id	sid	tid	token	lemma	pos
ejpam-5175	1	1	european	european	PROPN
ejpam-5175	1	2	journal	journal	PROPN
ejpam-5175	1	3	of	of	ADP
ejpam-5175	1	4	pure	pure	ADJ
ejpam-5175	1	5	and	and	CCONJ
ejpam-5175	1	6	applied	apply	VERB
ejpam-5175	1	7	mathematics	mathematic	NOUN
ejpam-5175	1	8	vol	vol	NOUN
ejpam-5175	1	9	.	.	PROPN
ejpam-5175	2	1	17	17	NUM
ejpam-5175	2	2	,	,	PUNCT
ejpam-5175	2	3	no	no	INTJ
ejpam-5175	2	4	.	.	NOUN
ejpam-5175	2	5	3	3	NUM
ejpam-5175	2	6	,	,	PUNCT
ejpam-5175	2	7	2024	2024	NUM
ejpam-5175	2	8	,	,	PUNCT
ejpam-5175	2	9	1717	1717	NUM
ejpam-5175	2	10	-	-	SYM
ejpam-5175	2	11	1726	1726	NUM
ejpam-5175	2	12	issn	issn	PROPN
ejpam-5175	2	13	1307	1307	NUM
ejpam-5175	2	14	-	-	SYM
ejpam-5175	2	15	5543	5543	NUM
ejpam-5175	2	16	–	–	PUNCT
ejpam-5175	3	1	ejpam.com	ejpam.com	X
ejpam-5175	3	2	published	publish	VERB
ejpam-5175	3	3	by	by	ADP
ejpam-5175	3	4	new	new	PROPN
ejpam-5175	3	5	york	york	PROPN
ejpam-5175	3	6	business	business	PROPN
ejpam-5175	3	7	global	global	PROPN
ejpam-5175	3	8	on	on	ADP
ejpam-5175	3	9	the	the	DET
ejpam-5175	3	10	representations	representation	NOUN
ejpam-5175	3	11	and	and	CCONJ
ejpam-5175	3	12	characters	character	NOUN
ejpam-5175	3	13	of	of	ADP
ejpam-5175	3	14	quaternions	quaternion	NOUN
ejpam-5175	3	15	group	group	NOUN
ejpam-5175	3	16	q8	q8	PROPN
ejpam-5175	3	17	abdallah	abdallah	PROPN
ejpam-5175	3	18	labsir1,∗	labsir1,∗	PROPN
ejpam-5175	3	19	,	,	PUNCT
ejpam-5175	3	20	el	el	PROPN
ejpam-5175	3	21	mokhtar	mokhtar	PROPN
ejpam-5175	3	22	fanich2	fanich2	ADJ
ejpam-5175	3	23	1	1	NUM
ejpam-5175	3	24	laboratory	laboratory	NOUN
ejpam-5175	3	25	of	of	ADP
ejpam-5175	3	26	applied	apply	VERB
ejpam-5175	3	27	mathematics	mathematic	NOUN
ejpam-5175	3	28	and	and	CCONJ
ejpam-5175	3	29	intelligent	intelligent	ADJ
ejpam-5175	3	30	systems	system	NOUN
ejpam-5175	3	31	engineering	engineering	NOUN
ejpam-5175	3	32	(	(	PUNCT
ejpam-5175	3	33	maisi	maisi	NUM
ejpam-5175	3	34	)	)	PUNCT
ejpam-5175	3	35	,	,	PUNCT
ejpam-5175	3	36	national	national	ADJ
ejpam-5175	3	37	school	school	NOUN
ejpam-5175	3	38	of	of	ADP
ejpam-5175	3	39	applied	apply	VERB
ejpam-5175	3	40	sciences	science	NOUN
ejpam-5175	3	41	,	,	PUNCT
ejpam-5175	3	42	ibn	ibn	PROPN
ejpam-5175	3	43	zohr	zohr	NOUN
ejpam-5175	3	44	university	university	PROPN
ejpam-5175	3	45	,	,	PUNCT
ejpam-5175	3	46	agadir	agadir	PROPN
ejpam-5175	3	47	,	,	PUNCT
ejpam-5175	3	48	morocco	morocco	PROPN
ejpam-5175	3	49	2	2	NUM
ejpam-5175	3	50	laboratory	laboratory	NOUN
ejpam-5175	3	51	of	of	ADP
ejpam-5175	3	52	analysis	analysis	NOUN
ejpam-5175	3	53	,	,	PUNCT
ejpam-5175	3	54	modeling	modeling	NOUN
ejpam-5175	3	55	and	and	CCONJ
ejpam-5175	3	56	simulation	simulation	NOUN
ejpam-5175	3	57	,	,	PUNCT
ejpam-5175	3	58	department	department	NOUN
ejpam-5175	3	59	of	of	ADP
ejpam-5175	3	60	mathematics	mathematics	PROPN
ejpam-5175	3	61	and	and	CCONJ
ejpam-5175	3	62	computer	computer	NOUN
ejpam-5175	3	63	science	science	NOUN
ejpam-5175	3	64	,	,	PUNCT
ejpam-5175	3	65	ben	ben	PROPN
ejpam-5175	3	66	m’sick	m’sick	PROPN
ejpam-5175	3	67	’s	’s	PART
ejpam-5175	3	68	faculty	faculty	NOUN
ejpam-5175	3	69	of	of	ADP
ejpam-5175	3	70	sciences	science	NOUN
ejpam-5175	3	71	,	,	PUNCT
ejpam-5175	3	72	hassan	hassan	PROPN
ejpam-5175	3	73	ii	ii	PROPN
ejpam-5175	3	74	university	university	PROPN
ejpam-5175	3	75	of	of	ADP
ejpam-5175	3	76	casablanca	casablanca	PROPN
ejpam-5175	3	77	,	,	PUNCT
ejpam-5175	3	78	casablanca	casablanca	PROPN
ejpam-5175	3	79	,	,	PUNCT
ejpam-5175	3	80	morocco	morocco	PROPN
ejpam-5175	3	81	abstract	abstract	NOUN
ejpam-5175	3	82	.	.	PUNCT
ejpam-5175	4	1	we	we	PRON
ejpam-5175	4	2	are	be	AUX
ejpam-5175	4	3	interested	interested	ADJ
ejpam-5175	4	4	in	in	ADP
ejpam-5175	4	5	studying	study	VERB
ejpam-5175	4	6	the	the	DET
ejpam-5175	4	7	linear	linear	ADJ
ejpam-5175	4	8	representations	representation	NOUN
ejpam-5175	4	9	of	of	ADP
ejpam-5175	4	10	the	the	DET
ejpam-5175	4	11	quaternions	quaternions	ADJ
ejpam-5175	4	12	group	group	NOUN
ejpam-5175	4	13	q8	q8	PROPN
ejpam-5175	4	14	by	by	ADP
ejpam-5175	4	15	determining	determine	VERB
ejpam-5175	4	16	it	it	PRON
ejpam-5175	4	17	’s	’s	ADJ
ejpam-5175	4	18	charater	charater	NOUN
ejpam-5175	4	19	table	table	NOUN
ejpam-5175	4	20	and	and	CCONJ
ejpam-5175	4	21	irreducible	irreducible	ADJ
ejpam-5175	4	22	representations	representation	NOUN
ejpam-5175	4	23	which	which	PRON
ejpam-5175	4	24	allows	allow	VERB
ejpam-5175	4	25	us	we	PRON
ejpam-5175	4	26	to	to	PART
ejpam-5175	4	27	construct	construct	VERB
ejpam-5175	4	28	some	some	DET
ejpam-5175	4	29	representations	representation	NOUN
ejpam-5175	4	30	of	of	ADP
ejpam-5175	4	31	degre	degre	PROPN
ejpam-5175	4	32	6	6	NUM
ejpam-5175	4	33	and	and	CCONJ
ejpam-5175	4	34	8	8	NUM
ejpam-5175	4	35	of	of	ADP
ejpam-5175	4	36	q8	q8	PROPN
ejpam-5175	4	37	.	.	PROPN
ejpam-5175	5	1	2020	2020	NUM
ejpam-5175	5	2	mathematics	mathematics	PROPN
ejpam-5175	5	3	subject	subject	NOUN
ejpam-5175	5	4	classifications	classification	NOUN
ejpam-5175	5	5	:	:	PUNCT
ejpam-5175	5	6	20c15	20c15	NUM
ejpam-5175	5	7	,	,	PUNCT
ejpam-5175	5	8	20c20	20c20	NUM
ejpam-5175	5	9	,	,	PUNCT
ejpam-5175	5	10	20c30	20c30	NUM
ejpam-5175	5	11	,	,	PUNCT
ejpam-5175	5	12	20g20	20g20	NUM
ejpam-5175	5	13	key	key	ADJ
ejpam-5175	5	14	words	word	NOUN
ejpam-5175	5	15	and	and	CCONJ
ejpam-5175	5	16	phrases	phrase	NOUN
ejpam-5175	5	17	:	:	PUNCT
ejpam-5175	5	18	irreducible	irreducible	ADJ
ejpam-5175	5	19	representation	representation	NOUN
ejpam-5175	5	20	,	,	PUNCT
ejpam-5175	5	21	character	character	NOUN
ejpam-5175	5	22	table	table	NOUN
ejpam-5175	5	23	,	,	PUNCT
ejpam-5175	5	24	quaternions	quaternions	ADJ
ejpam-5175	5	25	group	group	NOUN
ejpam-5175	5	26	,	,	PUNCT
ejpam-5175	5	27	group	group	NOUN
ejpam-5175	5	28	q8	q8	PROPN
ejpam-5175	5	29	1	1	NUM
ejpam-5175	5	30	.	.	PUNCT
ejpam-5175	5	31	introduction	introduction	NOUN
ejpam-5175	5	32	group	group	NOUN
ejpam-5175	5	33	representation	representation	NOUN
ejpam-5175	5	34	theory	theory	NOUN
ejpam-5175	5	35	allows	allow	VERB
ejpam-5175	5	36	the	the	DET
ejpam-5175	5	37	study	study	NOUN
ejpam-5175	5	38	of	of	ADP
ejpam-5175	5	39	abstract	abstract	ADJ
ejpam-5175	5	40	groups	group	NOUN
ejpam-5175	5	41	by	by	ADP
ejpam-5175	5	42	representing	represent	VERB
ejpam-5175	5	43	their	their	PRON
ejpam-5175	5	44	elements	element	NOUN
ejpam-5175	5	45	by	by	ADP
ejpam-5175	5	46	invertible	invertible	ADJ
ejpam-5175	5	47	matrices	matrix	NOUN
ejpam-5175	5	48	.	.	PUNCT
ejpam-5175	6	1	we	we	PRON
ejpam-5175	6	2	then	then	ADV
ejpam-5175	6	3	have	have	VERB
ejpam-5175	6	4	the	the	DET
ejpam-5175	6	5	methods	method	NOUN
ejpam-5175	6	6	of	of	ADP
ejpam-5175	6	7	linear	linear	PROPN
ejpam-5175	6	8	algebra	algebra	NOUN
ejpam-5175	6	9	which	which	PRON
ejpam-5175	6	10	often	often	ADV
ejpam-5175	6	11	make	make	VERB
ejpam-5175	6	12	the	the	DET
ejpam-5175	6	13	study	study	NOUN
ejpam-5175	6	14	of	of	ADP
ejpam-5175	6	15	these	these	DET
ejpam-5175	6	16	groups	group	NOUN
ejpam-5175	6	17	easier	easy	ADJ
ejpam-5175	6	18	and	and	CCONJ
ejpam-5175	6	19	make	make	VERB
ejpam-5175	6	20	it	it	PRON
ejpam-5175	6	21	possible	possible	ADJ
ejpam-5175	6	22	to	to	PART
ejpam-5175	6	23	obtain	obtain	VERB
ejpam-5175	6	24	new	new	ADJ
ejpam-5175	6	25	properties	property	NOUN
ejpam-5175	6	26	.	.	PUNCT
ejpam-5175	7	1	the	the	DET
ejpam-5175	7	2	idea	idea	NOUN
ejpam-5175	7	3	is	be	AUX
ejpam-5175	7	4	to	to	PART
ejpam-5175	7	5	make	make	VERB
ejpam-5175	7	6	a	a	DET
ejpam-5175	7	7	group	group	NOUN
ejpam-5175	7	8	g	g	PROPN
ejpam-5175	7	9	act	act	NOUN
ejpam-5175	7	10	on	on	ADP
ejpam-5175	7	11	a	a	DET
ejpam-5175	7	12	vector	vector	NOUN
ejpam-5175	7	13	space	space	NOUN
ejpam-5175	7	14	v	v	ADP
ejpam-5175	7	15	such	such	ADJ
ejpam-5175	7	16	that	that	SCONJ
ejpam-5175	7	17	the	the	DET
ejpam-5175	7	18	action	action	NOUN
ejpam-5175	7	19	of	of	ADP
ejpam-5175	7	20	each	each	DET
ejpam-5175	7	21	element	element	NOUN
ejpam-5175	7	22	is	be	AUX
ejpam-5175	7	23	compatible	compatible	ADJ
ejpam-5175	7	24	with	with	ADP
ejpam-5175	7	25	the	the	DET
ejpam-5175	7	26	structure	structure	NOUN
ejpam-5175	7	27	of	of	ADP
ejpam-5175	7	28	the	the	DET
ejpam-5175	7	29	vector	vector	NOUN
ejpam-5175	7	30	space	space	NOUN
ejpam-5175	7	31	,	,	PUNCT
ejpam-5175	7	32	that	that	PRON
ejpam-5175	7	33	is	be	AUX
ejpam-5175	7	34	to	to	PART
ejpam-5175	7	35	say	say	VERB
ejpam-5175	7	36	it	it	PRON
ejpam-5175	7	37	is	be	AUX
ejpam-5175	7	38	an	an	DET
ejpam-5175	7	39	element	element	NOUN
ejpam-5175	7	40	of	of	ADP
ejpam-5175	7	41	gl(v	gl(v	X
ejpam-5175	7	42	)	)	PUNCT
ejpam-5175	7	43	the	the	DET
ejpam-5175	7	44	group	group	NOUN
ejpam-5175	7	45	of	of	ADP
ejpam-5175	7	46	linear	linear	PROPN
ejpam-5175	7	47	automorphisms	automorphism	NOUN
ejpam-5175	7	48	of	of	ADP
ejpam-5175	7	49	v	v	NUM
ejpam-5175	7	50	and	and	CCONJ
ejpam-5175	7	51	more	more	ADJ
ejpam-5175	7	52	only	only	ADV
ejpam-5175	7	53	a	a	DET
ejpam-5175	7	54	bijection	bijection	NOUN
ejpam-5175	7	55	of	of	ADP
ejpam-5175	7	56	v	v	NOUN
ejpam-5175	7	57	on	on	ADP
ejpam-5175	7	58	v	v	NOUN
ejpam-5175	7	59	.	.	PUNCT
