3511	248	40	=	=	SYM
ap-3511	248	41	{	{	PUNCT
ap-3511	248	42	r1r3	r1r3	PROPN
ap-3511	248	43	,	,	PUNCT
ap-3511	248	44	r2r1r3r2	r2r1r3r2	PROPN
ap-3511	248	45	,	,	PUNCT
ap-3511	248	46	r3r2r3r1r2r3	r3r2r3r1r2r3	PROPN
ap-3511	248	47	}	}	PUNCT
ap-3511	248	48	,	,	PUNCT
ap-3511	248	49	c4	c4	NOUN
ap-3511	248	50	=	=	SYM
ap-3511	248	51	{	{	PUNCT
ap-3511	248	52	r1r2	r1r2	NOUN
ap-3511	248	53	,	,	PUNCT
ap-3511	248	54	r2r1	r2r1	PROPN
ap-3511	248	55	,	,	PUNCT
ap-3511	248	56	r2r3	r2r3	PROPN
ap-3511	248	57	,	,	PUNCT
ap-3511	248	58	r3r2	r3r2	NOUN
ap-3511	248	59	,	,	PUNCT
ap-3511	248	60	r1r3r2r1	r1r3r2r1	NOUN
ap-3511	248	61	,	,	PUNCT
ap-3511	248	62	r1r2r1r3	r1r2r1r3	NOUN
ap-3511	248	63	,	,	PUNCT
ap-3511	248	64	r2r3r2r1	r2r3r2r1	NOUN
ap-3511	248	65	,	,	PUNCT
ap-3511	248	66	r1r2r3r2	r1r2r3r2	NOUN
ap-3511	248	67	}	}	PUNCT
ap-3511	248	68	,	,	PUNCT
ap-3511	248	69	c5	c5	PROPN
ap-3511	248	70	=	=	PROPN
ap-3511	248	71	{	{	PUNCT
ap-3511	248	72	r1r2r3	r1r2r3	PROPN
ap-3511	248	73	,	,	PUNCT
ap-3511	248	74	r2r3r1	r2r3r1	ADJ
ap-3511	248	75	,	,	PUNCT
ap-3511	248	76	r3r1r2	r3r1r2	VERB
ap-3511	248	77	,	,	PUNCT
ap-3511	248	78	r3r2r1	r3r2r1	NOUN
ap-3511	248	79	,	,	PUNCT
ap-3511	248	80	r3r2r3r1r2	r3r2r3r1r2	NUM
ap-3511	248	81	,	,	PUNCT
ap-3511	248	82	r1r2r1r3r2	r1r2r1r3r2	NUM
ap-3511	248	83	}	}	PUNCT
ap-3511	248	84	.	.	PUNCT
ap-3511	249	1	445	445	NUM
ap-3511	249	2	lenka	lenka	PROPN
ap-3511	249	3	háková	háková	PROPN
ap-3511	249	4	,	,	PUNCT
ap-3511	249	5	agnieszka	agnieszka	PROPN
ap-3511	249	6	tereszkiewicz	tereszkiewicz	PROPN
ap-3511	249	7	acta	acta	PROPN
ap-3511	249	8	polytechnica	polytechnica	PROPN
ap-3511	249	9	c1	c1	PROPN
ap-3511	249	10	c2	c2	PROPN
ap-3511	249	11	c3	c3	PROPN
ap-3511	249	12	c4	c4	PROPN
ap-3511	249	13	c5	c5	PROPN
ap-3511	249	14	χ1	χ1	PROPN
ap-3511	249	15	1	1	NUM
ap-3511	249	16	1	1	NUM
ap-3511	249	17	1	1	NUM
ap-3511	249	18	1	1	NUM
ap-3511	249	19	1	1	NUM
ap-3511	249	20	χ2	χ2	NOUN
ap-3511	249	21	1	1	NUM
ap-3511	249	22	−1	−1	NOUN
ap-3511	249	23	1	1	NUM
ap-3511	249	24	1	1	NUM
ap-3511	249	25	−1	−1	NOUN
ap-3511	249	26	χ3	χ3	NOUN
ap-3511	249	27	2	2	NUM
ap-3511	249	28	0	0	NUM
ap-3511	249	29	2	2	NUM
ap-3511	249	30	−1	−1	NOUN
ap-3511	249	31	0	0	NUM
ap-3511	249	32	χ4	χ4	NOUN
ap-3511	249	33	3	3	NUM
ap-3511	249	34	1	1	NUM
ap-3511	249	35	−1	−1	NOUN
ap-3511	249	36	0	0	NUM
ap-3511	249	37	−1	−1	NOUN
ap-3511	249	38	χ5	χ5	NOUN
ap-3511	249	39	3	3	NUM
ap-3511	249	40	−1	−1	NOUN
ap-3511	249	41	−1	−1	NOUN
ap-3511	249	42	0	0	NUM
ap-3511	249	43	1	1	NUM
ap-3511	249	44	c1	c1	PROPN
ap-3511	249	45	c2	c2	PROPN
ap-3511	249	46	c3	c3	PROPN
ap-3511	249	47	c4	c4	PROPN
ap-3511	249	48	c5	c5	PROPN
ap-3511	249	49	c6	c6	PROPN
ap-3511	249	50	c7	c7	PROPN
ap-3511	249	51	c8	c8	PROPN
ap-3511	249	52	c9	c9	PROPN
ap-3511	249	53	c10	c10	PROPN
ap-3511	249	54	χ1	χ1	PROPN
ap-3511	249	55	1	1	NUM
ap-3511	249	56	1	1	NUM
ap-3511	249	57	1	1	NUM
ap-3511	249	58	1	1	NUM
ap-3511	249	59	1	1	NUM
ap-3511	249	60	1	1	NUM
ap-3511	249	61	1	1	NUM
ap-3511	249	62	1	1	NUM
ap-3511	249	63	1	1	NUM
ap-3511	249	64	1	1	NUM
ap-3511	249	65	χ2	χ2	NOUN
ap-3511	249	66	1	1	NUM
ap-3511	249	67	−1	−1	NOUN
ap-3511	249	68	−1	−1	NOUN
ap-3511	249	69	1	1	NUM
ap-3511	249	70	1	1	NUM
ap-3511	249	71	1	1	NUM
ap-3511	249	72	−1	−1	NOUN
ap-3511	249	73	1	1	NUM
ap-3511	249	74	−1	−1	NOUN
ap-3511	249	75	−1	−1	NOUN
ap-3511	249	76	χ3	χ3	NOUN
ap-3511	249	77	1	1	NUM
ap-3511	249	78	1	1	NUM
ap-3511	249	79	−1	−1	NOUN
ap-3511	249	80	1	1	NUM
ap-3511	249	81	−1	−1	NOUN
ap-3511	249	82	−1	−1	NOUN
ap-3511	249	83	−1	−1	NOUN
ap-3511	249	84	1	1	NUM
ap-3511	249	85	1	1	NUM
ap-3511	249	86	−1	−1	NOUN
ap-3511	249	87	χ4	χ4	NOUN
ap-3511	249	88	1	1	NUM
ap-3511	249	89	−1	−1	NOUN
ap-3511	249	90	1	1	NUM
ap-3511	249	91	1	1	NUM
ap-3511	249	92	−1	−1	NOUN
ap-3511	249	93	−1	−1	NOUN
ap-3511	249	94	1	1	NUM
ap-3511	249	95	1	1	NUM
ap-3511	249	96	−1	−1	NOUN
ap-3511	249	97	1	1	NUM
ap-3511	249	98	χ5	χ5	NOUN
ap-3511	249	99	2	2	NUM
ap-3511	249	100	0	0	NUM
ap-3511	249	101	2	2	NUM
ap-3511	249	102	−1	−1	NOUN
ap-3511	249	103	0	0	NUM
ap-3511	249	104	0	0	NUM
ap-3511	249	105	−1	−1	NOUN
ap-3511	249	106	2	2	NUM
ap-3511	249	107	0	0	NUM
ap-3511	249	108	2	2	NUM
ap-3511	249	109	χ6	χ6	NOUN
ap-3511	249	110	2	2	NUM
ap-3511	249	111	0	0	NUM
ap-3511	249	112	−2	−2	NOUN
ap-3511	249	113	−1	−1	NOUN
ap-3511	249	114	0	0	NUM
ap-3511	249	115	0	0	NUM
ap-3511	249	116	1	1	NUM
ap-3511	249	117	2	2	NUM
ap-3511	249	118	0	0	NUM
ap-3511	249	119	−2	−2	NOUN
ap-3511	250	1	χ7	χ7	NOUN
ap-3511	250	2	3	3	NUM
ap-3511	250	3	1	1	NUM
ap-3511	250	4	−1	−1	NOUN
ap-3511	250	5	0	0	NUM
ap-3511	250	6	1	1	NUM
ap-3511	250	7	−1	−1	NOUN
ap-3511	250	8	0	0	NUM
ap-3511	250	9	−1	−1	NOUN
ap-3511	250	10	−1	−1	NOUN
ap-3511	250	11	3	3	NUM
ap-3511	250	12	χ8	χ8	PROPN
ap-3511	250	13	3	3	NUM
ap-3511	250	14	−1	−1	NOUN
ap-3511	250	15	−1	−1	NOUN
ap-3511	250	16	0	0	NUM
ap-3511	250	17	−1	−1	NOUN
ap-3511	250	18	1	1	NUM
ap-3511	250	19	0	0	NUM
ap-3511	250	20	−1	−1	NOUN
ap-3511	250	21	1	1	NUM
ap-3511	250	22	3	3	NUM
ap-3511	250	23	χ9	χ9	NOUN
ap-3511	250	24	3	3	NUM
ap-3511	250	25	1	1	NUM
ap-3511	250	26	1	1	NUM
ap-3511	250	27	0	0	NUM
ap-3511	250	28	−1	−1	NOUN
ap-3511	250	29	1	1	NUM
ap-3511	250	30	0	0	NUM
ap-3511	250	31	−1	−1	NOUN
ap-3511	250	32	−1	−1	NOUN
ap-3511	250	33	−3	−3	NOUN
ap-3511	250	34	χ10	χ10	NOUN
ap-3511	250	35	3	3	NUM
ap-3511	250	36	−1	−1	NOUN
ap-3511	250	37	1	1	NUM
ap-3511	250	38	0	0	NUM
ap-3511	250	39	1	1	NUM
ap-3511	250	40	−1	−1	NOUN
ap-3511	250	41	0	0	NUM
ap-3511	250	42	−1	−1	NOUN
ap-3511	250	43	1	1	NUM
ap-3511	250	44	−3	−3	NOUN
ap-3511	250	45	table	table	NOUN
ap-3511	250	46	2	2	NUM
ap-3511	250	47	.	.	PUNCT