ejpam-5175	8	1	this	this	DET
ejpam-5175	8	2	concept	concept	NOUN
ejpam-5175	8	3	emerges	emerge	VERB
ejpam-5175	8	4	at	at	ADP
ejpam-5175	8	5	the	the	DET
ejpam-5175	8	6	end	end	NOUN
ejpam-5175	8	7	of	of	ADP
ejpam-5175	8	8	the	the	DET
ejpam-5175	8	9	19th	19th	ADJ
ejpam-5175	8	10	century	century	NOUN
ejpam-5175	8	11	and	and	CCONJ
ejpam-5175	8	12	the	the	DET
ejpam-5175	8	13	general	general	ADJ
ejpam-5175	8	14	study	study	NOUN
ejpam-5175	8	15	of	of	ADP
ejpam-5175	8	16	the	the	DET
ejpam-5175	8	17	representations	representation	NOUN
ejpam-5175	8	18	of	of	ADP
ejpam-5175	8	19	a	a	DET
ejpam-5175	8	20	group	group	NOUN
ejpam-5175	8	21	is	be	AUX
ejpam-5175	8	22	largely	largely	ADV
ejpam-5175	8	23	developed	develop	VERB
ejpam-5175	8	24	by	by	ADP
ejpam-5175	8	25	william	william	PROPN
ejpam-5175	8	26	burnside	burnside	PROPN
ejpam-5175	8	27	and	and	CCONJ
ejpam-5175	8	28	ferdinand	ferdinand	PROPN
ejpam-5175	8	29	georg	georg	PROPN
ejpam-5175	8	30	frobenius	frobenius	NOUN
ejpam-5175	8	31	at	at	ADP
ejpam-5175	8	32	the	the	DET
ejpam-5175	8	33	beginning	beginning	NOUN
ejpam-5175	8	34	of	of	ADP
ejpam-5175	8	35	the	the	DET
ejpam-5175	8	36	20th	20th	ADJ
ejpam-5175	8	37	century[3	century[3	NOUN
ejpam-5175	8	38	]	]	PUNCT
ejpam-5175	8	39	.	.	PUNCT
ejpam-5175	9	1	representation	representation	NOUN
ejpam-5175	9	2	theory	theory	NOUN
ejpam-5175	9	3	has	have	AUX
ejpam-5175	9	4	enabled	enable	VERB
ejpam-5175	9	5	remarkable	remarkable	ADJ
ejpam-5175	9	6	advances	advance	NOUN
ejpam-5175	9	7	,	,	PUNCT
ejpam-5175	9	8	first	first	ADV
ejpam-5175	9	9	of	of	ADP
ejpam-5175	9	10	all	all	PRON
ejpam-5175	9	11	in	in	ADP
ejpam-5175	9	12	group	group	NOUN
ejpam-5175	9	13	theory	theory	NOUN
ejpam-5175	9	14	.	.	PUNCT
ejpam-5175	10	1	in	in	ADP
ejpam-5175	10	2	particular	particular	ADJ
ejpam-5175	10	3	,	,	PUNCT
ejpam-5175	10	4	it	it	PRON
ejpam-5175	10	5	plays	play	VERB
ejpam-5175	10	6	a	a	DET
ejpam-5175	10	7	fundamental	fundamental	ADJ
ejpam-5175	10	8	role	role	NOUN
ejpam-5175	10	9	in	in	ADP
ejpam-5175	10	10	the	the	DET
ejpam-5175	10	11	classification	classification	NOUN
ejpam-5175	10	12	theorem	theorem	NOUN
ejpam-5175	10	13	of	of	ADP
ejpam-5175	10	14	finite	finite	ADJ
ejpam-5175	10	15	simple	simple	ADJ
ejpam-5175	10	16	groups[5	groups[5	NOUN
ejpam-5175	10	17	]	]	PUNCT
ejpam-5175	10	18	.	.	PUNCT
ejpam-5175	11	1	the	the	DET
ejpam-5175	11	2	theory	theory	NOUN
ejpam-5175	11	3	of	of	ADP
ejpam-5175	11	4	representations	representation	NOUN
ejpam-5175	11	5	of	of	ADP
ejpam-5175	11	6	general	general	ADJ
ejpam-5175	11	7	groups	group	NOUN
ejpam-5175	11	8	(	(	PUNCT
ejpam-5175	11	9	not	not	PART
ejpam-5175	11	10	necessarily	necessarily	ADV
ejpam-5175	11	11	finite	finite	VERB
ejpam-5175	11	12	)	)	PUNCT
ejpam-5175	11	13	and	and	CCONJ
ejpam-5175	11	14	algebras	algebra	NOUN
ejpam-5175	11	15	also	also	ADV
ejpam-5175	11	16	has	have	VERB
ejpam-5175	11	17	numerous	numerous	ADJ
ejpam-5175	11	18	applications	application	NOUN
ejpam-5175	11	19	in	in	ADP
ejpam-5175	11	20	crystallographic	crystallographic	ADJ
ejpam-5175	11	21	chemistry	chemistry	NOUN
ejpam-5175	11	22	,	,	PUNCT
ejpam-5175	11	23	in	in	ADP
ejpam-5175	11	24	engineering	engineering	NOUN
ejpam-5175	11	25	and	and	CCONJ
ejpam-5175	11	26	especially	especially	ADV
ejpam-5175	11	27	in	in	ADP
ejpam-5175	11	28	∗corresponding	∗corresponde	VERB
ejpam-5175	11	29	author	author	NOUN
ejpam-5175	11	30	.	.	PUNCT
ejpam-5175	12	1	doi	doi	NOUN
ejpam-5175	12	2	:	:	PUNCT
ejpam-5175	12	3	https://doi.org/10.29020/nybg.ejpam.v17i3.5175	https://doi.org/10.29020/nybg.ejpam.v17i3.5175	NUM
ejpam-5175	12	4	email	email	NOUN
ejpam-5175	12	5	addresses	address	NOUN
ejpam-5175	12	6	:	:	PUNCT
ejpam-5175	12	7	abdallah.labsir@edu.uiz.ac.ma	abdallah.labsir@edu.uiz.ac.ma	PROPN
ejpam-5175	12	8	(	(	PUNCT
ejpam-5175	12	9	a.	a.	NOUN
ejpam-5175	12	10	labsir	labsir	PROPN
ejpam-5175	12	11	)	)	PUNCT
ejpam-5175	12	12	,	,	PUNCT
ejpam-5175	12	13	elmokhtar.fanich-etu@etu.univh2c.ma	elmokhtar.fanich-etu@etu.univh2c.ma	NOUN
ejpam-5175	12	14	(	(	PUNCT
ejpam-5175	12	15	e.	e.	PROPN
ejpam-5175	12	16	fanich	fanich	PROPN
ejpam-5175	12	17	)	)	PUNCT
ejpam-5175	12	18	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5175	13	1	1717	1717	NUM
ejpam-5175	13	2	©	©	ADP
ejpam-5175	13	3	2024	2024	NUM
ejpam-5175	13	4	ejpam	ejpam	NOUN
ejpam-5175	13	5	all	all	DET
ejpam-5175	13	6	rights	right	NOUN
ejpam-5175	13	7	reserved	reserve	VERB
ejpam-5175	13	8	.	.	PUNCT
ejpam-5175	14	1	a.	a.	NOUN
ejpam-5175	14	2	labsir	labsir	PROPN
ejpam-5175	14	3	,	,	PUNCT
ejpam-5175	14	4	e.	e.	PROPN
ejpam-5175	14	5	fanich	fanich	PROPN
ejpam-5175	14	6	/	/	SYM
ejpam-5175	14	7	eur	eur	PROPN
ejpam-5175	14	8	.	.	PUNCT
ejpam-5175	15	1	j.	j.	PROPN
ejpam-5175	15	2	pure	pure	PROPN
ejpam-5175	15	3	appl	appl	PROPN
ejpam-5175	15	4	.	.	PROPN
ejpam-5175	15	5	math	math	PROPN
ejpam-5175	15	6	,	,	PUNCT
ejpam-5175	15	7	17	17	NUM
ejpam-5175	15	8	(	(	PUNCT
ejpam-5175	15	9	3	3	NUM
ejpam-5175	15	10	)	)	PUNCT
ejpam-5175	15	11	(	(	PUNCT
ejpam-5175	15	12	2024	2024	NUM
ejpam-5175	15	13	)	)	PUNCT
ejpam-5175	15	14	,	,	PUNCT
ejpam-5175	15	15	1717	1717	NUM
ejpam-5175	15	16	-	-	SYM
ejpam-5175	15	17	1726	1726	NUM
ejpam-5175	15	18	1718	1718	NUM
ejpam-5175	15	19	quantum	quantum	NOUN
ejpam-5175	15	20	physics	physics	NOUN
ejpam-5175	15	21	:	:	PUNCT
ejpam-5175	15	22	the	the	DET
ejpam-5175	15	23	theory	theory	NOUN
ejpam-5175	15	24	of	of	ADP
ejpam-5175	15	25	representation	representation	NOUN
ejpam-5175	15	26	makes	make	VERB
ejpam-5175	15	27	it	it	PRON
ejpam-5175	15	28	possible	possible	ADJ
ejpam-5175	15	29	to	to	PART
ejpam-5175	15	30	analyze	analyze	VERB
ejpam-5175	15	31	the	the	DET
ejpam-5175	15	32	symmetries	symmetry	NOUN
ejpam-5175	15	33	of	of	ADP
ejpam-5175	15	34	a	a	DET
ejpam-5175	15	35	related	relate	VERB
ejpam-5175	15	36	physical	physical	ADJ
ejpam-5175	15	37	problem	problem	NOUN
ejpam-5175	15	38	with	with	ADP
ejpam-5175	15	39	a	a	DET
ejpam-5175	15	40	group	group	NOUN
ejpam-5175	15	41	by	by	ADP
ejpam-5175	15	42	classifying	classify	VERB
ejpam-5175	15	43	the	the	DET
ejpam-5175	15	44	solutions	solution	NOUN
ejpam-5175	15	45	of	of	ADP
ejpam-5175	15	46	this	this	DET
ejpam-5175	15	47	problem	problem	NOUN
ejpam-5175	15	48	according	accord	VERB
ejpam-5175	15	49	to	to	ADP
ejpam-5175	15	50	the	the	DET
ejpam-5175	15	51	irreducible	irreducible	ADJ
ejpam-5175	15	52	representations[2	representations[2	NOUN
ejpam-5175	15	53	]	]	PUNCT
ejpam-5175	15	54	.	.	PUNCT
ejpam-5175	16	1	in	in	ADP
ejpam-5175	16	2	this	this	DET
ejpam-5175	16	3	work	work	NOUN
ejpam-5175	16	4	,	,	PUNCT
ejpam-5175	16	5	we	we	PRON
ejpam-5175	16	6	recall	recall	VERB
ejpam-5175	16	7	first	first	ADV
ejpam-5175	16	8	some	some	DET
ejpam-5175	16	9	results	result	NOUN
ejpam-5175	16	10	on	on	ADP
ejpam-5175	16	11	the	the	DET
ejpam-5175	16	12	theory	theory	NOUN
ejpam-5175	16	13	of	of	ADP
ejpam-5175	16	14	reprentations	reprentation	NOUN
ejpam-5175	16	15	and	and	CCONJ
ejpam-5175	16	16	character	character	NOUN
ejpam-5175	16	17	of	of	ADP
ejpam-5175	16	18	finite	finite	ADJ
ejpam-5175	16	19	groups	group	NOUN
ejpam-5175	16	20	,	,	PUNCT
ejpam-5175	16	21	and	and	CCONJ
ejpam-5175	16	22	by	by	ADP
ejpam-5175	16	23	the	the	DET
ejpam-5175	16	24	end	end	NOUN
ejpam-5175	16	25	we	we	PRON
ejpam-5175	16	26	arrive	arrive	VERB
ejpam-5175	16	27	to	to	PART
ejpam-5175	16	28	determine	determine	VERB
ejpam-5175	16	29	the	the	DET
ejpam-5175	16	30	irreducible	irreducible	ADJ
ejpam-5175	16	31	representations	representation	NOUN
ejpam-5175	16	32	and	and	CCONJ
ejpam-5175	16	33	to	to	PART
ejpam-5175	16	34	draw	draw	VERB
ejpam-5175	16	35	up	up	ADP
ejpam-5175	16	36	the	the	DET
ejpam-5175	16	37	character	character	NOUN
ejpam-5175	16	38	table	table	NOUN
ejpam-5175	16	39	of	of	ADP
ejpam-5175	16	40	the	the	DET
ejpam-5175	16	41	quaternions	quaternions	PROPN
ejpam-5175	16	42	group	group	NOUN
ejpam-5175	16	43	q8	q8	PROPN
ejpam-5175	16	44	which	which	PRON
ejpam-5175	16	45	allows	allow	VERB
ejpam-5175	16	46	us	we	PRON
ejpam-5175	16	47	to	to	PART
ejpam-5175	16	48	construct	construct	VERB
ejpam-5175	16	49	some	some	DET
ejpam-5175	16	50	representations	representation	NOUN
ejpam-5175	16	51	of	of	ADP
ejpam-5175	16	52	degre	degre	PROPN
ejpam-5175	16	53	6	6	NUM
ejpam-5175	16	54	and	and	CCONJ
ejpam-5175	16	55	8	8	NUM
ejpam-5175	16	56	of	of	ADP
ejpam-5175	16	57	this	this	DET
ejpam-5175	16	58	group	group	NOUN
ejpam-5175	16	59	.	.	PUNCT
ejpam-5175	17	1	2	2	X
ejpam-5175	17	2	.	.	X
ejpam-5175	17	3	preleminaries	preleminarie	NOUN
ejpam-5175	17	4	let	let	VERB
ejpam-5175	17	5	e	e	PRON
ejpam-5175	17	6	be	be	AUX
ejpam-5175	17	7	a	a	DET
ejpam-5175	17	8	vector	vector	NOUN
ejpam-5175	17	9	space	space	NOUN
ejpam-5175	17	10	on	on	ADP
ejpam-5175	17	11	k	k	NOUN
ejpam-5175	17	12	,	,	PUNCT
ejpam-5175	17	13	where	where	SCONJ
ejpam-5175	17	14	k	k	PROPN
ejpam-5175	17	15	=	=	SYM
ejpam-5175	17	16	r	r	NOUN
ejpam-5175	17	17	or	or	CCONJ
ejpam-5175	17	18	c	c	NOUN
ejpam-5175	17	19	,	,	PUNCT
ejpam-5175	17	20	and	and	CCONJ
ejpam-5175	17	21	let	let	VERB
ejpam-5175	17	22	gl(e	gl(e	VERB
ejpam-5175	17	23	)	)	PUNCT
ejpam-5175	17	24	the	the	DET
ejpam-5175	17	25	group	group	NOUN
ejpam-5175	17	26	of	of	ADP
ejpam-5175	17	27	isomorphisms	isomorphisms	PROPN
ejpam-5175	17	28	of	of	ADP
ejpam-5175	17	29	e	e	PROPN
ejpam-5175	17	30	on	on	ADP
ejpam-5175	17	31	itself	itself	PRON
ejpam-5175	17	32	.	.	PUNCT
ejpam-5175	18	1	definition	definition	NOUN
ejpam-5175	18	2	1	1	NUM
ejpam-5175	18	3	(	(	PUNCT
ejpam-5175	18	4	see	see	VERB
ejpam-5175	18	5	[	[	X
ejpam-5175	18	6	3	3	NUM
ejpam-5175	18	7	]	]	NUM
ejpam-5175	18	8	)	)	PUNCT
ejpam-5175	18	9	.	.	PUNCT
ejpam-5175	19	1	a	a	DET
ejpam-5175	19	2	representation	representation	NOUN
ejpam-5175	19	3	of	of	ADP
ejpam-5175	19	4	dimension	dimension	NOUN
ejpam-5175	19	5	n	n	PROPN
ejpam-5175	19	6	of	of	ADP
ejpam-5175	19	7	a	a	DET
ejpam-5175	19	8	group	group	NOUN
ejpam-5175	19	9	g	g	NOUN
ejpam-5175	19	10	is	be	AUX
ejpam-5175	19	11	the	the	DET
ejpam-5175	19	12	data	datum	NOUN
ejpam-5175	19	13	of	of	ADP
ejpam-5175	19	14	a	a	DET
ejpam-5175	19	15	complex	complex	ADJ
ejpam-5175	19	16	vector	vector	NOUN
ejpam-5175	19	17	space	space	NOUN
ejpam-5175	19	18	e	e	NOUN
ejpam-5175	19	19	of	of	ADP
ejpam-5175	19	20	dimension	dimension	NOUN
ejpam-5175	19	21	n	n	CCONJ
ejpam-5175	19	22	,	,	PUNCT
ejpam-5175	19	23	and	and	CCONJ
ejpam-5175	19	24	of	of	ADP
ejpam-5175	19	25	a	a	DET
ejpam-5175	19	26	morphism	morphism	NOUN
ejpam-5175	19	27	of	of	ADP
ejpam-5175	19	28	groups	group	NOUN
ejpam-5175	19	29	τ	τ	X
ejpam-5175	19	30	:	:	PUNCT
ejpam-5175	19	31	g	g	PROPN
ejpam-5175	19	32	→	→	SYM
ejpam-5175	19	33	gl(e	gl(e	NOUN
ejpam-5175	19	34	)	)	PUNCT
ejpam-5175	19	35	for	for	ADP
ejpam-5175	19	36	example	example	NOUN
ejpam-5175	19	37	,	,	PUNCT
ejpam-5175	19	38	the	the	DET
ejpam-5175	19	39	standard	standard	ADJ
ejpam-5175	19	40	representation	representation	NOUN
ejpam-5175	19	41	of	of	ADP
ejpam-5175	19	42	sn	sn	PROPN
ejpam-5175	19	43	is	be	AUX
ejpam-5175	19	44	given	give	VERB
ejpam-5175	19	45	as	as	SCONJ
ejpam-5175	19	46	follows	follow	VERB
ejpam-5175	19	47	[	[	X
ejpam-5175	19	48	4	4	NUM
ejpam-5175	19	49	]	]	PUNCT
ejpam-5175	19	50	:	:	PUNCT
ejpam-5175	19	51	τ	τ	X
ejpam-5175	19	52	:	:	PUNCT
ejpam-5175	19	53	sn	sn	PROPN
ejpam-5175	19	54	→	→	SYM
ejpam-5175	19	55	gln(c	gln(c	PROPN
ejpam-5175	19	56	)	)	PUNCT
ejpam-5175	19	57	τσ(ei	τσ(ei	NOUN
ejpam-5175	19	58	)	)	PUNCT
ejpam-5175	19	59	=	=	SYM
ejpam-5175	19	60	eσ(i	eσ(i	X
ejpam-5175	19	61	)	)	PUNCT
ejpam-5175	19	62	we	we	PRON
ejpam-5175	19	63	obtain	obtain	VERB
ejpam-5175	19	64	the	the	DET
ejpam-5175	19	65	matrix	matrix	NOUN
ejpam-5175	19	66	of	of	ADP
ejpam-5175	19	67	τσ	τσ	NUM
ejpam-5175	19	68	by	by	ADP
ejpam-5175	19	69	permuting	permute	VERB
ejpam-5175	19	70	the	the	DET
ejpam-5175	19	71	columns	column	NOUN
ejpam-5175	19	72	of	of	ADP
ejpam-5175	19	73	the	the	DET
ejpam-5175	19	74	identity	identity	NOUN
ejpam-5175	19	75	matrix	matrix	NOUN
ejpam-5175	19	76	in	in	ADP
ejpam-5175	19	77	accordance	accordance	NOUN
ejpam-5175	19	78	to	to	ADP
ejpam-5175	19	79	σ	σ	PROPN
ejpam-5175	19	80	.	.	PUNCT
ejpam-5175	20	1	for	for	ADP
ejpam-5175	20	2	example	example	NOUN
ejpam-5175	20	3	,	,	PUNCT
ejpam-5175	20	4	for	for	ADP
ejpam-5175	20	5	n	n	NOUN
ejpam-5175	20	6	=	=	SYM
ejpam-5175	20	7	3	3	NUM
ejpam-5175	20	8	,	,	PUNCT
ejpam-5175	20	9	we	we	PRON
ejpam-5175	20	10	have	have	VERB
ejpam-5175	20	11	:	:	PUNCT
ejpam-5175	20	12	τ(12	τ(12	NUM
ejpam-5175	20	13	)	)	PUNCT
ejpam-5175	20	14	=	=	PUNCT
ejpam-5175	21	1			PROPN
ejpam-5175	21	2	0	0	NUM
ejpam-5175	21	3	1	1	NUM
ejpam-5175	21	4	0	0	NUM
ejpam-5175	21	5	1	1	NUM
ejpam-5175	21	6	0	0	NUM
ejpam-5175	21	7	0	0	NUM
ejpam-5175	21	8	0	0	NUM
ejpam-5175	21	9	0	0	NUM
ejpam-5175	21	10	1	1	NUM
ejpam-5175	21	11			PROPN
ejpam-5175	21	12	and	and	CCONJ
ejpam-5175	21	13	τ(123	τ(123	NOUN
ejpam-5175	21	14	)	)	PUNCT
ejpam-5175	21	15	=	=	SYM
ejpam-5175	22	1			PROPN
ejpam-5175	22	2	0	0	NUM
ejpam-5175	22	3	0	0	NUM
ejpam-5175	22	4	1	1	NUM
ejpam-5175	22	5	1	1	NUM
ejpam-5175	22	6	0	0	NUM
ejpam-5175	22	7	0	0	NUM
ejpam-5175	22	8	0	0	NUM
ejpam-5175	22	9	1	1	NUM
ejpam-5175	22	10	0	0	NUM
ejpam-5175	22	11			PROPN
ejpam-5175	22	12	furthermore	furthermore	ADV
ejpam-5175	22	13	,	,	PUNCT
ejpam-5175	22	14	if	if	SCONJ
ejpam-5175	22	15	t	t	PROPN
ejpam-5175	22	16	∈	∈	PROPN
ejpam-5175	22	17	s3	s3	PROPN
ejpam-5175	22	18	is	be	AUX
ejpam-5175	22	19	the	the	DET
ejpam-5175	22	20	transposition	transposition	NOUN
ejpam-5175	22	21	123	123	NUM
ejpam-5175	22	22	→	→	SYM
ejpam-5175	22	23	132	132	NUM
ejpam-5175	22	24	and	and	CCONJ
ejpam-5175	22	25	c	c	AUX
ejpam-5175	22	26	be	be	AUX
ejpam-5175	22	27	the	the	DET
ejpam-5175	22	28	circular	circular	ADJ
ejpam-5175	22	29	permutation	permutation	NOUN
ejpam-5175	22	30	123	123	NUM
ejpam-5175	22	31	→	→	SYM
ejpam-5175	22	32	231	231	NUM
ejpam-5175	22	33	which	which	PRON
ejpam-5175	22	34	generate	generate	VERB
ejpam-5175	22	35	s3	s3	PROPN
ejpam-5175	22	36	.	.	PUNCT
ejpam-5175	23	1	we	we	PRON
ejpam-5175	23	2	set	set	VERB
ejpam-5175	23	3	j	j	NOUN
ejpam-5175	23	4	=	=	PUNCT
ejpam-5175	23	5	e	e	PROPN
ejpam-5175	23	6	2iπ	2iπ	NOUN
ejpam-5175	23	7	3	3	NUM
ejpam-5175	23	8	.	.	PUNCT
ejpam-5175	24	1	we	we	PRON
ejpam-5175	24	2	can	can	AUX
ejpam-5175	24	3	represent	represent	VERB
ejpam-5175	24	4	s3	s3	PROPN
ejpam-5175	24	5	in	in	ADP
ejpam-5175	24	6	c2	c2	PROPN
ejpam-5175	24	7	by	by	ADP
ejpam-5175	24	8	setting	set	VERB
ejpam-5175	24	9	:	:	PUNCT
ejpam-5175	24	10	τ(e	τ(e	X
ejpam-5175	24	11	)	)	PUNCT
ejpam-5175	25	1	=	=	SYM
ejpam-5175	25	2	i	i	PROPN
ejpam-5175	25	3	,	,	PUNCT
ejpam-5175	25	4	τ(t	τ(t	ADJ
ejpam-5175	25	5	)	)	PUNCT
ejpam-5175	25	6	=	=	VERB
ejpam-5175	26	1	[	[	PUNCT
ejpam-5175	26	2	0	0	NUM
ejpam-5175	26	3	1	1	NUM
ejpam-5175	26	4	1	1	NUM
ejpam-5175	26	5	0	0	NUM
ejpam-5175	26	6	]	]	PUNCT
ejpam-5175	26	7	,	,	PUNCT
ejpam-5175	26	8	τ(c	τ(c	PROPN
ejpam-5175	26	9	)	)	PUNCT
ejpam-5175	26	10	=	=	PUNCT
ejpam-5175	26	11	[	[	PUNCT
ejpam-5175	26	12	j	j	NOUN
ejpam-5175	26	13	0	0	NUM
ejpam-5175	26	14	0	0	NUM
ejpam-5175	26	15	j2	j2	PROPN
ejpam-5175	26	16	]	]	PUNCT
ejpam-5175	26	17	in	in	ADP
ejpam-5175	26	18	particular	particular	ADJ
ejpam-5175	26	19	,	,	PUNCT
ejpam-5175	26	20	if	if	SCONJ
ejpam-5175	26	21	the	the	DET
ejpam-5175	26	22	vector	vector	NOUN
ejpam-5175	26	23	space	space	NOUN
ejpam-5175	26	24	e	e	NOUN
ejpam-5175	26	25	is	be	AUX
ejpam-5175	26	26	of	of	ADP
ejpam-5175	26	27	dimension	dimension	NOUN
ejpam-5175	26	28	n	n	NOUN
ejpam-5175	26	29	=	=	SYM
ejpam-5175	26	30	|g|	|g|	PROPN
ejpam-5175	26	31	with	with	ADP
ejpam-5175	26	32	basis	basis	NOUN
ejpam-5175	26	33	indexed	index	VERB
ejpam-5175	26	34	by	by	ADP
ejpam-5175	26	35	the	the	DET
ejpam-5175	26	36	elements	element	NOUN
ejpam-5175	26	37	of	of	ADP
ejpam-5175	26	38	g	g	NOUN
ejpam-5175	26	39	,	,	PUNCT
ejpam-5175	26	40	the	the	DET
ejpam-5175	26	41	representation	representation	NOUN
ejpam-5175	26	42	is	be	AUX
ejpam-5175	26	43	called	call	VERB
ejpam-5175	26	44	the	the	DET
ejpam-5175	26	45	regular	regular	ADJ
ejpam-5175	26	46	representation	representation	NOUN
ejpam-5175	26	47	of	of	ADP
ejpam-5175	26	48	g.	g.	PROPN
ejpam-5175	26	49	definition	definition	NOUN
ejpam-5175	26	50	2	2	NUM
ejpam-5175	26	51	(	(	PUNCT
ejpam-5175	26	52	see	see	VERB
ejpam-5175	26	53	[	[	X
ejpam-5175	26	54	3	3	NUM
ejpam-5175	26	55	]	]	NUM
ejpam-5175	26	56	)	)	PUNCT
ejpam-5175	26	57	.	.	PUNCT
ejpam-5175	27	1	let	let	VERB
ejpam-5175	27	2	τ	τ	NOUN
ejpam-5175	27	3	:	:	PUNCT
ejpam-5175	27	4	g	g	PROPN
ejpam-5175	27	5	→	→	SYM
ejpam-5175	27	6	gl(e	gl(e	CCONJ
ejpam-5175	27	7	)	)	PUNCT
ejpam-5175	27	8	be	be	AUX
ejpam-5175	27	9	a	a	DET
ejpam-5175	27	10	linear	linear	ADJ
ejpam-5175	27	11	representation	representation	NOUN
ejpam-5175	27	12	,	,	PUNCT
ejpam-5175	27	13	and	and	CCONJ
ejpam-5175	27	14	f	f	PROPN
ejpam-5175	27	15	a	a	DET
ejpam-5175	27	16	vector	vector	NOUN
ejpam-5175	27	17	subspace	subspace	NOUN
ejpam-5175	27	18	of	of	ADP
ejpam-5175	27	19	e	e	PROPN
ejpam-5175	27	20	stable	stable	ADJ
ejpam-5175	27	21	for	for	ADP
ejpam-5175	27	22	the	the	DET
ejpam-5175	27	23	operations	operation	NOUN
ejpam-5175	27	24	of	of	ADP
ejpam-5175	27	25	g	g	NOUN
ejpam-5175	27	26	,	,	PUNCT
ejpam-5175	27	27	then	then	ADV
ejpam-5175	27	28	τf	τf	ADP
ejpam-5175	27	29	:	:	PUNCT
ejpam-5175	27	30	g	g	PROPN
ejpam-5175	27	31	→	→	SYM
ejpam-5175	27	32	gl(f	gl(f	PROPN
ejpam-5175	27	33	)	)	PUNCT
ejpam-5175	27	34	is	be	AUX
ejpam-5175	27	35	a	a	DET
ejpam-5175	27	36	linear	linear	ADJ
ejpam-5175	27	37	representation	representation	NOUN
ejpam-5175	27	38	of	of	ADP
ejpam-5175	27	39	g	g	PROPN
ejpam-5175	27	40	in	in	ADP
ejpam-5175	27	41	f	f	PROPN
ejpam-5175	27	42	;	;	PUNCT
ejpam-5175	27	43	called	call	VERB
ejpam-5175	27	44	a	a	DET
ejpam-5175	27	45	sub	sub	NOUN
ejpam-5175	27	46	-	-	NOUN
ejpam-5175	27	47	representation	representation	NOUN
ejpam-5175	27	48	of	of	ADP
ejpam-5175	27	49	e.	e.	PROPN
ejpam-5175	27	50	in	in	ADP
ejpam-5175	27	51	addition	addition	NOUN
ejpam-5175	27	52	,	,	PUNCT
ejpam-5175	27	53	(	(	PUNCT
ejpam-5175	27	54	τ	τ	X
ejpam-5175	27	55	,	,	PUNCT