ap-3511	250	48	character	character	NOUN
ap-3511	250	49	tables	table	NOUN
ap-3511	250	50	of	of	ADP
ap-3511	250	51	weyl	weyl	VERB
ap-3511	250	52	groups	group	NOUN
ap-3511	250	53	of	of	ADP
ap-3511	250	54	a3	a3	NOUN
ap-3511	250	55	and	and	CCONJ
ap-3511	250	56	c3	c3	PROPN
ap-3511	250	57	.	.	PUNCT
ap-3511	251	1	the	the	DET
ap-3511	251	2	explicit	explicit	ADJ
ap-3511	251	3	formulas	formula	NOUN
ap-3511	251	4	of	of	ADP
ap-3511	251	5	functions	function	NOUN
ap-3511	251	6	φ3,4,5	φ3,4,5	NOUN
ap-3511	251	7	λ	λ	PROPN
ap-3511	251	8	(	(	PUNCT
ap-3511	251	9	x	x	X
ap-3511	251	10	)	)	PUNCT
ap-3511	251	11	are	be	AUX
ap-3511	251	12	φ3	φ3	NOUN
ap-3511	251	13	λ(x	λ(x	X
ap-3511	251	14	)	)	PUNCT
ap-3511	252	1	=	=	SYM
ap-3511	252	2	2e2πı〈λ	2e2πı〈λ	NUM
ap-3511	252	3	,	,	PUNCT
ap-3511	252	4	x	x	NOUN
ap-3511	252	5	〉	〉	NOUN
ap-3511	252	6	+	+	X
ap-3511	252	7	2e2πı〈r1r3λ	2e2πı〈r1r3λ	NOUN
ap-3511	252	8	,	,	PUNCT
ap-3511	252	9	x	x	X
ap-3511	252	10	〉	〉	NOUN
ap-3511	252	11	+	+	SYM
ap-3511	252	12	2e2πı〈r2r1r3r2λ	2e2πı〈r2r1r3r2λ	NUM
ap-3511	252	13	,	,	PUNCT
ap-3511	252	14	x	x	X
ap-3511	252	15	〉	〉	NOUN
ap-3511	252	16	+	+	CCONJ
ap-3511	252	17	2e2πı〈r3r2r3r1r2r3λ	2e2πı〈r3r2r3r1r2r3λ	NUM
ap-3511	252	18	,	,	PUNCT
ap-3511	252	19	x	x	NOUN
ap-3511	252	20	〉	〉	NOUN
ap-3511	252	21	−	−	NOUN
ap-3511	252	22	e2πı〈r1r2λ	e2πı〈r1r2λ	NOUN
ap-3511	252	23	,	,	PUNCT
ap-3511	252	24	x	x	NOUN
ap-3511	252	25	〉	〉	NOUN
ap-3511	252	26	−	−	PROPN
ap-3511	252	27	e2πı〈r2r1λ	e2πı〈r2r1λ	PROPN
ap-3511	252	28	,	,	PUNCT
ap-3511	252	29	x	x	NOUN
ap-3511	252	30	〉	〉	NOUN
ap-3511	252	31	−	−	PROPN
ap-3511	252	32	e2πı〈r2r3λ	e2πı〈r2r3λ	NOUN
ap-3511	252	33	,	,	PUNCT
ap-3511	252	34	x	x	PROPN
ap-3511	252	35	〉	〉	NOUN
ap-3511	252	36	−	−	PROPN
ap-3511	252	37	e2πı〈r3r2λ	e2πı〈r3r2λ	NOUN
ap-3511	252	38	,	,	PUNCT
ap-3511	252	39	x	x	PROPN
ap-3511	252	40	〉	〉	NOUN
ap-3511	252	41	−	−	PROPN
ap-3511	252	42	e2πı〈r1r3r2r1λ	e2πı〈r1r3r2r1λ	PROPN
ap-3511	252	43	,	,	PUNCT
ap-3511	252	44	x	x	PROPN
ap-3511	252	45	〉	〉	NOUN
ap-3511	252	46	−	−	NOUN
ap-3511	252	47	e2πı〈r1r2r1r3λ	e2πı〈r1r2r1r3λ	NOUN
ap-3511	252	48	,	,	PUNCT
ap-3511	252	49	x	x	NOUN
ap-3511	252	50	〉	〉	NOUN
ap-3511	252	51	−	−	PROPN
ap-3511	252	52	e2πı〈r2r3r2r1λ	e2πı〈r2r3r2r1λ	PROPN
ap-3511	252	53	,	,	PUNCT
ap-3511	252	54	x	x	PROPN
ap-3511	252	55	〉	〉	NOUN
ap-3511	252	56	−	−	X
ap-3511	252	57	e2πı〈r1r2r3r2λ	e2πı〈r1r2r3r2λ	PROPN
ap-3511	252	58	,	,	PUNCT
ap-3511	252	59	x	x	PROPN
ap-3511	252	60	〉	〉	NOUN
ap-3511	252	61	,	,	PUNCT
ap-3511	252	62	φ4	φ4	NOUN
ap-3511	252	63	λ(x	λ(x	X
ap-3511	252	64	)	)	PUNCT
ap-3511	252	65	=	=	SYM
ap-3511	253	1	3e2πı〈λ	3e2πı〈λ	NOUN
ap-3511	253	2	,	,	PUNCT
ap-3511	253	3	x	x	PROPN
ap-3511	253	4	〉	〉	NOUN
ap-3511	253	5	+	+	CCONJ
ap-3511	253	6	e2πı〈r1λ	e2πı〈r1λ	PROPN
ap-3511	253	7	,	,	PUNCT
ap-3511	253	8	x	x	PROPN
ap-3511	253	9	〉	〉	NOUN
ap-3511	253	10	+	+	CCONJ
ap-3511	253	11	e2πı〈r2λ	e2πı〈r2λ	ADJ
ap-3511	253	12	,	,	PUNCT
ap-3511	253	13	x	x	NOUN
ap-3511	253	14	〉	〉	NOUN
ap-3511	253	15	+	+	CCONJ
ap-3511	253	16	e2πı〈r3λ	e2πı〈r3λ	PROPN
ap-3511	253	17	,	,	PUNCT
ap-3511	253	18	x	x	X
ap-3511	253	19	〉	〉	NOUN
ap-3511	253	20	+	+	SYM
ap-3511	253	21	e2πı〈r1r2r1λ	e2πı〈r1r2r1λ	PROPN
ap-3511	253	22	,	,	PUNCT
ap-3511	253	23	x	x	PROPN
ap-3511	253	24	〉	〉	NOUN
ap-3511	253	25	+	+	CCONJ
ap-3511	253	26	e2πı〈r2r3r2λ	e2πı〈r2r3r2λ	PROPN
ap-3511	253	27	,	,	PUNCT
ap-3511	253	28	x	x	NOUN
ap-3511	253	29	〉	〉	NOUN
ap-3511	253	30	+	+	NOUN
ap-3511	253	31	e2πı〈r1r2r3r2r1λ	e2πı〈r1r2r3r2r1λ	NOUN
ap-3511	253	32	,	,	PUNCT
ap-3511	253	33	x	x	NOUN
ap-3511	253	34	〉	〉	NOUN
ap-3511	253	35	−	−	PROPN
ap-3511	253	36	e2πı〈r1r3λ	e2πı〈r1r3λ	SYM
ap-3511	253	37	,	,	PUNCT
ap-3511	253	38	x	x	PROPN
ap-3511	253	39	〉	〉	PROPN
ap-3511	253	40	−	−	PROPN
ap-3511	253	41	e2πı〈r2r1r3r2λ	e2πı〈r2r1r3r2λ	PROPN
ap-3511	253	42	,	,	PUNCT
ap-3511	253	43	x	x	NOUN
ap-3511	253	44	〉	〉	NOUN
ap-3511	253	45	−	−	NOUN
ap-3511	253	46	e2πı〈r3r2r3r1r2r3λ	e2πı〈r3r2r3r1r2r3λ	NOUN
ap-3511	253	47	,	,	PUNCT
ap-3511	253	48	x	x	X
ap-3511	253	49	〉	〉	NOUN
ap-3511	253	50	−	−	NOUN
ap-3511	253	51	e2πı〈r1r2r3λ	e2πı〈r1r2r3λ	NOUN
ap-3511	253	52	,	,	PUNCT
ap-3511	253	53	x	x	NOUN
ap-3511	253	54	〉	〉	NOUN
ap-3511	253	55	−	−	NOUN
ap-3511	253	56	e2πı〈r2r3r1λ	e2πı〈r2r3r1λ	PROPN
ap-3511	253	57	,	,	PUNCT
ap-3511	253	58	x	x	NOUN
ap-3511	253	59	〉	〉	NOUN
ap-3511	253	60	−	−	NOUN
ap-3511	253	61	e2πı〈r3r1r2λ	e2πı〈r3r1r2λ	X
ap-3511	253	62	,	,	PUNCT
ap-3511	253	63	x	x	NOUN
ap-3511	253	64	〉	〉	NOUN
ap-3511	253	65	−	−	PROPN
ap-3511	253	66	e2πı〈r3r2r1λ	e2πı〈r3r2r1λ	PROPN
ap-3511	253	67	,	,	PUNCT
ap-3511	253	68	x	x	PROPN
ap-3511	253	69	〉	〉	NOUN
ap-3511	253	70	−	−	NOUN
ap-3511	253	71	e2πı〈r3r2r3r1r2λ	e2πı〈r3r2r3r1r2λ	NOUN
ap-3511	253	72	,	,	PUNCT
ap-3511	253	73	x	x	NOUN
ap-3511	253	74	〉	〉	NOUN
ap-3511	253	75	−	−	PROPN
ap-3511	253	76	e2πı〈r1r2r1r3r2λ	e2πı〈r1r2r1r3r2λ	NOUN
ap-3511	253	77	,	,	PUNCT
ap-3511	253	78	x	x	NOUN
ap-3511	253	79	〉	〉	NOUN
ap-3511	253	80	,	,	PUNCT
ap-3511	253	81	φ5	φ5	ADJ
ap-3511	253	82	λ(x	λ(x	X
ap-3511	253	83	)	)	PUNCT
ap-3511	253	84	=	=	SYM
ap-3511	254	1	3e2πı〈λ	3e2πı〈λ	NOUN
ap-3511	254	2	,	,	PUNCT
ap-3511	254	3	x	x	PROPN
ap-3511	254	4	〉	〉	NOUN
ap-3511	254	5	−	−	PROPN
ap-3511	254	6	e2πı〈r1λ	e2πı〈r1λ	PROPN
ap-3511	254	7	,	,	PUNCT
ap-3511	254	8	x	x	PROPN
ap-3511	254	9	〉	〉	NOUN
ap-3511	254	10	−	−	PROPN
ap-3511	254	11	e2πı〈r2λ	e2πı〈r2λ	NOUN
ap-3511	254	12	,	,	PUNCT
ap-3511	254	13	x	x	NOUN
ap-3511	254	14	〉	〉	NOUN
ap-3511	254	15	−	−	NOUN
ap-3511	254	16	e2πı〈r3λ	e2πı〈r3λ	PROPN
ap-3511	254	17	,	,	PUNCT
ap-3511	254	18	x	x	NOUN
ap-3511	254	19	〉	〉	NOUN
ap-3511	254	20	−	−	PROPN
ap-3511	254	21	e2πı〈r1r2r1λ	e2πı〈r1r2r1λ	PROPN
ap-3511	254	22	,	,	PUNCT
ap-3511	254	23	x	x	PROPN
ap-3511	254	24	〉	〉	NOUN
ap-3511	254	25	−	−	NOUN
ap-3511	254	26	e2πı〈r2r3r2λ	e2πı〈r2r3r2λ	PROPN
ap-3511	254	27	,	,	PUNCT
ap-3511	254	28	x	x	NOUN
ap-3511	254	29	〉	〉	NOUN
ap-3511	254	30	−	−	NOUN
ap-3511	254	31	e2πı〈r1r2r3r2r1λ	e2πı〈r1r2r3r2r1λ	NOUN
ap-3511	254	32	,	,	PUNCT
ap-3511	254	33	x	x	NOUN
ap-3511	254	34	〉	〉	NOUN
ap-3511	254	35	−	−	PROPN
ap-3511	254	36	e2πı〈r1r3λ	e2πı〈r1r3λ	SYM
ap-3511	254	37	,	,	PUNCT
ap-3511	254	38	x	x	PROPN
ap-3511	254	39	〉	〉	PROPN
ap-3511	254	40	−	−	PROPN
ap-3511	254	41	e2πı〈r2r1r3r2λ	e2πı〈r2r1r3r2λ	PROPN
ap-3511	254	42	,	,	PUNCT
ap-3511	254	43	x	x	NOUN
ap-3511	254	44	〉	〉	NOUN
ap-3511	254	45	−	−	NOUN
ap-3511	254	46	e2πı〈r3r2r3r1r2r3λ	e2πı〈r3r2r3r1r2r3λ	NOUN
ap-3511	254	47	,	,	PUNCT
ap-3511	254	48	x	x	X
ap-3511	254	49	〉	〉	NOUN
ap-3511	254	50	+	+	CCONJ
ap-3511	254	51	e2πı〈r1r2r3λ	e2πı〈r1r2r3λ	NOUN
ap-3511	254	52	,	,	PUNCT
ap-3511	254	53	x	x	NOUN
ap-3511	254	54	〉	〉	NOUN
ap-3511	254	55	+	+	NUM
ap-3511	254	56	e2πı〈r2r3r1λ	e2πı〈r2r3r1λ	PROPN
ap-3511	254	57	,	,	PUNCT
ap-3511	254	58	x	x	NOUN
ap-3511	254	59	〉	〉	NOUN
ap-3511	254	60	+	+	SYM
ap-3511	254	61	e2πı〈r3r1r2λ	e2πı〈r3r1r2λ	NUM
ap-3511	254	62	,	,	PUNCT
ap-3511	254	63	x	x	NOUN
ap-3511	254	64	〉	〉	NOUN
ap-3511	254	65	+	+	SYM
ap-3511	254	66	e2πı〈r3r2r1λ	e2πı〈r3r2r1λ	PROPN
ap-3511	254	67	,	,	PUNCT
ap-3511	254	68	x	x	NOUN
ap-3511	254	69	〉	〉	NOUN
ap-3511	254	70	+	+	CCONJ
ap-3511	254	71	e2πı〈r3r2r3r1r2λ	e2πı〈r3r2r3r1r2λ	NOUN
ap-3511	254	72	,	,	PUNCT
ap-3511	254	73	x	x	NOUN
ap-3511	254	74	〉	〉	NOUN
ap-3511	254	75	+	+	NUM
ap-3511	254	76	e2πı〈r1r2r1r3r2λ	e2πı〈r1r2r1r3r2λ	NOUN
ap-3511	254	77	,	,	PUNCT
ap-3511	254	78	x	x	NOUN
ap-3511	254	79	〉	〉	NOUN
ap-3511	254	80	.	.	PUNCT
ap-3511	255	1	the	the	DET
ap-3511	255	2	linear	linear	ADJ
ap-3511	255	3	dependence	dependence	NOUN
ap-3511	255	4	relations	relation	NOUN
ap-3511	255	5	of	of	ADP
ap-3511	255	6	functions	function	NOUN
ap-3511	255	7	φ3,4,5	φ3,4,5	NOUN
ap-3511	255	8	λ	λ	X
ap-3511	255	9	(	(	PUNCT
ap-3511	255	10	x	x	NOUN
ap-3511	255	11	)	)	PUNCT
ap-3511	255	12	for	for	ADP
ap-3511	255	13	labels	label	NOUN
ap-3511	255	14	from	from	ADP
ap-3511	255	15	the	the	DET
ap-3511	255	16	same	same	ADJ
ap-3511	255	17	w	w	NOUN
ap-3511	255	18	–	–	PUNCT
ap-3511	255	19	orbit	orbit	NOUN
ap-3511	255	20	are∑	are∑	CCONJ
ap-3511	255	21	w∈w	w∈w	VERB
ap-3511	255	22	(	(	PUNCT
ap-3511	255	23	a3	a3	NOUN
ap-3511	255	24	)	)	PUNCT
ap-3511	255	25	φ3	φ3	NOUN
ap-3511	255	26	wλ(x	wλ(x	PUNCT
ap-3511	255	27	)	)	PUNCT
ap-3511	255	28	=	=	PUNCT
ap-3511	255	29	∑	∑	PUNCT
ap-3511	255	30	w∈w	w∈w	X
ap-3511	255	31	(	(	PUNCT
ap-3511	255	32	a3	a3	NOUN
ap-3511	255	33	)	)	PUNCT
ap-3511	255	34	χ2(w)φ3	χ2(w)φ3	PROPN
ap-3511	255	35	wλ(x	wλ(x	PUNCT
ap-3511	255	36	)	)	PUNCT
ap-3511	256	1	=	=	PUNCT
ap-3511	256	2	∑	∑	PUNCT
ap-3511	256	3	w∈w	w∈w	X
ap-3511	256	4	(	(	PUNCT
ap-3511	256	5	a3	a3	NOUN
ap-3511	256	6	)	)	PUNCT
ap-3511	256	7	χ4(w)φ3	χ4(w)φ3	PUNCT
ap-3511	256	8	wλ(x	wλ(x	PUNCT
ap-3511	256	9	)	)	PUNCT
ap-3511	256	10	=	=	PUNCT
ap-3511	257	1	∑	∑	PUNCT
ap-3511	257	2	w∈w	w∈w	X
ap-3511	257	3	(	(	PUNCT
ap-3511	257	4	a3	a3	NOUN
ap-3511	257	5	)	)	PUNCT
ap-3511	257	6	χ5(w)φ3	χ5(w)φ3	NOUN
ap-3511	257	7	wλ(x	wλ(x	PUNCT
ap-3511	257	8	)	)	PUNCT
ap-3511	257	9	=	=	SYM
ap-3511	257	10	0	0	NUM
ap-3511	257	11	,	,	PUNCT
ap-3511	257	12	∑	∑	ADV
ap-3511	257	13	w∈w	w∈w	X
ap-3511	257	14	(	(	PUNCT
ap-3511	257	15	a3	a3	NOUN
ap-3511	257	16	)	)	PUNCT
ap-3511	257	17	φ4	φ4	NOUN
ap-3511	257	18	wλ(x	wλ(x	PUNCT
ap-3511	257	19	)	)	PUNCT
ap-3511	257	20	=	=	PUNCT
ap-3511	257	21	∑	∑	PUNCT
ap-3511	257	22	w∈w	w∈w	X
ap-3511	257	23	(	(	PUNCT
ap-3511	257	24	a3	a3	NOUN
ap-3511	257	25	)	)	PUNCT
ap-3511	257	26	χ2(w)φ4	χ2(w)φ4	PROPN
ap-3511	257	27	wλ(x	wλ(x	PUNCT
ap-3511	257	28	)	)	PUNCT
ap-3511	257	29	=	=	SYM
ap-3511	258	1	∑	∑	PUNCT
ap-3511	258	2	w∈w	w∈w	X
ap-3511	258	3	(	(	PUNCT
ap-3511	258	4	a3	a3	NOUN
ap-3511	258	5	)	)	PUNCT
ap-3511	258	6	χ3(w)φ4	χ3(w)φ4	NOUN
ap-3511	258	7	wλ(x	wλ(x	PUNCT
ap-3511	258	8	)	)	PUNCT
ap-3511	258	9	=	=	PUNCT
ap-3511	258	10	∑	∑	PUNCT
ap-3511	258	11	w∈w	w∈w	X
ap-3511	258	12	(	(	PUNCT
ap-3511	258	13	a3	a3	NOUN
ap-3511	258	14	)	)	PUNCT
ap-3511	258	15	χ5(w)φ4	χ5(w)φ4	NOUN
ap-3511	258	16	wλ(x	wλ(x	PUNCT
ap-3511	258	17	)	)	PUNCT
ap-3511	259	1	=	=	SYM
ap-3511	259	2	0	0	NUM
ap-3511	259	3	,	,	PUNCT
ap-3511	259	4	∑	∑	ADV
ap-3511	259	5	w∈w	w∈w	X
ap-3511	259	6	(	(	PUNCT
ap-3511	259	7	a3	a3	NOUN
ap-3511	259	8	)	)	PUNCT
ap-3511	259	9	φ5	φ5	PROPN
ap-3511	259	10	wλ(x	wλ(x	PUNCT
ap-3511	259	11	)	)	PUNCT
ap-3511	259	12	=	=	SYM
ap-3511	260	1	∑	∑	PUNCT
ap-3511	260	2	w∈w	w∈w	X
ap-3511	260	3	(	(	PUNCT
ap-3511	260	4	a3	a3	NOUN
ap-3511	260	5	)	)	PUNCT
ap-3511	260	6	χ2(w)φ5	χ2(w)φ5	X
ap-3511	260	7	wλ(x	wλ(x	PUNCT
ap-3511	260	8	)	)	PUNCT
ap-3511	260	9	=	=	SYM
ap-3511	261	1	∑	∑	PUNCT
ap-3511	261	2	w∈w	w∈w	X
ap-3511	261	3	(	(	PUNCT
ap-3511	261	4	a3	a3	NOUN
ap-3511	261	5	)	)	PUNCT
ap-3511	261	6	χ3(w)φ5	χ3(w)φ5	X
ap-3511	261	7	wλ(x	wλ(x	PUNCT
ap-3511	261	8	)	)	PUNCT
ap-3511	261	9	=	=	PUNCT
ap-3511	261	10	∑	∑	PUNCT
ap-3511	261	11	w∈w	w∈w	X
ap-3511	261	12	(	(	PUNCT
ap-3511	261	13	a3	a3	NOUN
ap-3511	261	14	)	)	PUNCT
ap-3511	261	15	χ4(w)φ5	χ4(w)φ5	NOUN
ap-3511	261	16	wλ(x	wλ(x	PUNCT
ap-3511	261	17	)	)	PUNCT
ap-3511	261	18	=	=	SYM
ap-3511	262	1	0	0	X
ap-3511	262	2	.	.	PUNCT
ap-3511	263	1	the	the	DET
ap-3511	263	2	weyl	weyl	PROPN
ap-3511	263	3	group	group	NOUN
ap-3511	263	4	of	of	ADP
ap-3511	263	5	c3	c3	PROPN
ap-3511	263	6	decomposes	decompose	VERB
ap-3511	263	7	into	into	ADP
ap-3511	263	8	10	10	NUM
ap-3511	263	9	conjugacy	conjugacy	ADJ