ejpam-5175	27	56	e	e	NOUN
ejpam-5175	27	57	)	)	PUNCT
ejpam-5175	27	58	is	be	AUX
ejpam-5175	27	59	called	call	VERB
ejpam-5175	27	60	irreducible	irreducible	ADJ
ejpam-5175	27	61	if	if	SCONJ
ejpam-5175	27	62	e	e	NOUN
ejpam-5175	27	63	is	be	AUX
ejpam-5175	27	64	not	not	PART
ejpam-5175	27	65	reduced	reduce	VERB
ejpam-5175	27	66	to	to	ADP
ejpam-5175	27	67	0	0	NUM
ejpam-5175	27	68	,	,	PUNCT
ejpam-5175	27	69	and	and	CCONJ
ejpam-5175	27	70	if	if	SCONJ
ejpam-5175	27	71	no	no	DET
ejpam-5175	27	72	vector	vector	NOUN
ejpam-5175	27	73	subspace	subspace	NOUN
ejpam-5175	27	74	of	of	ADP
ejpam-5175	27	75	e	e	PROPN
ejpam-5175	27	76	is	be	AUX
ejpam-5175	27	77	stable	stable	ADJ
ejpam-5175	27	78	by	by	ADP
ejpam-5175	27	79	g	g	PROPN
ejpam-5175	27	80	,	,	PUNCT
ejpam-5175	27	81	except	except	SCONJ
ejpam-5175	27	82	0	0	NUM
ejpam-5175	27	83	and	and	CCONJ
ejpam-5175	27	84	e.	e.	PROPN
ejpam-5175	27	85	and	and	CCONJ
ejpam-5175	27	86	we	we	PRON
ejpam-5175	27	87	have	have	VERB
ejpam-5175	27	88	the	the	DET
ejpam-5175	27	89	following	follow	VERB
ejpam-5175	27	90	theorem	theorem	NOUN
ejpam-5175	27	91	:	:	PUNCT
ejpam-5175	27	92	theorem	theorem	ADJ
ejpam-5175	27	93	1	1	NUM
ejpam-5175	27	94	(	(	PUNCT
ejpam-5175	27	95	see	see	VERB
ejpam-5175	27	96	[	[	X
ejpam-5175	27	97	2	2	NUM
ejpam-5175	27	98	]	]	PUNCT
ejpam-5175	27	99	,	,	PUNCT
ejpam-5175	27	100	maschke	maschke	ADV
ejpam-5175	27	101	theorem	theorem	ADJ
ejpam-5175	27	102	)	)	PUNCT
ejpam-5175	27	103	.	.	PUNCT
ejpam-5175	28	1	every	every	DET
ejpam-5175	28	2	representation	representation	NOUN
ejpam-5175	28	3	is	be	AUX
ejpam-5175	28	4	a	a	DET
ejpam-5175	28	5	direct	direct	ADJ
ejpam-5175	28	6	sum	sum	NOUN
ejpam-5175	28	7	of	of	ADP
ejpam-5175	28	8	irreducible	irreducible	ADJ
ejpam-5175	28	9	representations	representation	NOUN
ejpam-5175	28	10	.	.	PUNCT
ejpam-5175	29	1	a.	a.	NOUN
ejpam-5175	29	2	labsir	labsir	PROPN
ejpam-5175	29	3	,	,	PUNCT
ejpam-5175	29	4	e.	e.	PROPN
ejpam-5175	29	5	fanich	fanich	PROPN
ejpam-5175	29	6	/	/	SYM
ejpam-5175	29	7	eur	eur	PROPN
ejpam-5175	29	8	.	.	PUNCT
ejpam-5175	30	1	j.	j.	PROPN
ejpam-5175	30	2	pure	pure	PROPN
ejpam-5175	30	3	appl	appl	PROPN
ejpam-5175	30	4	.	.	PROPN
ejpam-5175	30	5	math	math	PROPN
ejpam-5175	30	6	,	,	PUNCT
ejpam-5175	30	7	17	17	NUM
ejpam-5175	30	8	(	(	PUNCT
ejpam-5175	30	9	3	3	NUM
ejpam-5175	30	10	)	)	PUNCT
ejpam-5175	30	11	(	(	PUNCT
ejpam-5175	30	12	2024	2024	NUM
ejpam-5175	30	13	)	)	PUNCT
ejpam-5175	30	14	,	,	PUNCT
ejpam-5175	30	15	1717	1717	NUM
ejpam-5175	30	16	-	-	SYM
ejpam-5175	30	17	1726	1726	NUM
ejpam-5175	30	18	1719	1719	NUM
ejpam-5175	30	19	recall	recall	NOUN
ejpam-5175	30	20	here	here	ADV
ejpam-5175	30	21	the	the	DET
ejpam-5175	30	22	notion	notion	NOUN
ejpam-5175	30	23	of	of	ADP
ejpam-5175	30	24	the	the	DET
ejpam-5175	30	25	character	character	NOUN
ejpam-5175	30	26	which	which	PRON
ejpam-5175	30	27	is	be	AUX
ejpam-5175	30	28	a	a	DET
ejpam-5175	30	29	function	function	NOUN
ejpam-5175	30	30	on	on	ADP
ejpam-5175	30	31	g	g	NOUN
ejpam-5175	30	32	with	with	ADP
ejpam-5175	30	33	complex	complex	ADJ
ejpam-5175	30	34	values	value	NOUN
ejpam-5175	30	35	characterizing	characterize	VERB
ejpam-5175	30	36	the	the	DET
ejpam-5175	30	37	representation	representation	NOUN
ejpam-5175	30	38	.	.	PUNCT
ejpam-5175	31	1	definition	definition	NOUN
ejpam-5175	31	2	3	3	NUM
ejpam-5175	31	3	(	(	PUNCT
ejpam-5175	31	4	see	see	VERB
ejpam-5175	31	5	[	[	X
ejpam-5175	31	6	1	1	NUM
ejpam-5175	31	7	]	]	NUM
ejpam-5175	31	8	)	)	PUNCT
ejpam-5175	31	9	.	.	PUNCT
ejpam-5175	32	1	let	let	VERB
ejpam-5175	32	2	τ	τ	NOUN
ejpam-5175	32	3	:	:	PUNCT
ejpam-5175	32	4	g	g	PROPN
ejpam-5175	32	5	→	→	SYM
ejpam-5175	32	6	gl(e	gl(e	CCONJ
ejpam-5175	32	7	)	)	PUNCT
ejpam-5175	32	8	be	be	AUX
ejpam-5175	32	9	a	a	DET
ejpam-5175	32	10	linear	linear	ADJ
ejpam-5175	32	11	representation	representation	NOUN
ejpam-5175	32	12	of	of	ADP
ejpam-5175	32	13	a	a	DET
ejpam-5175	32	14	finite	finite	ADJ
ejpam-5175	32	15	group	group	NOUN
ejpam-5175	32	16	g	g	PROPN
ejpam-5175	32	17	in	in	ADP
ejpam-5175	32	18	the	the	DET
ejpam-5175	32	19	vector	vector	NOUN
ejpam-5175	32	20	space	space	NOUN
ejpam-5175	32	21	e.	e.	PROPN
ejpam-5175	33	1	the	the	DET
ejpam-5175	33	2	character	character	NOUN
ejpam-5175	33	3	of	of	ADP
ejpam-5175	33	4	g	g	PROPN
ejpam-5175	33	5	is	be	AUX
ejpam-5175	33	6	defined	define	VERB
ejpam-5175	33	7	as	as	ADP
ejpam-5175	33	8	follow	follow	NOUN
ejpam-5175	33	9	:	:	PUNCT
ejpam-5175	33	10	for	for	ADP
ejpam-5175	33	11	all	all	PRON
ejpam-5175	33	12	g	g	PROPN
ejpam-5175	33	13	∈	∈	PROPN
ejpam-5175	33	14	g	g	NOUN
ejpam-5175	33	15	,	,	PUNCT
ejpam-5175	33	16	χτ	χτ	PROPN
ejpam-5175	33	17	(	(	PUNCT
ejpam-5175	33	18	g	g	NOUN
ejpam-5175	33	19	)	)	PUNCT
ejpam-5175	33	20	=	=	SYM
ejpam-5175	33	21	tr(τg	tr(τg	NUM
ejpam-5175	33	22	)	)	PUNCT
ejpam-5175	33	23	.	.	PUNCT
ejpam-5175	34	1	furthermore	furthermore	ADV
ejpam-5175	34	2	,	,	PUNCT
ejpam-5175	34	3	two	two	NUM
ejpam-5175	34	4	representations	representation	NOUN
ejpam-5175	34	5	of	of	ADP
ejpam-5175	34	6	the	the	DET
ejpam-5175	34	7	same	same	ADJ
ejpam-5175	34	8	character	character	NOUN
ejpam-5175	34	9	are	be	AUX
ejpam-5175	34	10	isomorphic	isomorphic	ADJ
ejpam-5175	34	11	,	,	PUNCT
ejpam-5175	34	12	and	and	CCONJ
ejpam-5175	34	13	we	we	PRON
ejpam-5175	34	14	have	have	VERB
ejpam-5175	34	15	:	:	PUNCT
ejpam-5175	34	16	proposition	proposition	NOUN
ejpam-5175	34	17	1	1	NUM
ejpam-5175	34	18	(	(	PUNCT
ejpam-5175	34	19	see	see	VERB
ejpam-5175	34	20	[	[	X
ejpam-5175	34	21	2	2	NUM
ejpam-5175	34	22	]	]	NUM
ejpam-5175	34	23	)	)	PUNCT
ejpam-5175	34	24	.	.	PUNCT
ejpam-5175	35	1	the	the	DET
ejpam-5175	35	2	character	character	NOUN
ejpam-5175	35	3	rg	rg	PROPN
ejpam-5175	35	4	of	of	ADP
ejpam-5175	35	5	the	the	DET
ejpam-5175	35	6	regular	regular	ADJ
ejpam-5175	35	7	representation	representation	NOUN
ejpam-5175	35	8	is	be	AUX
ejpam-5175	35	9	given	give	VERB
ejpam-5175	35	10	by	by	ADP
ejpam-5175	35	11	:	:	PUNCT
ejpam-5175	35	12	rg(1	rg(1	NOUN
ejpam-5175	35	13	)	)	PUNCT
ejpam-5175	35	14	=	=	SYM
ejpam-5175	35	15	|g|	|g|	ADJ
ejpam-5175	35	16	,	,	PUNCT
ejpam-5175	35	17	and	and	CCONJ
ejpam-5175	35	18	rg(g	rg(g	NOUN
ejpam-5175	35	19	)	)	PUNCT
ejpam-5175	36	1	=	=	SYM
ejpam-5175	36	2	0	0	PUNCT
ejpam-5175	36	3	if	if	SCONJ
ejpam-5175	36	4	g	g	PROPN
ejpam-5175	36	5	̸=	̸=	PROPN
ejpam-5175	36	6	1	1	NUM
ejpam-5175	36	7	.	.	PUNCT
ejpam-5175	37	1	the	the	DET
ejpam-5175	37	2	importance	importance	NOUN
ejpam-5175	37	3	of	of	ADP
ejpam-5175	37	4	the	the	DET
ejpam-5175	37	5	regular	regular	ADJ
ejpam-5175	37	6	representation	representation	NOUN
ejpam-5175	37	7	lies	lie	VERB
ejpam-5175	37	8	in	in	ADP
ejpam-5175	37	9	the	the	DET
ejpam-5175	37	10	fact	fact	NOUN
ejpam-5175	37	11	that	that	SCONJ
ejpam-5175	37	12	an	an	DET
ejpam-5175	37	13	irreducible	irreducible	ADJ
ejpam-5175	37	14	representation	representation	NOUN
ejpam-5175	37	15	fi	fi	NOUN
ejpam-5175	37	16	is	be	AUX
ejpam-5175	37	17	contained	contain	VERB
ejpam-5175	37	18	in	in	ADP
ejpam-5175	37	19	it	it	PRON
ejpam-5175	37	20	a	a	DET
ejpam-5175	37	21	number	number	NOUN
ejpam-5175	37	22	of	of	ADP
ejpam-5175	37	23	times	time	NOUN
ejpam-5175	37	24	equal	equal	ADJ
ejpam-5175	37	25	to	to	ADP
ejpam-5175	37	26	its	its	PRON
ejpam-5175	37	27	degree	degree	NOUN
ejpam-5175	37	28	ni	ni	PROPN
ejpam-5175	37	29	.	.	PROPN
ejpam-5175	37	30	proposition	proposition	NOUN
ejpam-5175	37	31	2	2	NUM
ejpam-5175	37	32	(	(	PUNCT
ejpam-5175	37	33	see	see	VERB
ejpam-5175	37	34	[	[	X
ejpam-5175	37	35	2	2	NUM
ejpam-5175	37	36	]	]	NUM
ejpam-5175	37	37	)	)	PUNCT
ejpam-5175	37	38	.	.	PUNCT
ejpam-5175	38	1	the	the	DET
ejpam-5175	38	2	degrees	degree	NOUN
ejpam-5175	38	3	ni	ni	PROPN
ejpam-5175	38	4	verify	verify	VERB
ejpam-5175	38	5	the	the	DET
ejpam-5175	38	6	relation	relation	NOUN
ejpam-5175	38	7	∑	∑	PUNCT
ejpam-5175	38	8	n2	n2	PROPN
ejpam-5175	38	9	i	i	NOUN
ejpam-5175	38	10	=	=	PUNCT
ejpam-5175	38	11	|g|	|g|	PROPN
ejpam-5175	38	12	.	.	PUNCT
ejpam-5175	39	1	thus	thus	ADV
ejpam-5175	39	2	,	,	PUNCT
ejpam-5175	39	3	we	we	PRON
ejpam-5175	39	4	define	define	VERB
ejpam-5175	39	5	the	the	DET
ejpam-5175	39	6	character	character	NOUN
ejpam-5175	39	7	table	table	NOUN
ejpam-5175	39	8	of	of	ADP
ejpam-5175	39	9	a	a	DET
ejpam-5175	39	10	finite	finite	ADJ
ejpam-5175	39	11	group	group	NOUN
ejpam-5175	39	12	g	g	PROPN
ejpam-5175	39	13	as	as	SCONJ
ejpam-5175	39	14	follows	follow	VERB
ejpam-5175	39	15	:	:	PUNCT
ejpam-5175	39	16	let	let	VERB
ejpam-5175	39	17	c	c	NOUN
ejpam-5175	39	18	=	=	PUNCT
ejpam-5175	40	1	|conj(g)|	|conj(g)|	NOUN
ejpam-5175	40	2	the	the	DET
ejpam-5175	40	3	number	number	NOUN
ejpam-5175	40	4	of	of	ADP
ejpam-5175	40	5	conjugation	conjugation	NOUN
ejpam-5175	40	6	classes	class	NOUN
ejpam-5175	40	7	of	of	ADP
ejpam-5175	40	8	g.	g.	PROPN
ejpam-5175	40	9	the	the	DET
ejpam-5175	40	10	character	character	NOUN
ejpam-5175	40	11	map	map	NOUN
ejpam-5175	40	12	of	of	ADP
ejpam-5175	40	13	g	g	PROPN
ejpam-5175	40	14	is	be	AUX
ejpam-5175	40	15	an	an	DET
ejpam-5175	40	16	array	array	NOUN