ap-3511	263	10	classes	class	NOUN
ap-3511	263	11	:	:	PUNCT
ap-3511	263	12	c3	c3	NOUN
ap-3511	263	13	:	:	PUNCT
ap-3511	263	14	c1	c1	PROPN
ap-3511	263	15	=	=	PUNCT
ap-3511	263	16	{	{	PUNCT
ap-3511	263	17	i	i	PROPN
ap-3511	263	18	d	d	PROPN
ap-3511	263	19	}	}	PUNCT
ap-3511	263	20	,	,	PUNCT
ap-3511	263	21	c2	c2	PROPN
ap-3511	263	22	=	=	SYM
ap-3511	263	23	{	{	PUNCT
ap-3511	263	24	r1	r1	PROPN
ap-3511	263	25	,	,	PUNCT
ap-3511	263	26	r2	r2	PROPN
ap-3511	263	27	,	,	PUNCT
ap-3511	263	28	r1r2r1	r1r2r1	NOUN
ap-3511	263	29	,	,	PUNCT
ap-3511	263	30	r3r2r3	r3r2r3	PROPN
ap-3511	263	31	,	,	PUNCT
ap-3511	263	32	r3r1r2r1r3	r3r1r2r1r3	PROPN
ap-3511	263	33	,	,	PUNCT
ap-3511	263	34	r2r1r3r2r3r2r1r2	r2r1r3r2r3r2r1r2	VERB
ap-3511	263	35	}	}	PUNCT
ap-3511	263	36	,	,	PUNCT
ap-3511	263	37	c3	c3	PROPN
ap-3511	263	38	=	=	SYM
ap-3511	263	39	{	{	PUNCT
ap-3511	263	40	r3	r3	PROPN
ap-3511	263	41	,	,	PUNCT
ap-3511	263	42	r2r3r2	r2r3r2	NOUN
ap-3511	263	43	,	,	PUNCT
ap-3511	263	44	r1r2r3r2r1	r1r2r3r2r1	NOUN
ap-3511	263	45	}	}	PUNCT
ap-3511	263	46	,	,	PUNCT
ap-3511	263	47	c4	c4	NOUN
ap-3511	263	48	=	=	SYM
ap-3511	263	49	{	{	PUNCT
ap-3511	263	50	r1r2	r1r2	NOUN
ap-3511	263	51	,	,	PUNCT
ap-3511	263	52	r2r1	r2r1	PROPN
ap-3511	263	53	,	,	PUNCT
ap-3511	263	54	r3r2r1r3	r3r2r1r3	PROPN
ap-3511	263	55	,	,	PUNCT
ap-3511	263	56	r1r3r2r3	r1r3r2r3	PROPN
ap-3511	263	57	,	,	PUNCT
ap-3511	263	58	r3r2r3r1r2r1	r3r2r3r1r2r1	NOUN
ap-3511	263	59	,	,	PUNCT
ap-3511	263	60	r2r1r3r2r3r1	r2r1r3r2r3r1	ADJ
ap-3511	263	61	,	,	PUNCT
ap-3511	263	62	r3r1r2r1r3r2	r3r1r2r1r3r2	NOUN
ap-3511	263	63	,	,	PUNCT
ap-3511	263	64	r2r1r3r2r3r2	r2r1r3r2r3r2	NOUN
ap-3511	263	65	}	}	PUNCT
ap-3511	263	66	,	,	PUNCT
ap-3511	263	67	c5	c5	PROPN
ap-3511	263	68	=	=	PROPN
ap-3511	263	69	{	{	PUNCT
ap-3511	263	70	r1r3	r1r3	PROPN
ap-3511	263	71	,	,	PUNCT
ap-3511	263	72	r2r3r1r2	r2r3r1r2	PROPN
ap-3511	263	73	,	,	PUNCT
ap-3511	263	74	r1r2r3r1r2r1	r1r2r3r1r2r1	NOUN
ap-3511	263	75	,	,	PUNCT
ap-3511	263	76	r3r2r1r3r2r3	r3r2r1r3r2r3	VERB
ap-3511	263	77	,	,	PUNCT
ap-3511	263	78	r1r3r2r1r3r2r3r1	r1r3r2r1r3r2r3r1	PROPN
ap-3511	263	79	,	,	PUNCT
ap-3511	263	80	r2r1r3r2r1r3r2r3	r2r1r3r2r1r3r2r3	PROPN
ap-3511	263	81	}	}	PUNCT
ap-3511	263	82	,	,	PUNCT
ap-3511	263	83	c6	c6	PROPN
ap-3511	263	84	=	=	PUNCT
ap-3511	263	85	{	{	PUNCT
ap-3511	263	86	r3r2	r3r2	PROPN
ap-3511	263	87	,	,	PUNCT
ap-3511	263	88	r1r3r2r1	r1r3r2r1	NOUN
ap-3511	263	89	,	,	PUNCT
ap-3511	263	90	r2r3r2r1	r2r3r2r1	NOUN
ap-3511	263	91	,	,	PUNCT
ap-3511	263	92	r2r3	r2r3	NOUN
ap-3511	263	93	,	,	PUNCT
ap-3511	263	94	r1r2r3r1	r1r2r3r1	NOUN
ap-3511	263	95	,	,	PUNCT
ap-3511	263	96	r1r2r3r2	r1r2r3r2	NOUN
ap-3511	263	97	}	}	PUNCT
ap-3511	263	98	,	,	PUNCT
ap-3511	263	99	c7	c7	PROPN
ap-3511	263	100	=	=	PROPN
ap-3511	263	101	{	{	PUNCT
ap-3511	263	102	r3r1r2	r3r1r2	PROPN
ap-3511	263	103	,	,	PUNCT
ap-3511	263	104	r1r2r3	r1r2r3	PROPN
ap-3511	263	105	,	,	PUNCT
ap-3511	263	106	r2r3r1	r2r3r1	ADJ
ap-3511	263	107	,	,	PUNCT
ap-3511	263	108	r3r2r1	r3r2r1	NOUN
ap-3511	263	109	,	,	PUNCT
ap-3511	263	110	r2r3r1r2r1	r2r3r1r2r1	NOUN
ap-3511	263	111	,	,	PUNCT
ap-3511	263	112	r1r2r1r3r2	r1r2r1r3r2	PROPN
ap-3511	263	113	,	,	PUNCT
ap-3511	263	114	r3r2r1r3r2r1r3	r3r2r1r3r2r1r3	X
ap-3511	263	115	,	,	PUNCT
ap-3511	263	116	r3r2r1r2r3r2r3	r3r2r1r2r3r2r3	NUM
ap-3511	263	117	}	}	PUNCT
ap-3511	263	118	,	,	PUNCT
ap-3511	263	119	c8	c8	PROPN
ap-3511	263	120	=	=	SYM
ap-3511	263	121	{	{	PUNCT
ap-3511	263	122	r2r3r2r3	r2r3r2r3	PROPN
ap-3511	263	123	,	,	PUNCT
ap-3511	263	124	r1r3r2r3r2r1	r1r3r2r3r2r1	NOUN
ap-3511	263	125	,	,	PUNCT
ap-3511	263	126	r2r1r3r2r3r1r2r1	r2r1r3r2r3r1r2r1	NOUN
ap-3511	263	127	}	}	PUNCT
ap-3511	263	128	,	,	PUNCT
ap-3511	263	129	c9	c9	NOUN
ap-3511	263	130	=	=	SYM
ap-3511	263	131	{	{	PUNCT
ap-3511	263	132	r3r2r3r2r1	r3r2r3r2r1	NOUN
ap-3511	263	133	,	,	PUNCT
ap-3511	263	134	r3r2r3r1r2	r3r2r3r1r2	NUM
ap-3511	263	135	,	,	PUNCT
ap-3511	263	136	r1r2r3r2r3	r1r2r3r2r3	NUM
ap-3511	263	137	,	,	PUNCT
ap-3511	263	138	r2r3r1r2r3	r2r3r1r2r3	NUM
ap-3511	263	139	,	,	PUNCT
ap-3511	263	140	r1r3r2r3r1r2r1	r1r3r2r3r1r2r1	NOUN
ap-3511	263	141	,	,	PUNCT
ap-3511	263	142	r2r3r1r2r3r2r1	r2r3r1r2r3r2r1	NOUN
ap-3511	263	143	}	}	PUNCT
ap-3511	263	144	,	,	PUNCT
ap-3511	263	145	c10	c10	PROPN
ap-3511	263	146	=	=	SYM
ap-3511	263	147	{	{	PUNCT
ap-3511	263	148	r1r2r1r3r2r1r3r2r3	r1r2r1r3r2r1r3r2r3	PROPN
ap-3511	263	149	}	}	PUNCT
ap-3511	263	150	.	.	PUNCT
ap-3511	264	1	446	446	NUM
ap-3511	264	2	vol	vol	NOUN
ap-3511	264	3	.	.	PUNCT
ap-3511	265	1	56	56	NUM
ap-3511	265	2	no	no	NOUN
ap-3511	265	3	.	.	PUNCT
ap-3511	266	1	6/2016	6/2016	NUM
ap-3511	266	2	on	on	ADP
ap-3511	266	3	generalization	generalization	NOUN
ap-3511	266	4	of	of	ADP
ap-3511	266	5	special	special	ADJ
ap-3511	266	6	functions	function	NOUN
ap-3511	266	7	related	relate	VERB
ap-3511	266	8	to	to	ADP
ap-3511	266	9	weyl	weyl	VERB
ap-3511	266	10	groups	group	NOUN
ap-3511	266	11	the	the	DET
ap-3511	266	12	explicit	explicit	ADJ
ap-3511	266	13	formulas	formula	NOUN
ap-3511	266	14	and	and	CCONJ
ap-3511	266	15	linear	linear	ADJ
ap-3511	266	16	dependency	dependency	NOUN
ap-3511	266	17	relations	relation	NOUN
ap-3511	266	18	can	can	AUX
ap-3511	266	19	be	be	AUX
ap-3511	266	20	written	write	VERB
ap-3511	266	21	down	down	ADP
ap-3511	266	22	using	use	VERB
ap-3511	266	23	definition	definition	NOUN
ap-3511	266	24	11	11	NUM
ap-3511	266	25	and	and	CCONJ
ap-3511	266	26	corollary	corollary	ADJ
ap-3511	266	27	6	6	NUM
ap-3511	266	28	.	.	NOUN
ap-3511	266	29	6	6	NUM
ap-3511	266	30	.	.	X
ap-3511	266	31	concluding	conclude	VERB
ap-3511	266	32	remarks	remark	NOUN
ap-3511	266	33	(	(	PUNCT
ap-3511	266	34	1	1	NUM
ap-3511	266	35	.	.	PUNCT
ap-3511	266	36	)	)	PUNCT
ap-3511	267	1	the	the	DET
ap-3511	267	2	paper	paper	NOUN
ap-3511	267	3	[	[	X
ap-3511	267	4	7	7	X
ap-3511	267	5	]	]	PUNCT
ap-3511	267	6	was	be	AUX
ap-3511	267	7	inspired	inspire	VERB
ap-3511	267	8	by	by	ADP
ap-3511	267	9	an	an	DET
ap-3511	267	10	extended	extended	ADJ
ap-3511	267	11	possibility	possibility	NOUN
ap-3511	267	12	of	of	ADP
ap-3511	267	13	applications	application	NOUN
ap-3511	267	14	of	of	ADP
ap-3511	267	15	immanants	immanant	NOUN
ap-3511	267	16	in	in	ADP
ap-3511	267	17	physics	physics	NOUN
ap-3511	267	18	.	.	PUNCT
ap-3511	268	1	we	we	PRON
ap-3511	268	2	believe	believe	VERB
ap-3511	268	3	that	that	SCONJ
ap-3511	268	4	this	this	DET
ap-3511	268	5	generalization	generalization	NOUN
ap-3511	268	6	will	will	AUX
ap-3511	268	7	find	find	VERB
ap-3511	268	8	its	its	PRON
ap-3511	268	9	applications	application	NOUN
ap-3511	268	10	as	as	ADV
ap-3511	268	11	well	well	ADV
ap-3511	268	12	.	.	PUNCT
ap-3511	269	1	(	(	PUNCT
ap-3511	269	2	2	2	NUM
ap-3511	269	3	.	.	PUNCT
ap-3511	269	4	)	)	PUNCT
ap-3511	270	1	in	in	ADP
ap-3511	270	2	order	order	NOUN
ap-3511	270	3	to	to	PART
ap-3511	270	4	define	define	VERB
ap-3511	270	5	the	the	DET
ap-3511	270	6	fourier	fourier	NOUN
ap-3511	270	7	transform	transform	NOUN
ap-3511	270	8	using	use	VERB
ap-3511	270	9	families	family	NOUN
ap-3511	270	10	of	of	ADP
ap-3511	270	11	character	character	NOUN
ap-3511	270	12	functions	function	NOUN
ap-3511	270	13	as	as	ADP
ap-3511	270	14	in	in	ADP
ap-3511	270	15	[	[	X
ap-3511	270	16	5	5	NUM
ap-3511	270	17	]	]	PUNCT
ap-3511	270	18	we	we	PRON
ap-3511	270	19	need	need	VERB
ap-3511	270	20	to	to	PART
ap-3511	270	21	decide	decide	VERB
ap-3511	270	22	about	about	ADP
ap-3511	270	23	the	the	DET
ap-3511	270	24	completeness	completeness	NOUN
ap-3511	270	25	of	of	ADP
ap-3511	270	26	the	the	DET
ap-3511	270	27	orthogonal	orthogonal	ADJ
ap-3511	270	28	set	set	NOUN
ap-3511	270	29	of	of	ADP
ap-3511	270	30	character	character	NOUN
ap-3511	270	31	functions	function	NOUN
ap-3511	270	32	.	.	PUNCT
ap-3511	271	1	(	(	PUNCT
ap-3511	271	2	3	3	NUM
ap-3511	271	3	.	.	PUNCT
ap-3511	271	4	)	)	PUNCT
ap-3511	272	1	there	there	PRON
ap-3511	272	2	are	be	VERB
ap-3511	272	3	other	other	ADJ
ap-3511	272	4	directions	direction	NOUN
ap-3511	272	5	of	of	ADP
ap-3511	272	6	future	future	ADJ
ap-3511	272	7	research	research	NOUN
ap-3511	272	8	inspired	inspire	VERB
ap-3511	272	9	directly	directly	ADV
ap-3511	272	10	by	by	ADP
ap-3511	272	11	orbit	orbit	NOUN
ap-3511	272	12	functions	function	NOUN
ap-3511	272	13	.	.	PUNCT
ap-3511	273	1	for	for	ADP
ap-3511	273	2	example	example	NOUN
ap-3511	273	3	,	,	PUNCT
ap-3511	273	4	in	in	ADP
ap-3511	273	5	[	[	PUNCT
ap-3511	273	6	13	13	NUM
ap-3511	273	7	]	]	PUNCT
ap-3511	273	8	orbit	orbit	NOUN
ap-3511	273	9	functions	function	NOUN
ap-3511	273	10	with	with	ADP
ap-3511	273	11	the	the	DET
ap-3511	273	12	lowest	low	ADJ
ap-3511	273	13	labels	label	NOUN
ap-3511	273	14	are	be	AUX
ap-3511	273	15	used	use	VERB
ap-3511	273	16	as	as	ADP
ap-3511	273	17	variables	variable	NOUN
ap-3511	273	18	of	of	ADP
ap-3511	273	19	orthogonal	orthogonal	ADJ
ap-3511	273	20	polynomials	polynomial	NOUN
ap-3511	273	21	.	.	PUNCT
ap-3511	274	1	references	reference	NOUN
ap-3511	274	2	[	[	X
ap-3511	274	3	1	1	X
ap-3511	274	4	]	]	PUNCT
ap-3511	274	5	anatoliy	anatoliy	ADJ
ap-3511	274	6	klimyk	klimyk	NOUN
ap-3511	274	7	,	,	PUNCT
ap-3511	274	8	jiří	jiří	NOUN
ap-3511	274	9	patera	patera	NOUN
ap-3511	274	10	,	,	PUNCT
ap-3511	274	11	orbit	orbit	NOUN
ap-3511	274	12	functions	function	NOUN
ap-3511	274	13	,	,	PUNCT
ap-3511	274	14	sigma	sigma	NOUN
ap-3511	274	15	2	2	NUM
ap-3511	274	16	(	(	PUNCT
ap-3511	274	17	2006	2006	NUM
ap-3511	274	18	)	)	PUNCT
ap-3511	274	19	,	,	PUNCT
ap-3511	274	20	006	006	NUM
ap-3511	274	21	,	,	PUNCT
ap-3511	274	22	60	60	NUM
ap-3511	274	23	pages	page	NOUN
ap-3511	274	24	,	,	PUNCT
ap-3511	274	25	doi:10.3842	doi:10.3842	NOUN
ap-3511	274	26	/	/	SYM
ap-3511	274	27	sigma.2006.006	sigma.2006.006	NOUN
ap-3511	274	28	.	.	PUNCT
ap-3511	275	1	[	[	X
ap-3511	275	2	2	2	X
ap-3511	275	3	]	]	PUNCT
ap-3511	275	4	anatoliy	anatoliy	ADJ
ap-3511	275	5	klimyk	klimyk	NOUN
ap-3511	275	6	,	,	PUNCT
ap-3511	275	7	jiří	jiří	NOUN
ap-3511	275	8	patera	patera	NOUN
ap-3511	275	9	,	,	PUNCT
ap-3511	275	10	antisymmetric	antisymmetric	PROPN
ap-3511	275	11	orbit	orbit	NOUN
ap-3511	275	12	functions	function	NOUN
ap-3511	275	13	,	,	PUNCT
ap-3511	275	14	sigma	sigma	PROPN
ap-3511	275	15	(	(	PUNCT
ap-3511	275	16	symmetry	symmetry	NOUN
ap-3511	275	17	,	,	PUNCT
ap-3511	275	18	integrability	integrability	NOUN
ap-3511	275	19	and	and	CCONJ
ap-3511	275	20	geometry	geometry	NOUN
ap-3511	275	21	:	:	PUNCT
ap-3511	275	22	methods	method	NOUN
ap-3511	275	23	and	and	CCONJ
ap-3511	275	24	applications	application	NOUN
ap-3511	275	25	)	)	PUNCT
ap-3511	275	26	3	3	NUM
ap-3511	275	27	(	(	PUNCT
ap-3511	275	28	2007	2007	NUM
ap-3511	275	29	)	)	PUNCT
ap-3511	275	30	,	,	PUNCT
ap-3511	275	31	023	023	NUM
ap-3511	275	32	,	,	PUNCT
ap-3511	275	33	83	83	NUM
ap-3511	275	34	pages	page	NOUN
ap-3511	275	35	,	,	PUNCT
ap-3511	275	36	doi:10.3842	doi:10.3842	NOUN
ap-3511	275	37	/	/	SYM
ap-3511	275	38	sigma.2007.023	sigma.2007.023	PROPN
ap-3511	275	39	.	.	PUNCT
ap-3511	276	1	[	[	X
ap-3511	276	2	3	3	X
ap-3511	276	3	]	]	X
ap-3511	276	4	robert	robert	PROPN
ap-3511	276	5	v.	v.	PROPN
ap-3511	276	6	moody	moody	PROPN
ap-3511	276	7	,	,	PUNCT
ap-3511	276	8	jiří	jiří	NOUN
ap-3511	276	9	patera	patera	NOUN
ap-3511	276	10	,	,	PUNCT