ejpam-5175	40	17	c	c	NOUN
ejpam-5175	40	18	×	×	NOUN
ejpam-5175	40	19	c	c	NOUN
ejpam-5175	40	20	of	of	ADP
ejpam-5175	40	21	which	which	PRON
ejpam-5175	40	22	the	the	DET
ejpam-5175	40	23	entries	entry	NOUN
ejpam-5175	40	24	are	be	AUX
ejpam-5175	40	25	the	the	DET
ejpam-5175	40	26	values	value	NOUN
ejpam-5175	40	27	of	of	ADP
ejpam-5175	40	28	the	the	DET
ejpam-5175	40	29	irreducible	irreducible	ADJ
ejpam-5175	40	30	characters	character	NOUN
ejpam-5175	40	31	on	on	ADP
ejpam-5175	40	32	the	the	DET
ejpam-5175	40	33	conjugation	conjugation	NOUN
ejpam-5175	40	34	classes	class	NOUN
ejpam-5175	40	35	of	of	ADP
ejpam-5175	40	36	g	g	NOUN
ejpam-5175	40	37	,	,	PUNCT
ejpam-5175	40	38	the	the	DET
ejpam-5175	40	39	coefficient	coefficient	NOUN
ejpam-5175	40	40	at	at	ADP
ejpam-5175	40	41	the	the	DET
ejpam-5175	40	42	intersection	intersection	NOUN
ejpam-5175	40	43	of	of	ADP
ejpam-5175	40	44	the	the	DET
ejpam-5175	40	45	column	column	NOUN
ejpam-5175	40	46	corresponding	correspond	VERB
ejpam-5175	40	47	to	to	ADP
ejpam-5175	40	48	the	the	DET
ejpam-5175	40	49	character	character	NOUN
ejpam-5175	40	50	χ	χ	NOUN
ejpam-5175	40	51	of	of	ADP
ejpam-5175	40	52	the	the	DET
ejpam-5175	40	53	line	line	NOUN
ejpam-5175	40	54	corresponding	correspond	VERB
ejpam-5175	40	55	to	to	ADP
ejpam-5175	40	56	the	the	DET
ejpam-5175	40	57	conjugation	conjugation	NOUN
ejpam-5175	40	58	class	class	NOUN
ejpam-5175	40	59	c	c	NOUN
ejpam-5175	40	60	,	,	PUNCT
ejpam-5175	40	61	being	be	AUX
ejpam-5175	40	62	χ(c	χ(c	NOUN
ejpam-5175	40	63	)	)	PUNCT
ejpam-5175	40	64	.	.	PUNCT
ejpam-5175	41	1	it	it	PRON
ejpam-5175	41	2	’s	’	VERB
ejpam-5175	41	3	sort	sort	ADV
ejpam-5175	41	4	of	of	ADV
ejpam-5175	41	5	the	the	DET
ejpam-5175	41	6	card	card	NOUN
ejpam-5175	41	7	of	of	ADP
ejpam-5175	41	8	the	the	DET
ejpam-5175	41	9	group	group	NOUN
ejpam-5175	41	10	g[3	g[3	PROPN
ejpam-5175	41	11	]	]	X
ejpam-5175	41	12	.	.	PUNCT
ejpam-5175	42	1	for	for	ADP
ejpam-5175	42	2	example	example	NOUN
ejpam-5175	42	3	,	,	PUNCT
ejpam-5175	42	4	the	the	DET
ejpam-5175	42	5	group	group	NOUN
ejpam-5175	42	6	{	{	PUNCT
ejpam-5175	42	7	±1	±1	PROPN
ejpam-5175	42	8	}	}	PUNCT
ejpam-5175	42	9	has	have	VERB
ejpam-5175	42	10	two	two	NUM
ejpam-5175	42	11	conjugation	conjugation	NOUN
ejpam-5175	42	12	classes	class	NOUN
ejpam-5175	42	13	1	1	NUM
ejpam-5175	42	14	and	and	CCONJ
ejpam-5175	42	15	-1	-1	ADJ
ejpam-5175	42	16	,	,	PUNCT
ejpam-5175	42	17	and	and	CCONJ
ejpam-5175	42	18	two	two	NUM
ejpam-5175	42	19	irreducible	irreducible	ADJ
ejpam-5175	42	20	characters	character	NOUN
ejpam-5175	42	21	1	1	NUM
ejpam-5175	42	22	and	and	CCONJ
ejpam-5175	42	23	χ	χ	X
ejpam-5175	42	24	(	(	PUNCT
ejpam-5175	42	25	of	of	ADP
ejpam-5175	42	26	dimension	dimension	NOUN
ejpam-5175	42	27	1	1	NUM
ejpam-5175	42	28	since	since	SCONJ
ejpam-5175	42	29	{	{	PUNCT
ejpam-5175	42	30	±1	±1	ADJ
ejpam-5175	42	31	}	}	PUNCT
ejpam-5175	42	32	is	be	AUX
ejpam-5175	42	33	commutative	commutative	ADJ
ejpam-5175	42	34	)	)	PUNCT
ejpam-5175	42	35	;	;	PUNCT
ejpam-5175	42	36	its	its	PRON
ejpam-5175	42	37	character	character	NOUN
ejpam-5175	42	38	table	table	NOUN
ejpam-5175	42	39	is	be	AUX
ejpam-5175	42	40	very	very	ADV
ejpam-5175	42	41	easy	easy	ADJ
ejpam-5175	42	42	to	to	PART
ejpam-5175	42	43	establish	establish	VERB
ejpam-5175	42	44	:	:	PUNCT
ejpam-5175	42	45	1	1	NUM
ejpam-5175	42	46	-1	-1	PUNCT
ejpam-5175	42	47	χ1	χ1	NOUN
ejpam-5175	42	48	1	1	NUM
ejpam-5175	42	49	1	1	NUM
ejpam-5175	42	50	χ2	χ2	PROPN
ejpam-5175	42	51	1	1	NUM
ejpam-5175	42	52	-1	-1	ADP
ejpam-5175	42	53	the	the	DET
ejpam-5175	42	54	example	example	NOUN
ejpam-5175	42	55	of	of	ADP
ejpam-5175	42	56	the	the	DET
ejpam-5175	42	57	group	group	NOUN
ejpam-5175	42	58	{	{	PUNCT
ejpam-5175	42	59	±1	±1	PROPN
ejpam-5175	42	60	}	}	PUNCT
ejpam-5175	42	61	is	be	AUX
ejpam-5175	42	62	a	a	DET
ejpam-5175	42	63	little	little	ADJ
ejpam-5175	42	64	too	too	ADV
ejpam-5175	42	65	trivial	trivial	ADJ
ejpam-5175	42	66	to	to	PART
ejpam-5175	42	67	give	give	VERB
ejpam-5175	42	68	an	an	DET
ejpam-5175	42	69	idea	idea	NOUN
ejpam-5175	42	70	of	of	ADP
ejpam-5175	42	71	how	how	SCONJ
ejpam-5175	42	72	we	we	PRON
ejpam-5175	42	73	can	can	AUX
ejpam-5175	42	74	construct	construct	VERB
ejpam-5175	42	75	the	the	DET
ejpam-5175	42	76	character	character	NOUN
ejpam-5175	42	77	table	table	NOUN
ejpam-5175	42	78	of	of	ADP
ejpam-5175	42	79	a	a	DET
ejpam-5175	42	80	group	group	NOUN
ejpam-5175	42	81	.	.	PUNCT
ejpam-5175	43	1	there	there	PRON
ejpam-5175	43	2	are	be	VERB
ejpam-5175	43	3	other	other	ADJ
ejpam-5175	43	4	groups	group	NOUN
ejpam-5175	43	5	when	when	SCONJ
ejpam-5175	43	6	we	we	PRON
ejpam-5175	43	7	use	use	VERB
ejpam-5175	43	8	other	other	ADJ
ejpam-5175	43	9	techniques	technique	NOUN
ejpam-5175	43	10	(	(	PUNCT
ejpam-5175	43	11	burnside	burnside	NOUN
ejpam-5175	43	12	formula	formula	NOUN
ejpam-5175	43	13	,	,	PUNCT
ejpam-5175	43	14	character	character	NOUN
ejpam-5175	43	15	orthogonality	orthogonality	NOUN
ejpam-5175	43	16	relationships	relationship	NOUN
ejpam-5175	43	17	,	,	PUNCT
ejpam-5175	43	18	etc	etc	X
ejpam-5175	43	19	.	.	X
ejpam-5175	43	20	)	)	PUNCT
ejpam-5175	43	21	to	to	PART
ejpam-5175	43	22	establish	establish	VERB
ejpam-5175	43	23	character	character	NOUN
ejpam-5175	43	24	tables	table	NOUN
ejpam-5175	43	25	.	.	PUNCT
ejpam-5175	44	1	for	for	ADP
ejpam-5175	44	2	example	example	NOUN
ejpam-5175	44	3	the	the	DET
ejpam-5175	44	4	character	character	NOUN
ejpam-5175	44	5	table	table	NOUN
ejpam-5175	44	6	of	of	ADP
ejpam-5175	44	7	the	the	DET
ejpam-5175	44	8	symmetric	symmetric	ADJ
ejpam-5175	44	9	group	group	NOUN
ejpam-5175	44	10	σ3	σ3	PROPN
ejpam-5175	44	11	is	be	AUX
ejpam-5175	44	12	given	give	VERB
ejpam-5175	44	13	as	as	SCONJ
ejpam-5175	44	14	follows	follow	VERB
ejpam-5175	44	15	:	:	PUNCT
ejpam-5175	44	16	first	first	ADV
ejpam-5175	44	17	recall	recall	VERB
ejpam-5175	44	18	that	that	PRON
ejpam-5175	44	19	:	:	PUNCT
ejpam-5175	44	20	σ3	σ3	PROPN
ejpam-5175	44	21	=	=	SYM
ejpam-5175	44	22	{	{	PUNCT
ejpam-5175	44	23	1	1	NUM
ejpam-5175	44	24	,	,	PUNCT
ejpam-5175	44	25	(	(	PUNCT
ejpam-5175	44	26	12	12	NUM
ejpam-5175	44	27	)	)	PUNCT
ejpam-5175	44	28	,	,	PUNCT
ejpam-5175	44	29	(	(	PUNCT
ejpam-5175	44	30	23	23	NUM
ejpam-5175	44	31	)	)	PUNCT
ejpam-5175	44	32	,	,	PUNCT
ejpam-5175	44	33	(	(	PUNCT
ejpam-5175	44	34	13	13	NUM
ejpam-5175	44	35	)	)	PUNCT
ejpam-5175	44	36	,	,	PUNCT
ejpam-5175	44	37	(	(	PUNCT
ejpam-5175	44	38	123	123	NUM
ejpam-5175	44	39	)	)	PUNCT
ejpam-5175	44	40	,	,	PUNCT
ejpam-5175	44	41	(	(	PUNCT
ejpam-5175	44	42	132	132	NUM
ejpam-5175	44	43	)	)	PUNCT
ejpam-5175	44	44	}	}	PUNCT
ejpam-5175	44	45	σ3	σ3	PROPN
ejpam-5175	44	46	has	have	VERB
ejpam-5175	44	47	3	3	NUM
ejpam-5175	44	48	characters	character	NOUN
ejpam-5175	44	49	because	because	SCONJ
ejpam-5175	44	50	that	that	PRON
ejpam-5175	44	51	is	be	AUX
ejpam-5175	44	52	its	its	PRON
ejpam-5175	44	53	number	number	NOUN
ejpam-5175	44	54	of	of	ADP
ejpam-5175	44	55	conjugation	conjugation	NOUN
ejpam-5175	44	56	classes	class	NOUN
ejpam-5175	44	57	.	.	PUNCT
ejpam-5175	45	1	first	first	ADV
ejpam-5175	45	2	there	there	PRON
ejpam-5175	45	3	is	be	VERB
ejpam-5175	45	4	the	the	DET
ejpam-5175	45	5	trivial	trivial	ADJ
ejpam-5175	45	6	character	character	NOUN
ejpam-5175	45	7	χ1	χ1	NOUN
ejpam-5175	45	8	.	.	PUNCT
ejpam-5175	46	1	then	then	ADV
ejpam-5175	46	2	the	the	DET
ejpam-5175	46	3	morphism	morphism	NOUN
ejpam-5175	46	4	χ2	χ2	PROPN
ejpam-5175	46	5	given	give	VERB
ejpam-5175	46	6	by	by	ADP
ejpam-5175	46	7	the	the	DET
ejpam-5175	46	8	signature	signature	NOUN
ejpam-5175	46	9	of	of	ADP
ejpam-5175	46	10	the	the	DET
ejpam-5175	46	11	elements	element	NOUN
ejpam-5175	46	12	of	of	ADP
ejpam-5175	46	13	σ3	σ3	PROPN
ejpam-5175	46	14	.	.	PUNCT
ejpam-5175	47	1	then	then	ADV
ejpam-5175	47	2	by	by	ADP
ejpam-5175	47	3	burnside	burnside	PROPN
ejpam-5175	47	4	’s	’s	PART
ejpam-5175	47	5	formula	formula	NOUN
ejpam-5175	47	6	we	we	PRON
ejpam-5175	47	7	obtain	obtain	VERB
ejpam-5175	47	8	that	that	SCONJ
ejpam-5175	47	9	the	the	DET
ejpam-5175	47	10	third	third	ADJ
ejpam-5175	47	11	character	character	NOUN
ejpam-5175	47	12	χ3	χ3	NOUN
ejpam-5175	47	13	is	be	AUX
ejpam-5175	47	14	such	such	ADJ
ejpam-5175	47	15	that	that	DET
ejpam-5175	47	16	n3	n3	NOUN
ejpam-5175	47	17	=	=	NOUN
ejpam-5175	47	18	2	2	X
ejpam-5175	47	19	.	.	X
ejpam-5175	47	20	we	we	PRON
ejpam-5175	47	21	therefore	therefore	ADV
ejpam-5175	47	22	obtain	obtain	VERB
ejpam-5175	47	23	for	for	ADP
ejpam-5175	47	24	the	the	DET
ejpam-5175	47	25	moment	moment	NOUN
ejpam-5175	47	26	the	the	DET
ejpam-5175	47	27	following	follow	VERB
ejpam-5175	47	28	character	character	NOUN
ejpam-5175	47	29	table[1	table[1	PROPN
ejpam-5175	47	30	]	]	PUNCT
ejpam-5175	47	31	.	.	PUNCT
ejpam-5175	48	1	a.	a.	PROPN
ejpam-5175	48	2	labsir	labsir	PROPN
ejpam-5175	48	3	,	,	PUNCT
ejpam-5175	48	4	e.	e.	PROPN
ejpam-5175	48	5	fanich	fanich	PROPN
ejpam-5175	48	6	/	/	SYM
ejpam-5175	48	7	eur	eur	PROPN
ejpam-5175	48	8	.	.	PUNCT
ejpam-5175	49	1	j.	j.	PROPN
ejpam-5175	49	2	pure	pure	PROPN
ejpam-5175	49	3	appl	appl	PROPN