ap-3511	276	11	orthogonality	orthogonality	NOUN
ap-3511	276	12	within	within	ADP
ap-3511	276	13	the	the	DET
ap-3511	276	14	families	family	NOUN
ap-3511	276	15	of	of	ADP
ap-3511	276	16	c-	c-	X
ap-3511	276	17	,	,	PUNCT
ap-3511	276	18	s-	s-	X
ap-3511	276	19	,	,	PUNCT
ap-3511	276	20	and	and	CCONJ
ap-3511	276	21	e	e	NOUN
ap-3511	276	22	-	-	NOUN
ap-3511	276	23	functions	function	NOUN
ap-3511	276	24	of	of	ADP
ap-3511	276	25	any	any	DET
ap-3511	276	26	compact	compact	ADJ
ap-3511	276	27	semisimple	semisimple	NOUN
ap-3511	276	28	lie	lie	NOUN
ap-3511	276	29	group	group	NOUN
ap-3511	276	30	,	,	PUNCT
ap-3511	276	31	sigma	sigma	PROPN
ap-3511	276	32	,	,	PUNCT
ap-3511	276	33	2	2	NUM
ap-3511	276	34	,	,	PUNCT
ap-3511	276	35	(	(	PUNCT
ap-3511	276	36	2006	2006	NUM
ap-3511	276	37	)	)	PUNCT
ap-3511	276	38	,	,	PUNCT
ap-3511	276	39	076	076	NUM
ap-3511	276	40	,	,	PUNCT
ap-3511	276	41	doi:10.3842	doi:10.3842	NOUN
ap-3511	276	42	/	/	SYM
ap-3511	276	43	sigma.2006.076	sigma.2006.076	NOUN
ap-3511	276	44	.	.	PUNCT
ap-3511	277	1	[	[	X
ap-3511	277	2	4	4	NUM
ap-3511	277	3	]	]	X
ap-3511	277	4	r.	r.	PROPN
ap-3511	277	5	v.	v.	PROPN
ap-3511	277	6	moody	moody	PROPN
ap-3511	277	7	,	,	PUNCT
ap-3511	277	8	l.	l.	PROPN
ap-3511	277	9	motlochová	motlochová	PROPN
ap-3511	277	10	,	,	PUNCT
ap-3511	277	11	j.	j.	PROPN
ap-3511	277	12	patera	patera	PROPN
ap-3511	277	13	,	,	PUNCT
ap-3511	277	14	gaussian	gaussian	ADJ
ap-3511	277	15	cubature	cubature	NOUN
ap-3511	277	16	arising	arise	VERB
ap-3511	277	17	from	from	ADP
ap-3511	277	18	hybrid	hybrid	ADJ
ap-3511	277	19	characters	character	NOUN
ap-3511	277	20	of	of	ADP
ap-3511	277	21	simple	simple	ADJ
ap-3511	277	22	lie	lie	NOUN
ap-3511	277	23	groups	group	NOUN
ap-3511	277	24	,	,	PUNCT
ap-3511	277	25	j.	j.	PROPN
ap-3511	277	26	fourier	fourier	PROPN
ap-3511	277	27	anal	anal	PROPN
ap-3511	277	28	.	.	PUNCT
ap-3511	278	1	appl	appl	PROPN
ap-3511	278	2	.	.	PROPN
ap-3511	278	3	,	,	PUNCT
ap-3511	278	4	2014	2014	NUM
ap-3511	278	5	,	,	PUNCT
ap-3511	278	6	vol	vol	NOUN
ap-3511	278	7	.	.	PROPN
ap-3511	278	8	20	20	NUM
ap-3511	278	9	,	,	PUNCT
ap-3511	278	10	issue	issue	NOUN
ap-3511	278	11	6	6	NUM
ap-3511	278	12	,	,	PUNCT
ap-3511	278	13	doi:10.1007	doi:10.1007	ADJ
ap-3511	278	14	/	/	SYM
ap-3511	278	15	s00041	s00041	NOUN
ap-3511	278	16	-	-	PUNCT
ap-3511	278	17	014	014	NUM
ap-3511	278	18	-	-	PUNCT
ap-3511	278	19	9355	9355	NUM
ap-3511	278	20	-	-	SYM
ap-3511	278	21	0	0	NUM
ap-3511	278	22	.	.	PUNCT
ap-3511	279	1	[	[	X
ap-3511	279	2	5	5	NUM
ap-3511	279	3	]	]	PUNCT
ap-3511	279	4	jiří	jiří	NOUN
ap-3511	279	5	hrivnák	hrivnák	NOUN
ap-3511	279	6	,	,	PUNCT
ap-3511	279	7	jiří	jiří	NOUN
ap-3511	279	8	patera	patera	NOUN
ap-3511	279	9	,	,	PUNCT
ap-3511	279	10	on	on	ADP
ap-3511	279	11	discretization	discretization	NOUN
ap-3511	279	12	of	of	ADP
ap-3511	279	13	tori	tori	NOUN
ap-3511	279	14	of	of	ADP
ap-3511	279	15	compact	compact	ADJ
ap-3511	279	16	simple	simple	ADJ
ap-3511	279	17	lie	lie	NOUN
ap-3511	279	18	groups	group	NOUN
ap-3511	279	19	,	,	PUNCT
ap-3511	279	20	j.	j.	PROPN
ap-3511	279	21	phys	phys	PROPN
ap-3511	279	22	.	.	PUNCT
ap-3511	280	1	a	a	DET
ap-3511	280	2	:	:	PUNCT
ap-3511	280	3	math	math	NOUN
ap-3511	280	4	.	.	PUNCT
ap-3511	281	1	theor	theor	PROPN
ap-3511	281	2	.	.	PUNCT
ap-3511	282	1	42	42	NUM
ap-3511	282	2	(	(	PUNCT
ap-3511	282	3	2009	2009	NUM
ap-3511	282	4	)	)	PUNCT
ap-3511	282	5	,	,	PUNCT
ap-3511	282	6	doi:10.1088/1751	doi:10.1088/1751	NOUN
ap-3511	282	7	-	-	PUNCT
ap-3511	282	8	8113/42/38/385208	8113/42/38/385208	NOUN
ap-3511	282	9	.	.	PUNCT
ap-3511	283	1	[	[	X
ap-3511	283	2	6	6	NUM
ap-3511	283	3	]	]	X
ap-3511	283	4	lenka	lenka	PROPN
ap-3511	283	5	háková	háková	PROPN
ap-3511	283	6	,	,	PUNCT
ap-3511	283	7	jiří	jiří	NOUN
ap-3511	283	8	hrivnák	hrivnák	PROPN
ap-3511	283	9	,	,	PUNCT
ap-3511	283	10	jiří	jiří	NOUN
ap-3511	283	11	patera	patera	NOUN
ap-3511	283	12	,	,	PUNCT
ap-3511	283	13	four	four	NUM
ap-3511	283	14	families	family	NOUN
ap-3511	283	15	of	of	ADP
ap-3511	283	16	weyl	weyl	PROPN
ap-3511	283	17	group	group	NOUN
ap-3511	283	18	orbit	orbit	NOUN
ap-3511	283	19	functions	function	NOUN
ap-3511	283	20	of	of	ADP
ap-3511	283	21	b3	b3	PROPN
ap-3511	283	22	and	and	CCONJ
ap-3511	283	23	c3	c3	PROPN
ap-3511	283	24	,	,	PUNCT
ap-3511	283	25	j.	j.	PROPN
ap-3511	283	26	math	math	PROPN
ap-3511	283	27	.	.	PUNCT
ap-3511	284	1	phys	phy	NOUN
ap-3511	284	2	.	.	PUNCT
ap-3511	285	1	54,(2013	54,(2013	NUM
ap-3511	285	2	)	)	PUNCT
ap-3511	285	3	,	,	PUNCT
ap-3511	285	4	doi:10.1063/1.4817340	doi:10.1063/1.4817340	NOUN
ap-3511	285	5	.	.	PUNCT
ap-3511	286	1	[	[	X
ap-3511	286	2	7	7	X
ap-3511	286	3	]	]	X
ap-3511	286	4	lenka	lenka	PROPN
ap-3511	286	5	háková	háková	PROPN
ap-3511	286	6	,	,	PUNCT
ap-3511	286	7	agnieszka	agnieszka	PROPN
ap-3511	286	8	tereskiewicz	tereskiewicz	PROPN
ap-3511	286	9	,	,	PUNCT
ap-3511	286	10	on	on	ADP
ap-3511	286	11	immanant	immanant	ADJ
ap-3511	286	12	functions	function	NOUN
ap-3511	286	13	related	relate	VERB
ap-3511	286	14	to	to	ADP
ap-3511	286	15	weyl	weyl	VERB
ap-3511	286	16	groups	group	NOUN
ap-3511	286	17	of	of	ADP
ap-3511	286	18	an	an	DET
ap-3511	286	19	,	,	PUNCT
ap-3511	286	20	journal	journal	NOUN
ap-3511	286	21	of	of	ADP
ap-3511	286	22	mathematical	mathematical	ADJ
ap-3511	286	23	physics	physics	NOUN
ap-3511	286	24	,	,	PUNCT
ap-3511	286	25	2014	2014	NUM
ap-3511	286	26	,	,	PUNCT
ap-3511	286	27	vol.55	vol.55	NOUN
ap-3511	286	28	,	,	PUNCT
ap-3511	286	29	issue	issue	NOUN
ap-3511	286	30	11	11	NUM
ap-3511	286	31	,	,	PUNCT
ap-3511	286	32	doi:10.1063/1.4901556	doi:10.1063/1.4901556	NOUN
ap-3511	286	33	.	.	PUNCT
ap-3511	287	1	[	[	X
ap-3511	287	2	8	8	NUM
ap-3511	287	3	]	]	X
ap-3511	287	4	gordon	gordon	PROPN
ap-3511	287	5	james	james	PROPN
ap-3511	287	6	,	,	PUNCT
ap-3511	287	7	martin	martin	PROPN
ap-3511	287	8	liebeck	liebeck	PROPN
ap-3511	287	9	,	,	PUNCT
ap-3511	287	10	representations	representation	NOUN
ap-3511	287	11	and	and	CCONJ
ap-3511	287	12	characters	character	NOUN
ap-3511	287	13	of	of	ADP
ap-3511	287	14	groups	group	NOUN
ap-3511	287	15	,	,	PUNCT
ap-3511	287	16	second	second	ADJ
ap-3511	287	17	edition	edition	NOUN
ap-3511	287	18	.	.	PUNCT
ap-3511	288	1	cambridge	cambridge	PROPN
ap-3511	288	2	university	university	PROPN
ap-3511	288	3	press	press	PROPN
ap-3511	288	4	,	,	PUNCT
ap-3511	288	5	new	new	PROPN
ap-3511	288	6	york	york	PROPN
ap-3511	288	7	,	,	PUNCT
ap-3511	288	8	(	(	PUNCT
ap-3511	288	9	2001	2001	NUM
ap-3511	288	10	)	)	PUNCT
ap-3511	288	11	.	.	PUNCT
ap-3511	289	1	viii+458	viii+458	ADJ
ap-3511	289	2	pp	pp	X
ap-3511	289	3	.	.	PUNCT
ap-3511	290	1	isbn	isbn	ADJ
ap-3511	290	2	:	:	PUNCT
ap-3511	290	3	0	0	NUM
ap-3511	290	4	-	-	SYM
ap-3511	290	5	521	521	NUM
ap-3511	290	6	-	-	PUNCT
ap-3511	290	7	00392	00392	NUM
ap-3511	290	8	-	-	PUNCT
ap-3511	290	9	x.	x.	NOUN
ap-3511	291	1	[	[	X
ap-3511	291	2	9	9	NUM
ap-3511	291	3	]	]	PUNCT
ap-3511	291	4	barry	barry	PROPN
ap-3511	291	5	simon	simon	PROPN
ap-3511	291	6	,	,	PUNCT
ap-3511	291	7	representations	representation	NOUN
ap-3511	291	8	of	of	ADP
ap-3511	291	9	finite	finite	ADJ
ap-3511	291	10	and	and	CCONJ
ap-3511	291	11	compact	compact	ADJ
ap-3511	291	12	groups	group	NOUN
ap-3511	291	13	,	,	PUNCT
ap-3511	291	14	graduate	graduate	NOUN
ap-3511	291	15	studies	study	NOUN
ap-3511	291	16	in	in	ADP
ap-3511	291	17	mathematics	mathematic	NOUN
ap-3511	291	18	,	,	PUNCT
ap-3511	291	19	10	10	NUM
ap-3511	291	20	.	.	PUNCT
ap-3511	292	1	american	american	PROPN
ap-3511	292	2	mathematical	mathematical	PROPN
ap-3511	292	3	society	society	NOUN
ap-3511	292	4	,	,	PUNCT
ap-3511	292	5	providence	providence	NOUN
ap-3511	292	6	,	,	PUNCT
ap-3511	292	7	ri	ri	PROPN
ap-3511	292	8	,	,	PUNCT
ap-3511	292	9	(	(	PUNCT
ap-3511	292	10	1996	1996	NUM
ap-3511	292	11	)	)	PUNCT
ap-3511	293	1	xii+266	xii+266	PROPN
ap-3511	294	1	pp	pp	ADJ
ap-3511	294	2	.	.	PUNCT
ap-3511	295	1	isbn	isbn	ADJ
ap-3511	295	2	:	:	PUNCT
ap-3511	295	3	0	0	NUM
ap-3511	295	4	-	-	PUNCT
ap-3511	295	5	8218	8218	NUM
ap-3511	295	6	-	-	PUNCT
ap-3511	295	7	0453	0453	NUM
ap-3511	295	8	-	-	SYM
ap-3511	295	9	7	7	NUM
ap-3511	295	10	.	.	PUNCT
ap-3511	296	1	[	[	X
ap-3511	296	2	10	10	NUM
ap-3511	296	3	]	]	X
ap-3511	296	4	meinolf	meinolf	PROPN
ap-3511	296	5	geck	geck	PROPN
ap-3511	296	6	,	,	PUNCT
ap-3511	296	7	gãűtz	gãűtz	PROPN
ap-3511	296	8	pfeiffer	pfeiffer	PROPN
ap-3511	296	9	,	,	PUNCT
ap-3511	296	10	characters	character	NOUN
ap-3511	296	11	of	of	ADP
ap-3511	296	12	finite	finite	ADJ
ap-3511	296	13	coxeter	coxeter	NOUN
ap-3511	296	14	groups	group	NOUN
ap-3511	296	15	and	and	CCONJ
ap-3511	296	16	iwahori	iwahori	NOUN
ap-3511	296	17	-	-	PUNCT
ap-3511	296	18	hecke	hecke	PROPN
ap-3511	296	19	algebras	algebras	PROPN
ap-3511	296	20	,	,	PUNCT
ap-3511	296	21	london	london	PROPN
ap-3511	296	22	mathematical	mathematical	ADJ
ap-3511	296	23	society	society	NOUN
ap-3511	296	24	monographs	monograph	NOUN
ap-3511	296	25	.	.	PUNCT
ap-3511	297	1	new	new	ADJ
ap-3511	297	2	series	series	NOUN
ap-3511	297	3	,	,	PUNCT
ap-3511	297	4	21	21	NUM
ap-3511	297	5	.	.	PUNCT
ap-3511	298	1	the	the	DET
ap-3511	298	2	clarendon	clarendon	PROPN
ap-3511	298	3	press	press	NOUN
ap-3511	298	4	,	,	PUNCT
ap-3511	298	5	oxford	oxford	PROPN
ap-3511	298	6	university	university	PROPN
ap-3511	298	7	press	press	NOUN
ap-3511	298	8	,	,	PUNCT
ap-3511	298	9	new	new	PROPN
ap-3511	298	10	york	york	PROPN
ap-3511	298	11	,	,	PUNCT
ap-3511	298	12	2000	2000	NUM
ap-3511	298	13	.	.	PUNCT
ap-3511	299	1	[	[	X
ap-3511	299	2	11	11	NUM
ap-3511	299	3	]	]	PUNCT
ap-3511	299	4	jiří	jiří	NOUN
ap-3511	299	5	hrivnák	hrivnák	NOUN
ap-3511	299	6	,	,	PUNCT
ap-3511	299	7	lenka	lenka	PROPN
ap-3511	299	8	motlochová	motlochová	PROPN
ap-3511	299	9	,	,	PUNCT
ap-3511	299	10	jiří	jiří	NOUN
ap-3511	299	11	patera	patera	NOUN
ap-3511	299	12	,	,	PUNCT
ap-3511	299	13	on	on	ADP
ap-3511	299	14	discretization	discretization	NOUN
ap-3511	299	15	of	of	ADP
ap-3511	299	16	tori	tori	NOUN
ap-3511	299	17	of	of	ADP
ap-3511	299	18	compact	compact	ADJ
ap-3511	299	19	simple	simple	ADJ
ap-3511	299	20	lie	lie	NOUN
ap-3511	299	21	groups	groups	PROPN
ap-3511	299	22	ii	ii	PROPN
ap-3511	299	23	,	,	PUNCT
ap-3511	299	24	,	,	PUNCT
ap-3511	299	25	j.	j.	PROPN
ap-3511	299	26	phys	phys	PROPN
ap-3511	299	27	.	.	PUNCT
ap-3511	300	1	a	a	DET
ap-3511	300	2	:	:	PUNCT
ap-3511	300	3	math	math	NOUN
ap-3511	300	4	.	.	PUNCT
ap-3511	301	1	theor	theor	PROPN
ap-3511	301	2	.	.	PUNCT
ap-3511	302	1	45	45	NUM
ap-3511	302	2	,	,	PUNCT
ap-3511	302	3	(	(	PUNCT
ap-3511	302	4	2012	2012	NUM
ap-3511	302	5	)	)	PUNCT
ap-3511	302	6	,	,	PUNCT
ap-3511	302	7	doi:10.1088/1751	doi:10.1088/1751	ADV
ap-3511	302	8	-	-	PUNCT
ap-3511	302	9	8113/45/25/255201	8113/45/25/255201	NUM
ap-3511	302	10	.	.	PUNCT
ap-3511	303	1	[	[	X
ap-3511	303	2	12	12	NUM
ap-3511	303	3	]	]	X
ap-3511	303	4	agnes	agnes	PROPN
ap-3511	303	5	andreassian	andreassian	PROPN
ap-3511	303	6	,	,	PUNCT
ap-3511	303	7	macdonald	macdonald	PROPN
ap-3511	303	8	characters	character	NOUN
ap-3511	303	9	of	of	ADP
ap-3511	303	10	weyl	weyl	VERB
ap-3511	303	11	groups	group	NOUN
ap-3511	303	12	of	of	ADP
ap-3511	303	13	rank	rank	NOUN
ap-3511	303	14	≤	≤	NUM
ap-3511	303	15	4	4	NUM
ap-3511	303	16	,	,	PUNCT
ap-3511	303	17	ph.d	ph.d	PROPN