ejpam-5175	49	4	.	.	PROPN
ejpam-5175	49	5	math	math	PROPN
ejpam-5175	49	6	,	,	PUNCT
ejpam-5175	49	7	17	17	NUM
ejpam-5175	49	8	(	(	PUNCT
ejpam-5175	49	9	3	3	NUM
ejpam-5175	49	10	)	)	PUNCT
ejpam-5175	49	11	(	(	PUNCT
ejpam-5175	49	12	2024	2024	NUM
ejpam-5175	49	13	)	)	PUNCT
ejpam-5175	49	14	,	,	PUNCT
ejpam-5175	49	15	1717	1717	NUM
ejpam-5175	49	16	-	-	SYM
ejpam-5175	49	17	1726	1726	NUM
ejpam-5175	49	18	1720	1720	NUM
ejpam-5175	49	19	1	1	NUM
ejpam-5175	49	20	(	(	PUNCT
ejpam-5175	49	21	12	12	NUM
ejpam-5175	49	22	)	)	PUNCT
ejpam-5175	49	23	(	(	PUNCT
ejpam-5175	49	24	123	123	NUM
ejpam-5175	49	25	)	)	PUNCT
ejpam-5175	49	26	χ1	χ1	NOUN
ejpam-5175	49	27	1	1	NUM
ejpam-5175	49	28	1	1	NUM
ejpam-5175	49	29	1	1	NUM
ejpam-5175	49	30	χ2	χ2	NOUN
ejpam-5175	49	31	1	1	NUM
ejpam-5175	49	32	-1	-1	SYM
ejpam-5175	49	33	1	1	NUM
ejpam-5175	49	34	χ3	χ3	NOUN
ejpam-5175	49	35	2	2	NUM
ejpam-5175	49	36	a	a	DET
ejpam-5175	49	37	b	b	NOUN
ejpam-5175	49	38	to	to	PART
ejpam-5175	49	39	have	have	VERB
ejpam-5175	49	40	a	a	PRON
ejpam-5175	49	41	and	and	CCONJ
ejpam-5175	49	42	b	b	NOUN
ejpam-5175	49	43	just	just	ADV
ejpam-5175	49	44	use	use	VERB
ejpam-5175	49	45	the	the	DET
ejpam-5175	49	46	orthogonality	orthogonality	NOUN
ejpam-5175	49	47	of	of	ADP
ejpam-5175	49	48	the	the	DET
ejpam-5175	49	49	character	character	NOUN
ejpam-5175	49	50	table	table	NOUN
ejpam-5175	49	51	columns	column	NOUN
ejpam-5175	49	52	.	.	PUNCT
ejpam-5175	50	1	so	so	ADV
ejpam-5175	50	2	we	we	PRON
ejpam-5175	50	3	get	get	VERB
ejpam-5175	50	4	a	a	DET
ejpam-5175	50	5	=	=	NOUN
ejpam-5175	50	6	0	0	NUM
ejpam-5175	50	7	and	and	CCONJ
ejpam-5175	50	8	b	b	X
ejpam-5175	50	9	=	=	SYM
ejpam-5175	50	10	−1	−1	NOUN
ejpam-5175	50	11	.	.	PUNCT
ejpam-5175	51	1	hence	hence	ADV
ejpam-5175	51	2	finally	finally	ADV
ejpam-5175	51	3	:	:	PUNCT
ejpam-5175	51	4	1	1	NUM
ejpam-5175	51	5	(	(	PUNCT
ejpam-5175	51	6	12	12	NUM
ejpam-5175	51	7	)	)	PUNCT
ejpam-5175	51	8	(	(	PUNCT
ejpam-5175	51	9	123	123	NUM
ejpam-5175	51	10	)	)	PUNCT
ejpam-5175	51	11	χ1	χ1	NOUN
ejpam-5175	51	12	1	1	NUM
ejpam-5175	51	13	1	1	NUM
ejpam-5175	51	14	1	1	NUM
ejpam-5175	51	15	χ2	χ2	NOUN
ejpam-5175	51	16	1	1	NUM
ejpam-5175	51	17	-1	-1	SYM
ejpam-5175	51	18	1	1	NUM
ejpam-5175	51	19	χ3	χ3	NOUN
ejpam-5175	51	20	2	2	NUM
ejpam-5175	51	21	0	0	NUM
ejpam-5175	51	22	−1	−1	NOUN
ejpam-5175	51	23	3	3	NUM
ejpam-5175	51	24	.	.	PUNCT
ejpam-5175	51	25	representations	representation	NOUN
ejpam-5175	51	26	and	and	CCONJ
ejpam-5175	51	27	the	the	DET
ejpam-5175	51	28	characters	character	NOUN
ejpam-5175	51	29	of	of	ADP
ejpam-5175	51	30	the	the	DET
ejpam-5175	51	31	quaternion	quaternion	NOUN
ejpam-5175	51	32	group	group	NOUN
ejpam-5175	51	33	q8	q8	PROPN
ejpam-5175	51	34	recall	recall	VERB
ejpam-5175	51	35	that	that	SCONJ
ejpam-5175	51	36	the	the	DET
ejpam-5175	51	37	non	non	ADJ
ejpam-5175	51	38	-	-	ADJ
ejpam-5175	51	39	commutative	commutative	ADJ
ejpam-5175	51	40	field	field	NOUN
ejpam-5175	51	41	h	h	NOUN
ejpam-5175	51	42	of	of	ADP
ejpam-5175	51	43	quaternions	quaternion	NOUN
ejpam-5175	51	44	can	can	AUX
ejpam-5175	51	45	be	be	AUX
ejpam-5175	51	46	obtained	obtain	VERB
ejpam-5175	51	47	from	from	ADP
ejpam-5175	51	48	the	the	DET
ejpam-5175	51	49	field	field	NOUN
ejpam-5175	51	50	c	c	NOUN
ejpam-5175	51	51	by	by	ADP
ejpam-5175	51	52	the	the	DET
ejpam-5175	51	53	construction	construction	NOUN
ejpam-5175	51	54	of	of	ADP
ejpam-5175	51	55	cayley	cayley	ADJ
ejpam-5175	51	56	-	-	PUNCT
ejpam-5175	51	57	dickson	dickson	NOUN
ejpam-5175	51	58	:	:	PUNCT
ejpam-5175	51	59	we	we	PRON
ejpam-5175	51	60	provide	provide	VERB
ejpam-5175	51	61	the	the	DET
ejpam-5175	51	62	set	set	ADJ
ejpam-5175	51	63	c2	c2	PROPN
ejpam-5175	51	64	of	of	ADP
ejpam-5175	51	65	pairs	pair	NOUN
ejpam-5175	51	66	(	(	PUNCT
ejpam-5175	51	67	z	z	NOUN
ejpam-5175	51	68	,	,	PUNCT
ejpam-5175	51	69	w	w	NOUN
ejpam-5175	51	70	)	)	PUNCT
ejpam-5175	51	71	of	of	ADP
ejpam-5175	51	72	complex	complex	ADJ
ejpam-5175	51	73	numbers	number	NOUN
ejpam-5175	51	74	of	of	ADP
ejpam-5175	51	75	the	the	DET
ejpam-5175	51	76	following	follow	VERB
ejpam-5175	51	77	addition	addition	NOUN
ejpam-5175	51	78	and	and	CCONJ
ejpam-5175	51	79	multiplication	multiplication	NOUN
ejpam-5175	51	80	:	:	PUNCT
ejpam-5175	51	81	(	(	PUNCT
ejpam-5175	51	82	z	z	NOUN
ejpam-5175	51	83	,	,	PUNCT
ejpam-5175	51	84	w	w	PROPN
ejpam-5175	51	85	)	)	PUNCT
ejpam-5175	51	86	+	+	CCONJ
ejpam-5175	51	87	(	(	PUNCT
ejpam-5175	51	88	z′	z′	NOUN
ejpam-5175	51	89	,	,	PUNCT
ejpam-5175	51	90	w′	w′	NOUN
ejpam-5175	51	91	)	)	PUNCT
ejpam-5175	51	92	=	=	SYM
ejpam-5175	51	93	(	(	PUNCT
ejpam-5175	51	94	z	z	NOUN
ejpam-5175	51	95	+	+	NOUN
ejpam-5175	51	96	z′	z′	NUM
ejpam-5175	51	97	,	,	PUNCT
ejpam-5175	51	98	w	w	NOUN
ejpam-5175	51	99	+	+	ADJ
ejpam-5175	51	100	w′	w′	NOUN
ejpam-5175	51	101	)	)	PUNCT
ejpam-5175	51	102	(	(	PUNCT
ejpam-5175	51	103	z	z	NOUN
ejpam-5175	51	104	,	,	PUNCT
ejpam-5175	51	105	w).(z′	w).(z′	NOUN
ejpam-5175	51	106	,	,	PUNCT
ejpam-5175	51	107	w′	w′	NOUN
ejpam-5175	51	108	)	)	PUNCT
ejpam-5175	51	109	=	=	SYM
ejpam-5175	51	110	(	(	PUNCT
ejpam-5175	51	111	zz′	zz′	NUM
ejpam-5175	51	112	−	−	NOUN
ejpam-5175	51	113	w′w	w′w	NOUN
ejpam-5175	51	114	,	,	PUNCT
ejpam-5175	51	115	w′z	w′z	NOUN
ejpam-5175	51	116	+	+	CCONJ
ejpam-5175	51	117	wz′	wz′	NOUN
ejpam-5175	51	118	)	)	PUNCT
ejpam-5175	51	119	note	note	VERB
ejpam-5175	51	120	that	that	SCONJ
ejpam-5175	51	121	this	this	DET
ejpam-5175	51	122	construction	construction	NOUN
ejpam-5175	51	123	carried	carry	VERB
ejpam-5175	51	124	out	out	ADP
ejpam-5175	51	125	from	from	ADP
ejpam-5175	51	126	the	the	DET
ejpam-5175	51	127	field	field	NOUN
ejpam-5175	51	128	r	r	NOUN
ejpam-5175	51	129	of	of	ADP
ejpam-5175	51	130	the	the	DET
ejpam-5175	51	131	real	real	ADJ
ejpam-5175	51	132	numbers	number	NOUN
ejpam-5175	51	133	produces	produce	VERB
ejpam-5175	51	134	the	the	DET
ejpam-5175	51	135	field	field	NOUN
ejpam-5175	51	136	c.	c.	NOUN
ejpam-5175	51	137	the	the	DET
ejpam-5175	51	138	application	application	NOUN
ejpam-5175	51	139	z	z	PROPN
ejpam-5175	51	140	→	→	SYM
ejpam-5175	51	141	(	(	PUNCT
ejpam-5175	51	142	z	z	NOUN
ejpam-5175	51	143	,	,	PUNCT
ejpam-5175	51	144	0	0	NUM
ejpam-5175	51	145	)	)	PUNCT
ejpam-5175	51	146	allows	allow	VERB
ejpam-5175	51	147	us	we	PRON
ejpam-5175	51	148	to	to	PART
ejpam-5175	51	149	canonically	canonically	ADV
ejpam-5175	51	150	identify	identify	VERB
ejpam-5175	51	151	c	c	NOUN
ejpam-5175	51	152	to	to	ADP
ejpam-5175	51	153	a	a	DET
ejpam-5175	51	154	subfield	subfield	NOUN
ejpam-5175	51	155	of	of	ADP
ejpam-5175	51	156	h.	h.	NOUN
ejpam-5175	51	157	we	we	PRON
ejpam-5175	51	158	set	set	VERB
ejpam-5175	51	159	j	j	PROPN
ejpam-5175	51	160	=	=	SYM
ejpam-5175	51	161	(	(	PUNCT
ejpam-5175	51	162	0	0	NUM
ejpam-5175	51	163	,	,	PUNCT
ejpam-5175	51	164	1	1	X
ejpam-5175	51	165	)	)	PUNCT
ejpam-5175	51	166	we	we	PRON
ejpam-5175	51	167	have	have	VERB
ejpam-5175	51	168	j2	j2	PROPN
ejpam-5175	51	169	=	=	SYM
ejpam-5175	51	170	−1	−1	NOUN
ejpam-5175	51	171	and	and	CCONJ
ejpam-5175	51	172	jz	jz	PROPN
ejpam-5175	51	173	=	=	PROPN
ejpam-5175	51	174	zj	zj	PROPN
ejpam-5175	51	175	for	for	ADP
ejpam-5175	51	176	all	all	DET
ejpam-5175	51	177	z	z	NOUN
ejpam-5175	51	178	∈	∈	PROPN
ejpam-5175	51	179	c	c	NOUN
ejpam-5175	51	180	(	(	PUNCT
ejpam-5175	51	181	in	in	ADP
ejpam-5175	51	182	particular	particular	ADJ
ejpam-5175	52	1	k	k	NOUN
ejpam-5175	52	2	=	=	PUNCT
ejpam-5175	52	3	ij	ij	NOUN
ejpam-5175	52	4	=	=	SYM
ejpam-5175	52	5	−ji	−ji	PROPN
ejpam-5175	52	6	)	)	PUNCT
ejpam-5175	52	7	.	.	PUNCT
ejpam-5175	53	1	any	any	DET
ejpam-5175	53	2	element	element	NOUN
ejpam-5175	53	3	h	h	NOUN
ejpam-5175	53	4	=	=	PUNCT
ejpam-5175	53	5	(	(	PUNCT
ejpam-5175	53	6	z	z	NOUN
ejpam-5175	53	7	,	,	PUNCT
ejpam-5175	53	8	w	w	NOUN
ejpam-5175	53	9	)	)	PUNCT
ejpam-5175	53	10	of	of	ADP
ejpam-5175	53	11	h	h	NOUN
ejpam-5175	53	12	is	be	AUX
ejpam-5175	53	13	then	then	ADV
ejpam-5175	53	14	uniquely	uniquely	ADV
ejpam-5175	53	15	written	write	VERB
ejpam-5175	53	16	h	h	NOUN
ejpam-5175	54	1	=	=	PUNCT
ejpam-5175	55	1	z+	z+	NUM
ejpam-5175	55	2	jw	jw	PROPN
ejpam-5175	55	3	with	with	ADP
ejpam-5175	55	4	z	z	PROPN
ejpam-5175	55	5	,	,	PUNCT
ejpam-5175	55	6	w	w	PROPN
ejpam-5175	55	7	∈	∈	PROPN
ejpam-5175	55	8	c	c	NOUN
ejpam-5175	55	9	so	so	SCONJ
ejpam-5175	55	10	that	that	SCONJ
ejpam-5175	55	11	(	(	PUNCT
ejpam-5175	55	12	1	1	NUM
ejpam-5175	55	13	,	,	PUNCT
ejpam-5175	55	14	j	j	NOUN
ejpam-5175	55	15	)	)	PUNCT
ejpam-5175	55	16	is	be	AUX
ejpam-5175	55	17	a	a	DET
ejpam-5175	55	18	basis	basis	NOUN
ejpam-5175	55	19	of	of	ADP
ejpam-5175	55	20	the	the	DET
ejpam-5175	55	21	c	c	NOUN
ejpam-5175	55	22	-	-	PUNCT
ejpam-5175	55	23	vector	vector	NOUN
ejpam-5175	55	24	space	space	NOUN
ejpam-5175	55	25	h	h	NOUN
ejpam-5175	55	26	while	while	SCONJ
ejpam-5175	55	27	(	(	PUNCT
ejpam-5175	55	28	1	1	NUM
ejpam-5175	55	29	,	,	PUNCT
ejpam-5175	55	30	i	i	PRON
ejpam-5175	55	31	,	,	PUNCT
ejpam-5175	55	32	j	j	PROPN
ejpam-5175	55	33	,	,	PUNCT
ejpam-5175	55	34	k	k	NOUN
ejpam-5175	55	35	)	)	PUNCT
ejpam-5175	55	36	is	be	AUX