ap-3511	303	18	.	.	PUNCT
ap-3511	304	1	thesis	thesis	NOUN
ap-3511	304	2	,	,	PUNCT
ap-3511	304	3	1973	1973	NUM
ap-3511	304	4	,	,	PUNCT
ap-3511	304	5	university	university	NOUN
ap-3511	304	6	of	of	ADP
ap-3511	304	7	british	british	PROPN
ap-3511	304	8	colombia	colombia	PROPN
ap-3511	304	9	.	.	PUNCT
ap-3511	305	1	[	[	X
ap-3511	305	2	13	13	NUM
ap-3511	305	3	]	]	SYM
ap-3511	305	4	maryna	maryna	NOUN
ap-3511	305	5	nesterenko	nesterenko	PROPN
ap-3511	305	6	,	,	PUNCT
ap-3511	305	7	jiří	jiří	NOUN
ap-3511	305	8	patera	patera	NOUN
ap-3511	305	9	,	,	PUNCT
ap-3511	305	10	marzena	marzena	PROPN
ap-3511	305	11	szajewska	szajewska	PROPN
ap-3511	305	12	,	,	PUNCT
ap-3511	305	13	agnieszka	agnieszka	PROPN
ap-3511	305	14	tereszkiewicz	tereszkiewicz	PROPN
ap-3511	305	15	,	,	PUNCT
ap-3511	305	16	orthogonal	orthogonal	ADJ
ap-3511	305	17	polynomials	polynomial	NOUN
ap-3511	305	18	of	of	ADP
ap-3511	305	19	compact	compact	ADJ
ap-3511	305	20	simple	simple	ADJ
ap-3511	305	21	lie	lie	NOUN
ap-3511	305	22	groups	group	NOUN
ap-3511	305	23	:	:	PUNCT
ap-3511	305	24	branching	branch	VERB
ap-3511	305	25	rules	rule	NOUN
ap-3511	305	26	for	for	ADP
ap-3511	305	27	polynomials	polynomial	NOUN
ap-3511	305	28	,	,	PUNCT
ap-3511	305	29	j.	j.	PROPN
ap-3511	305	30	phys	phys	PROPN
ap-3511	305	31	.	.	PUNCT
ap-3511	306	1	a	a	DET
ap-3511	306	2	43	43	NUM
ap-3511	306	3	(	(	PUNCT
ap-3511	306	4	2010	2010	NUM
ap-3511	306	5	)	)	PUNCT
ap-3511	306	6	,	,	PUNCT
ap-3511	306	7	no	no	INTJ
ap-3511	306	8	.	.	NOUN
ap-3511	306	9	49	49	NUM
ap-3511	306	10	,	,	PUNCT
ap-3511	306	11	495207	495207	NUM
ap-3511	306	12	,	,	PUNCT
ap-3511	306	13	27	27	NUM
ap-3511	306	14	pp	pp	ADJ
ap-3511	306	15	,	,	PUNCT
ap-3511	306	16	doi:10.1088/1751	doi:10.1088/1751	NOUN
ap-3511	306	17	-	-	PUNCT
ap-3511	306	18	8113/43/49/495207	8113/43/49/495207	NOUN
ap-3511	306	19	.	.	PUNCT
ap-3511	307	1	447	447	NUM
ap-3511	307	2	http://dx.doi.org/10.3842/sigma.2006.006	http://dx.doi.org/10.3842/sigma.2006.006	NOUN
ap-3511	307	3	http://dx.doi.org/10.3842/sigma.2007.023	http://dx.doi.org/10.3842/sigma.2007.023	NOUN
ap-3511	307	4	http://dx.doi.org/10.3842/sigma.2006.076	http://dx.doi.org/10.3842/sigma.2006.076	NOUN
ap-3511	307	5	http://dx.doi.org/10.1007/s00041-014-9355-0	http://dx.doi.org/10.1007/s00041-014-9355-0	PUNCT
ap-3511	307	6	http://dx.doi.org/10.1088/1751-8113/42/38/385208	http://dx.doi.org/10.1088/1751-8113/42/38/385208	VERB
ap-3511	307	7	http://dx.doi.org/10.1063/1.4817340	http://dx.doi.org/10.1063/1.4817340	ADV
ap-3511	307	8	http://dx.doi.org/10.1063/1.4901556	http://dx.doi.org/10.1063/1.4901556	NOUN
ap-3511	307	9	http://dx.doi.org/10.1088/1751-8113/45/25/255201	http://dx.doi.org/10.1088/1751-8113/45/25/255201	X
ap-3511	307	10	http://dx.doi.org/10.1088/1751-8113/43/49/495207	http://dx.doi.org/10.1088/1751-8113/43/49/495207	X
ap-3511	307	11	acta	acta	PROPN
ap-3511	307	12	polytechnica	polytechnica	PROPN
ap-3511	307	13	56(6):440–447	56(6):440–447	PROPN
ap-3511	307	14	,	,	PUNCT
ap-3511	307	15	2016	2016	NUM
ap-3511	307	16	1	1	NUM
ap-3511	307	17	introduction	introduction	NOUN
ap-3511	307	18	2	2	NUM
ap-3511	307	19	preliminaries	preliminary	NOUN
ap-3511	307	20	2.1	2.1	NUM
ap-3511	307	21	irreducible	irreducible	ADJ
ap-3511	307	22	characters	character	NOUN
ap-3511	307	23	of	of	ADP
ap-3511	307	24	symmetric	symmetric	ADJ
ap-3511	307	25	groups	group	NOUN
ap-3511	307	26	2.2	2.2	NUM
ap-3511	307	27	weyl	weyl	VERB
ap-3511	307	28	groups	group	NOUN
ap-3511	307	29	of	of	ADP
ap-3511	307	30	simple	simple	ADJ
ap-3511	307	31	lie	lie	NOUN
ap-3511	307	32	algebras	algebra	VERB
ap-3511	307	33	3	3	NUM
ap-3511	307	34	special	special	ADJ
ap-3511	307	35	functions	function	NOUN
ap-3511	307	36	related	relate	VERB
ap-3511	307	37	to	to	ADP
ap-3511	307	38	weyl	weyl	VERB
ap-3511	307	39	groups	group	NOUN
ap-3511	307	40	3.1	3.1	NUM
ap-3511	307	41	weyl	weyl	VERB
ap-3511	307	42	group	group	NOUN
ap-3511	307	43	orbit	orbit	NOUN
ap-3511	307	44	functions	function	NOUN
ap-3511	307	45	3.2	3.2	NUM
ap-3511	307	46	character	character	NOUN
ap-3511	307	47	functions	function	NOUN
ap-3511	307	48	4	4	NUM
ap-3511	307	49	properties	property	NOUN
ap-3511	307	50	of	of	ADP
ap-3511	307	51	character	character	NOUN
ap-3511	307	52	functions	function	NOUN
ap-3511	307	53	4.1	4.1	NUM
ap-3511	307	54	general	general	ADJ
ap-3511	307	55	properties	property	NOUN
ap-3511	307	56	4.2	4.2	NUM
ap-3511	307	57	continuous	continuous	ADJ
ap-3511	307	58	and	and	CCONJ
ap-3511	307	59	discrete	discrete	ADJ
ap-3511	307	60	orthogonality	orthogonality	NOUN
ap-3511	307	61	4.3	4.3	NUM
ap-3511	307	62	linear	linear	ADJ
ap-3511	307	63	independency	independency	NOUN
ap-3511	307	64	of	of	ADP
ap-3511	307	65	character	character	NOUN
ap-3511	307	66	functions	function	NOUN
ap-3511	307	67	5	5	NUM
ap-3511	307	68	character	character	NOUN
ap-3511	307	69	functions	function	NOUN
ap-3511	307	70	related	relate	VERB
ap-3511	307	71	to	to	ADP
ap-3511	307	72	weyl	weyl	VERB
ap-3511	307	73	groups	group	NOUN
ap-3511	307	74	of	of	ADP
ap-3511	307	75	rank	rank	NOUN
ap-3511	307	76	2	2	NUM
ap-3511	307	77	and	and	CCONJ
ap-3511	307	78	3	3	NUM
ap-3511	307	79	5.1	5.1	NUM
ap-3511	307	80	weyl	weyl	VERB
ap-3511	307	81	groups	group	NOUN
ap-3511	307	82	of	of	ADP
ap-3511	307	83	rank	rank	NOUN
ap-3511	307	84	2	2	NUM
ap-3511	307	85	5.2	5.2	NUM
ap-3511	307	86	weyl	weyl	VERB
ap-3511	307	87	groups	group	NOUN
ap-3511	307	88	of	of	ADP
ap-3511	307	89	rank	rank	NOUN
ap-3511	307	90	3	3	NUM
ap-3511	307	91	6	6	NUM
ap-3511	307	92	concluding	conclude	VERB
ap-3511	307	93	remarks	remark	NOUN
ap-3511	307	94	references	reference	NOUN