ejpam-5175	55	37	a	a	DET
ejpam-5175	55	38	basis	basis	NOUN
ejpam-5175	55	39	of	of	ADP
ejpam-5175	55	40	the	the	DET
ejpam-5175	55	41	r	r	NOUN
ejpam-5175	55	42	-	-	PUNCT
ejpam-5175	55	43	vector	vector	NOUN
ejpam-5175	55	44	space	space	NOUN
ejpam-5175	55	45	h.	h.	NOUN
ejpam-5175	55	46	we	we	PRON
ejpam-5175	55	47	have	have	VERB
ejpam-5175	55	48	:	:	PUNCT
ejpam-5175	56	1			NUM
ejpam-5175	56	2	i2	i2	PROPN
ejpam-5175	56	3	=	=	PROPN
ejpam-5175	56	4	j2	j2	PROPN
ejpam-5175	56	5	=	=	SYM
ejpam-5175	56	6	k2	k2	PROPN
ejpam-5175	56	7	=	=	SYM
ejpam-5175	56	8	−1	−1	NOUN
ejpam-5175	56	9	ij	ij	NOUN
ejpam-5175	56	10	=	=	NOUN
ejpam-5175	56	11	−ji	−ji	PROPN
ejpam-5175	57	1	=	=	SYM
ejpam-5175	57	2	k	k	PROPN
ejpam-5175	57	3	jk	jk	PROPN
ejpam-5175	57	4	=	=	PUNCT
ejpam-5175	58	1	−kj	−kj	INTJ
ejpam-5175	59	1	=	=	NOUN
ejpam-5175	60	1	i	i	PRON
ejpam-5175	60	2	ki	ki	INTJ
ejpam-5175	60	3	=	=	PUNCT
ejpam-5175	60	4	−ik	−ik	NOUN
ejpam-5175	60	5	=	=	SYM
ejpam-5175	60	6	j	j	NOUN
ejpam-5175	60	7	we	we	PRON
ejpam-5175	60	8	again	again	ADV
ejpam-5175	60	9	set	set	VERB
ejpam-5175	60	10	h	h	NOUN
ejpam-5175	61	1	=	=	PUNCT
ejpam-5175	61	2	z	z	NOUN
ejpam-5175	62	1	−	−	PROPN
ejpam-5175	62	2	jw	jw	NOUN
ejpam-5175	62	3	so	so	SCONJ
ejpam-5175	62	4	that	that	SCONJ
ejpam-5175	62	5	h	h	NOUN
ejpam-5175	62	6	=	=	NOUN
ejpam-5175	62	7	h	h	PROPN
ejpam-5175	62	8	and	and	CCONJ
ejpam-5175	62	9	hh′	hh′	PROPN
ejpam-5175	63	1	=	=	PUNCT
ejpam-5175	63	2	h′h	h′h	PROPN
ejpam-5175	63	3	for	for	ADP
ejpam-5175	63	4	all	all	DET
ejpam-5175	63	5	h	h	NOUN
ejpam-5175	63	6	,	,	PUNCT
ejpam-5175	63	7	h′	h′	PROPN
ejpam-5175	63	8	∈	∈	PROPN
ejpam-5175	63	9	h.	h.	NOUN
ejpam-5175	64	1	we	we	PRON
ejpam-5175	64	2	then	then	ADV
ejpam-5175	64	3	have	have	VERB
ejpam-5175	64	4	n(h	n(h	NOUN
ejpam-5175	64	5	)	)	PUNCT
ejpam-5175	65	1	=	=	PUNCT
ejpam-5175	65	2	hh̄	hh̄	NOUN
ejpam-5175	65	3	∈	∈	PROPN
ejpam-5175	65	4	r+	r+	NOUN
ejpam-5175	65	5	and	and	CCONJ
ejpam-5175	65	6	n(hh′	n(hh′	NOUN
ejpam-5175	65	7	)	)	PUNCT
ejpam-5175	65	8	=	=	SYM
ejpam-5175	65	9	n(h)n(h′	n(h)n(h′	ADJ
ejpam-5175	65	10	)	)	PUNCT
ejpam-5175	65	11	.	.	PUNCT
ejpam-5175	66	1	then	then	ADV
ejpam-5175	66	2	all	all	DET
ejpam-5175	66	3	h	h	NOUN
ejpam-5175	66	4	∈	∈	PROPN
ejpam-5175	66	5	h∗	h∗	NOUN
ejpam-5175	66	6	is	be	AUX
ejpam-5175	66	7	invertible	invertible	ADJ
ejpam-5175	66	8	and	and	CCONJ
ejpam-5175	66	9	we	we	PRON
ejpam-5175	66	10	have	have	VERB
ejpam-5175	66	11	h−1	h−1	PROPN
ejpam-5175	66	12	=	=	SYM
ejpam-5175	66	13	1	1	NUM
ejpam-5175	66	14	n(h	n(h	PROPN
ejpam-5175	66	15	)	)	PUNCT
ejpam-5175	66	16	h.	h.	PROPN
ejpam-5175	66	17	a.	a.	NOUN
ejpam-5175	66	18	labsir	labsir	PROPN
ejpam-5175	66	19	,	,	PUNCT
ejpam-5175	66	20	e.	e.	PROPN
ejpam-5175	66	21	fanich	fanich	PROPN
ejpam-5175	66	22	/	/	SYM
ejpam-5175	66	23	eur	eur	PROPN
ejpam-5175	66	24	.	.	PUNCT
ejpam-5175	67	1	j.	j.	PROPN
ejpam-5175	67	2	pure	pure	PROPN
ejpam-5175	67	3	appl	appl	PROPN
ejpam-5175	67	4	.	.	PROPN
ejpam-5175	67	5	math	math	PROPN
ejpam-5175	67	6	,	,	PUNCT
ejpam-5175	67	7	17	17	NUM
ejpam-5175	67	8	(	(	PUNCT
ejpam-5175	67	9	3	3	NUM
ejpam-5175	67	10	)	)	PUNCT
ejpam-5175	67	11	(	(	PUNCT
ejpam-5175	67	12	2024	2024	NUM
ejpam-5175	67	13	)	)	PUNCT
ejpam-5175	67	14	,	,	PUNCT
ejpam-5175	67	15	1717	1717	NUM
ejpam-5175	67	16	-	-	SYM
ejpam-5175	67	17	1726	1726	NUM
ejpam-5175	67	18	1721	1721	NUM
ejpam-5175	67	19	finally	finally	ADV
ejpam-5175	67	20	,	,	PUNCT
ejpam-5175	67	21	we	we	PRON
ejpam-5175	67	22	have	have	VERB
ejpam-5175	67	23	the	the	DET
ejpam-5175	67	24	canonical	canonical	ADJ
ejpam-5175	67	25	representation	representation	NOUN
ejpam-5175	67	26	of	of	ADP
ejpam-5175	67	27	the	the	DET
ejpam-5175	67	28	r	r	NOUN
ejpam-5175	67	29	-	-	PUNCT
ejpam-5175	67	30	algebra	algebra	NOUN
ejpam-5175	67	31	h	h	NOUN
ejpam-5175	67	32	:	:	PUNCT
ejpam-5175	68	1	π	π	NOUN
ejpam-5175	68	2	:	:	PUNCT
ejpam-5175	68	3	h	h	NOUN
ejpam-5175	68	4	→	→	SYM
ejpam-5175	68	5	m2(c	m2(c	NOUN
ejpam-5175	68	6	)	)	PUNCT
ejpam-5175	68	7	h	h	NOUN
ejpam-5175	68	8	=	=	PUNCT
ejpam-5175	68	9	z	z	PROPN
ejpam-5175	69	1	+	+	NUM
ejpam-5175	69	2	jw	jw	PROPN
ejpam-5175	69	3	→	→	SYM
ejpam-5175	69	4	(	(	PUNCT
ejpam-5175	69	5	z	z	NOUN
ejpam-5175	69	6	−w	−w	ADV
ejpam-5175	69	7	w	w	PROPN
ejpam-5175	69	8	z	z	PROPN
ejpam-5175	69	9	)	)	PUNCT
ejpam-5175	69	10	note	note	NOUN
ejpam-5175	69	11	that	that	SCONJ
ejpam-5175	69	12	we	we	PRON
ejpam-5175	69	13	have	have	VERB
ejpam-5175	69	14	n(h	n(h	NOUN
ejpam-5175	69	15	)	)	PUNCT
ejpam-5175	69	16	=	=	SYM
ejpam-5175	69	17	det(π(h	det(π(h	NOUN
ejpam-5175	69	18	)	)	PUNCT
ejpam-5175	69	19	)	)	PUNCT
ejpam-5175	70	1	so	so	SCONJ
ejpam-5175	70	2	that	that	SCONJ
ejpam-5175	70	3	the	the	DET
ejpam-5175	70	4	matrix	matrix	NOUN
ejpam-5175	70	5	π(h	π(h	NOUN
ejpam-5175	70	6	)	)	PUNCT
ejpam-5175	70	7	is	be	AUX
ejpam-5175	70	8	invertible	invertible	ADJ
ejpam-5175	70	9	if	if	SCONJ
ejpam-5175	70	10	and	and	CCONJ
ejpam-5175	70	11	only	only	ADV
ejpam-5175	70	12	if	if	SCONJ
ejpam-5175	70	13	h	h	PRON
ejpam-5175	70	14	̸=	̸=	PROPN
ejpam-5175	70	15	0	0	NUM
ejpam-5175	70	16	.	.	PUNCT
ejpam-5175	71	1	in	in	ADP
ejpam-5175	71	2	particular	particular	ADJ
ejpam-5175	71	3	,	,	PUNCT
ejpam-5175	71	4	we	we	PRON
ejpam-5175	71	5	have	have	AUX
ejpam-5175	71	6	:	:	PUNCT
ejpam-5175	71	7	π(±1	π(±1	VERB
ejpam-5175	71	8	)	)	PUNCT
ejpam-5175	71	9	=	=	SYM
ejpam-5175	71	10	±	±	NOUN
ejpam-5175	71	11	(	(	PUNCT
ejpam-5175	71	12	1	1	NUM
ejpam-5175	71	13	0	0	NUM
ejpam-5175	71	14	0	0	NUM
ejpam-5175	71	15	1	1	NUM
ejpam-5175	71	16	)	)	PUNCT
ejpam-5175	71	17	π(±i	π(±i	NOUN
ejpam-5175	71	18	)	)	PUNCT
ejpam-5175	72	1	=	=	SYM
ejpam-5175	72	2	±	±	NOUN
ejpam-5175	72	3	(	(	PUNCT
ejpam-5175	72	4	i	i	NOUN
ejpam-5175	72	5	0	0	NUM
ejpam-5175	72	6	0	0	NUM
ejpam-5175	72	7	−i	−i	ADJ
ejpam-5175	72	8	)	)	PUNCT
ejpam-5175	72	9	π(±j	π(±j	PROPN
ejpam-5175	72	10	)	)	PUNCT
ejpam-5175	72	11	=	=	SYM
ejpam-5175	72	12	±	±	NOUN
ejpam-5175	72	13	(	(	PUNCT
ejpam-5175	72	14	0	0	NUM
ejpam-5175	72	15	−1	−1	NOUN
ejpam-5175	72	16	1	1	NUM
ejpam-5175	72	17	0	0	NUM
ejpam-5175	72	18	)	)	PUNCT
ejpam-5175	72	19	π(±k	π(±k	NOUN
ejpam-5175	72	20	)	)	PUNCT
ejpam-5175	72	21	=	=	SYM
ejpam-5175	72	22	±	±	NOUN
ejpam-5175	72	23	(	(	PUNCT
ejpam-5175	72	24	0	0	NUM
ejpam-5175	73	1	−i	−i	ADJ
ejpam-5175	73	2	−i	−i	PROPN
ejpam-5175	73	3	0	0	NUM
ejpam-5175	73	4	)	)	PUNCT
ejpam-5175	73	5	the	the	DET
ejpam-5175	73	6	quaternion	quaternion	NOUN
ejpam-5175	73	7	group	group	NOUN
ejpam-5175	73	8	:	:	PUNCT
ejpam-5175	73	9	q8	q8	PROPN
ejpam-5175	74	1	=	=	SYM
ejpam-5175	74	2	<	<	X
ejpam-5175	74	3	i	i	PROPN
ejpam-5175	74	4	,	,	PUNCT
ejpam-5175	74	5	j	j	PROPN
ejpam-5175	74	6	>	>	X
ejpam-5175	74	7	=	=	X
ejpam-5175	74	8	{	{	PUNCT
ejpam-5175	74	9	1,−1	1,−1	PROPN
ejpam-5175	74	10	,	,	PUNCT
ejpam-5175	74	11	i,−i	i,−i	PROPN
ejpam-5175	74	12	,	,	PUNCT
ejpam-5175	74	13	j,−j	j,−j	PROPN
ejpam-5175	74	14	,	,	PUNCT
ejpam-5175	74	15	k,−k	k,−k	PROPN
ejpam-5175	74	16	}	}	PUNCT
ejpam-5175	74	17	the	the	DET
ejpam-5175	74	18	group	group	NOUN
ejpam-5175	74	19	q8	q8	PROPN
ejpam-5175	74	20	has	have	VERB
ejpam-5175	74	21	5	5	NUM
ejpam-5175	74	22	conjugation	conjugation	NOUN
ejpam-5175	74	23	classes	class	NOUN
ejpam-5175	74	24	:	:	PUNCT
ejpam-5175	74	25	k1	k1	PROPN
ejpam-5175	74	26	=	=	SYM
ejpam-5175	74	27	{	{	PUNCT
ejpam-5175	74	28	1	1	NUM
ejpam-5175	74	29	}	}	PUNCT
ejpam-5175	74	30	k2	k2	NOUN
ejpam-5175	74	31	=	=	SYM
ejpam-5175	74	32	{	{	PUNCT
ejpam-5175	74	33	−1	−1	NOUN
ejpam-5175	74	34	}	}	PUNCT
ejpam-5175	74	35	k3	k3	VERB
ejpam-5175	74	36	=	=	SYM
ejpam-5175	74	37	{	{	PUNCT
ejpam-5175	74	38	i,−i	i,−i	NOUN
ejpam-5175	74	39	}	}	PUNCT
ejpam-5175	74	40	k4	k4	NOUN
ejpam-5175	74	41	=	=	SYM
ejpam-5175	74	42	{	{	PUNCT
ejpam-5175	74	43	j,−j	j,−j	PROPN
ejpam-5175	74	44	}	}	PUNCT
ejpam-5175	74	45	k5	k5	PROPN
ejpam-5175	74	46	=	=	SYM
ejpam-5175	74	47	{	{	PUNCT
ejpam-5175	74	48	k,−k	k,−k	PROPN
ejpam-5175	74	49	}	}	PUNCT
ejpam-5175	74	50	3.1	3.1	NUM
ejpam-5175	74	51	.	.	PUNCT
ejpam-5175	75	1	character	character	NOUN
ejpam-5175	75	2	table	table	NOUN
ejpam-5175	75	3	of	of	ADP
ejpam-5175	75	4	group	group	NOUN
ejpam-5175	75	5	q8	q8	PROPN
ejpam-5175	75	6	we	we	PRON
ejpam-5175	75	7	have	have	VERB
ejpam-5175	75	8	the	the	DET
ejpam-5175	75	9	group	group	NOUN
ejpam-5175	75	10	{	{	PUNCT
ejpam-5175	75	11	±1	±1	PROPN
ejpam-5175	75	12	}	}	PUNCT
ejpam-5175	75	13	is	be	AUX
ejpam-5175	75	14	distinguished	distinguish	VERB
ejpam-5175	75	15	in	in	ADP
ejpam-5175	75	16	q8	q8	PROPN
ejpam-5175	75	17	and	and	CCONJ
ejpam-5175	75	18	q8/{±1	q8/{±1	PROPN
ejpam-5175	75	19	}	}	PUNCT
ejpam-5175	75	20	≈	≈	PROPN
ejpam-5175	75	21	v	v	NOUN
ejpam-5175	75	22	(	(	PUNCT
ejpam-5175	75	23	v	v	NOUN
ejpam-5175	75	24	:	:	PUNCT
ejpam-5175	75	25	klein	klein	PROPN
ejpam-5175	75	26	group	group	PROPN
ejpam-5175	75	27	)	)	PUNCT
ejpam-5175	75	28	and	and	CCONJ
ejpam-5175	75	29	according	accord	VERB
ejpam-5175	75	30	to	to	ADP
ejpam-5175	75	31	the	the	DET
ejpam-5175	75	32	burnside	burnside	NOUN
ejpam-5175	75	33	formula	formula	NOUN
ejpam-5175	75	34	(	(	PUNCT
ejpam-5175	75	35	n2	n2	ADJ
ejpam-5175	75	36	1	1	NUM
ejpam-5175	75	37	+	+	CCONJ
ejpam-5175	75	38	n2	n2	ADJ
ejpam-5175	75	39	2	2	NUM
ejpam-5175	75	40	+	+	SYM
ejpam-5175	75	41	n2	n2	ADJ
ejpam-5175	75	42	3	3	NUM
ejpam-5175	75	43	+	+	SYM
ejpam-5175	75	44	n2	n2	ADJ
ejpam-5175	75	45	4	4	NUM
ejpam-5175	75	46	+	+	SYM
ejpam-5175	75	47	n2	n2	ADJ
ejpam-5175	75	48	5	5	NUM
ejpam-5175	75	49	=	=	SYM
ejpam-5175	75	50	8)	8)	NUM
ejpam-5175	75	51	,	,	PUNCT
ejpam-5175	75	52	we	we	PRON
ejpam-5175	75	53	will	will	AUX
ejpam-5175	75	54	have	have	VERB
ejpam-5175	75	55	n5	n5	NOUN
ejpam-5175	75	56	=	=	SYM
ejpam-5175	75	57	2	2	NUM
ejpam-5175	75	58	so	so	SCONJ
ejpam-5175	75	59	the	the	DET
ejpam-5175	75	60	character	character	NOUN
ejpam-5175	75	61	table	table	NOUN
ejpam-5175	75	62	of	of	ADP
ejpam-5175	75	63	q8	q8	PROPN
ejpam-5175	75	64	is	be	AUX
ejpam-5175	75	65	of	of	ADP
ejpam-5175	75	66	the	the	DET
ejpam-5175	75	67	form	form	NOUN
ejpam-5175	75	68	:	:	PUNCT
ejpam-5175	75	69	k1	k1	PROPN
ejpam-5175	75	70	k2	k2	PROPN
ejpam-5175	75	71	k3	k3	VERB
ejpam-5175	75	72	k4	k4	PROPN
ejpam-5175	75	73	k5	k5	PROPN
ejpam-5175	75	74	χ1	χ1	PROPN
ejpam-5175	75	75	1	1	NUM
ejpam-5175	75	76	1	1	NUM
ejpam-5175	75	77	1	1	NUM
ejpam-5175	75	78	1	1	NUM
ejpam-5175	75	79	1	1	NUM
ejpam-5175	75	80	χ2	χ2	NOUN
ejpam-5175	75	81	1	1	NUM
ejpam-5175	75	82	1	1	NUM
ejpam-5175	75	83	1	1	NUM
ejpam-5175	75	84	-1	-1	PUNCT
ejpam-5175	75	85	-1	-1	PUNCT
ejpam-5175	75	86	χ3	χ3	VERB
ejpam-5175	75	87	1	1	NUM
ejpam-5175	75	88	1	1	NUM
ejpam-5175	75	89	-1	-1	SYM
ejpam-5175	75	90	1	1	NUM
ejpam-5175	75	91	-1	-1	PUNCT
ejpam-5175	75	92	χ4	χ4	NOUN
ejpam-5175	75	93	1	1	NUM
ejpam-5175	75	94	1	1	NUM
ejpam-5175	75	95	-1	-1	NOUN
ejpam-5175	75	96	-1	-1	NOUN
ejpam-5175	75	97	1	1	NUM
ejpam-5175	75	98	χ5	χ5	NOUN
ejpam-5175	75	99	2	2	NUM
ejpam-5175	75	100	a	a	DET
ejpam-5175	75	101	b	b	NOUN
ejpam-5175	75	102	c	c	NOUN
ejpam-5175	76	1	d	d	X
ejpam-5175	76	2	then	then	ADV
ejpam-5175	76	3	by	by	ADP
ejpam-5175	76	4	orthogonality	orthogonality	NOUN
ejpam-5175	76	5	of	of	ADP
ejpam-5175	76	6	the	the	DET
ejpam-5175	76	7	columns	column	NOUN
ejpam-5175	76	8	we	we	PRON
ejpam-5175	76	9	obtain	obtain	VERB
ejpam-5175	76	10	a	a	DET
ejpam-5175	76	11	=	=	NOUN
ejpam-5175	76	12	−2	−2	NOUN
ejpam-5175	76	13	et	et	NOUN
ejpam-5175	76	14	b	b	NOUN
ejpam-5175	76	15	=	=	SYM
ejpam-5175	76	16	c	c	NOUN
ejpam-5175	76	17	=	=	SYM
ejpam-5175	77	1	d	d	NOUN
ejpam-5175	77	2	=	=	SYM
ejpam-5175	77	3	0	0	PROPN
ejpam-5175	77	4	.	.	PUNCT
ejpam-5175	78	1	finally	finally	ADV
ejpam-5175	78	2	the	the	DET
ejpam-5175	78	3	character	character	NOUN
ejpam-5175	78	4	table	table	NOUN
ejpam-5175	78	5	of	of	ADP
ejpam-5175	78	6	q8	q8	PROPN
ejpam-5175	78	7	is	be	AUX
ejpam-5175	78	8	as	as	SCONJ
ejpam-5175	78	9	follows	follow	VERB
ejpam-5175	78	10	:	:	PUNCT
ejpam-5175	78	11	k1	k1	PROPN
ejpam-5175	78	12	k2	k2	PROPN
ejpam-5175	78	13	k3	k3	VERB
ejpam-5175	78	14	k4	k4	PROPN
ejpam-5175	78	15	k5	k5	PROPN
ejpam-5175	78	16	χ1	χ1	PROPN
ejpam-5175	78	17	1	1	NUM
ejpam-5175	78	18	1	1	NUM
ejpam-5175	78	19	1	1	NUM
ejpam-5175	78	20	1	1	NUM
ejpam-5175	78	21	1	1	NUM
ejpam-5175	78	22	χ2	χ2	NOUN
ejpam-5175	78	23	1	1	NUM
ejpam-5175	78	24	1	1	NUM
ejpam-5175	78	25	1	1	NUM
ejpam-5175	78	26	-1	-1	PUNCT
ejpam-5175	78	27	-1	-1	PUNCT
ejpam-5175	78	28	χ3	χ3	VERB
ejpam-5175	78	29	1	1	NUM
ejpam-5175	78	30	1	1	NUM
ejpam-5175	78	31	-1	-1	SYM
ejpam-5175	78	32	1	1	NUM
ejpam-5175	78	33	-1	-1	PUNCT
ejpam-5175	78	34	χ4	χ4	NOUN
ejpam-5175	78	35	1	1	NUM
ejpam-5175	78	36	1	1	NUM
ejpam-5175	78	37	-1	-1	NOUN
ejpam-5175	78	38	-1	-1	NOUN
ejpam-5175	78	39	1	1	NUM
ejpam-5175	78	40	χ5	χ5	NOUN
ejpam-5175	78	41	2	2	NUM
ejpam-5175	78	42	-2	-2	NOUN
ejpam-5175	78	43	0	0	NUM
ejpam-5175	78	44	0	0	SYM
ejpam-5175	78	45	0	0	NUM
ejpam-5175	78	46	a.	a.	NOUN
ejpam-5175	78	47	labsir	labsir	PROPN
ejpam-5175	78	48	,	,	PUNCT
ejpam-5175	78	49	e.	e.	PROPN
ejpam-5175	78	50	fanich	fanich	PROPN
ejpam-5175	78	51	/	/	SYM
ejpam-5175	78	52	eur	eur	PROPN
ejpam-5175	78	53	.	.	PUNCT
ejpam-5175	79	1	j.	j.	PROPN
ejpam-5175	79	2	pure	pure	PROPN
ejpam-5175	79	3	appl	appl	PROPN
ejpam-5175	79	4	.	.	PROPN
ejpam-5175	79	5	math	math	PROPN
ejpam-5175	79	6	,	,	PUNCT
ejpam-5175	79	7	17	17	NUM
ejpam-5175	79	8	(	(	PUNCT
ejpam-5175	79	9	3	3	NUM
ejpam-5175	79	10	)	)	PUNCT
ejpam-5175	79	11	(	(	PUNCT
ejpam-5175	79	12	2024	2024	NUM
ejpam-5175	79	13	)	)	PUNCT
ejpam-5175	79	14	,	,	PUNCT
ejpam-5175	79	15	1717	1717	NUM
ejpam-5175	79	16	-	-	SYM
ejpam-5175	79	17	1726	1726	NUM
ejpam-5175	79	18	1722	1722	NUM
ejpam-5175	79	19	3.2	3.2	NUM
ejpam-5175	79	20	.	.	PUNCT
ejpam-5175	80	1	irreducible	irreducible	ADJ
ejpam-5175	80	2	representations	representation	NOUN
ejpam-5175	80	3	of	of	ADP
ejpam-5175	80	4	the	the	DET
ejpam-5175	80	5	group	group	NOUN
ejpam-5175	80	6	q8	q8	PROPN
ejpam-5175	80	7	3.2.1	3.2.1	NUM
ejpam-5175	80	8	.	.	PUNCT
ejpam-5175	81	1	realization	realization	NOUN
ejpam-5175	81	2	of	of	ADP
ejpam-5175	81	3	irreducible	irreducible	ADJ
ejpam-5175	81	4	representations	representation	NOUN
ejpam-5175	81	5	of	of	ADP
ejpam-5175	81	6	degree	degree	NOUN
ejpam-5175	81	7	1	1	NUM
ejpam-5175	81	8	let	let	VERB
ejpam-5175	81	9	τ	τ	PROPN
ejpam-5175	81	10	:	:	PUNCT
ejpam-5175	81	11	h	h	PROPN
ejpam-5175	81	12	→	→	SYM
ejpam-5175	81	13	c∗	c∗	PROPN
ejpam-5175	81	14	be	be	AUX
ejpam-5175	81	15	a	a	DET
ejpam-5175	81	16	1	1	NUM
ejpam-5175	81	17	-	-	PUNCT
ejpam-5175	81	18	dimensional	dimensional	ADJ
ejpam-5175	81	19	representation	representation	NOUN
ejpam-5175	81	20	of	of	ADP
ejpam-5175	81	21	h.	h.	PROPN
ejpam-5175	81	22	then	then	ADV
ejpam-5175	81	23	τ	τ	PROPN
ejpam-5175	81	24	can	can	AUX
ejpam-5175	81	25	not	not	PART
ejpam-5175	81	26	be	be	AUX
ejpam-5175	81	27	faithful	faithful	ADJ
ejpam-5175	81	28	,	,	PUNCT
ejpam-5175	81	29	otherwise	otherwise	ADV
ejpam-5175	81	30	h	h	NOUN
ejpam-5175	81	31	would	would	AUX
ejpam-5175	81	32	be	be	AUX
ejpam-5175	81	33	abelian	abelian	ADJ
ejpam-5175	81	34	.	.	PUNCT
ejpam-5175	82	1	therefore	therefore	ADV
ejpam-5175	82	2	,	,	PUNCT
ejpam-5175	82	3	kerτ	kerτ	PROPN
ejpam-5175	82	4	is	be	AUX
ejpam-5175	82	5	a	a	DET
ejpam-5175	82	6	distinguished	distinguished	ADJ
ejpam-5175	82	7	subgroup	subgroup	NOUN
ejpam-5175	82	8	of	of	ADP
ejpam-5175	82	9	h	h	NOUN
ejpam-5175	82	10	,	,	PUNCT
ejpam-5175	82	11	kerτ	kerτ	ADJ
ejpam-5175	82	12	̸=	̸=	PROPN
ejpam-5175	82	13	{	{	PUNCT
ejpam-5175	82	14	1	1	NUM
ejpam-5175	82	15	}	}	PUNCT
ejpam-5175	82	16	.	.	PUNCT
ejpam-5175	83	1	if	if	SCONJ
ejpam-5175	83	2	kerτ	kerτ	ADJ
ejpam-5175	83	3	=	=	NOUN
ejpam-5175	83	4	h	h	NOUN
ejpam-5175	83	5	we	we	PRON
ejpam-5175	83	6	obtain	obtain	VERB
ejpam-5175	83	7	the	the	DET
ejpam-5175	83	8	trivial	trivial	ADJ
ejpam-5175	83	9	representation	representation	NOUN
ejpam-5175	83	10	τ1	τ1	NOUN
ejpam-5175	83	11	.	.	PUNCT
ejpam-5175	84	1	others	other	NOUN
ejpam-5175	84	2	possibilities	possibility	NOUN
ejpam-5175	84	3	for	for	ADP
ejpam-5175	84	4	kerτ	kerτ	ADJ
ejpam-5175	84	5	are	be	AUX
ejpam-5175	84	6	:	:	PUNCT
ejpam-5175	84	7	z(h	z(h	NUM
ejpam-5175	84	8	)	)	PUNCT
ejpam-5175	84	9	=	=	PRON
ejpam-5175	84	10	{	{	PUNCT
ejpam-5175	84	11	±1	±1	NOUN
ejpam-5175	84	12	}	}	PUNCT
ejpam-5175	84	13	,	,	PUNCT
ejpam-5175	85	1	i	i	PRON
ejpam-5175	85	2	=	=	PUNCT
ejpam-5175	85	3	{	{	PUNCT
ejpam-5175	85	4	±1,±i	±1,±i	PROPN
ejpam-5175	85	5	}	}	PUNCT
ejpam-5175	85	6	j	j	NOUN
ejpam-5175	85	7	=	=	PRON
ejpam-5175	85	8	{	{	PUNCT
ejpam-5175	85	9	±1,±j	±1,±j	PROPN
ejpam-5175	85	10	}	}	PUNCT
ejpam-5175	85	11	,	,	PUNCT
ejpam-5175	85	12	k	k	X
ejpam-5175	85	13	=	=	PRON
ejpam-5175	85	14	{	{	PUNCT
ejpam-5175	85	15	±1,±k	±1,±k	NOUN
ejpam-5175	85	16	}	}	PUNCT
ejpam-5175	85	17	but	but	CCONJ
ejpam-5175	85	18	,	,	PUNCT
ejpam-5175	85	19	h	h	X
ejpam-5175	85	20	/	/	SYM
ejpam-5175	85	21	i	i	PROPN
ejpam-5175	86	1	≈	≈	PROPN
ejpam-5175	86	2	h	h	PROPN
ejpam-5175	86	3	/	/	SYM
ejpam-5175	86	4	j	j	PROPN
ejpam-5175	87	1	≈	≈	PROPN
ejpam-5175	87	2	h	h	PROPN
ejpam-5175	87	3	/	/	SYM
ejpam-5175	87	4	k	k	PROPN
ejpam-5175	87	5	≈	≈	PROPN
ejpam-5175	87	6	z2	z2	PROPN
ejpam-5175	87	7	and	and	CCONJ
ejpam-5175	87	8	h	h	NOUN
ejpam-5175	87	9	/	/	SYM
ejpam-5175	87	10	z(h	z(h	PROPN
ejpam-5175	87	11	)	)	PUNCT
ejpam-5175	88	1	≈	≈	PROPN
ejpam-5175	88	2	z2	z2	PROPN
ejpam-5175	88	3	×	×	PROPN
ejpam-5175	88	4	z2	z2	PROPN
ejpam-5175	88	5	.	.	PUNCT
ejpam-5175	89	1	obviously	obviously	ADV
ejpam-5175	89	2	,	,	PUNCT
ejpam-5175	89	3	τ	τ	PROPN
ejpam-5175	89	4	is	be	AUX
ejpam-5175	89	5	factorized	factorize	VERB
ejpam-5175	89	6	as	as	ADP
ejpam-5175	89	7	the	the	DET
ejpam-5175	89	8	composite	composite	NOUN
ejpam-5175	89	9	of	of	ADP
ejpam-5175	89	10	the	the	DET
ejpam-5175	89	11	projection	projection	NOUN
ejpam-5175	89	12	on	on	ADP
ejpam-5175	89	13	the	the	DET
ejpam-5175	89	14	quotient	quotient	NOUN
ejpam-5175	89	15	h	h	NOUN
ejpam-5175	89	16	/	/	SYM
ejpam-5175	89	17	kerτ	kerτ	ADJ
ejpam-5175	89	18	→	→	NOUN
ejpam-5175	89	19	c∗.	c∗.	NOUN
ejpam-5175	89	20	furthermore	furthermore	ADV
ejpam-5175	89	21	,	,	PUNCT
ejpam-5175	89	22	there	there	PRON
ejpam-5175	89	23	is	be	VERB
ejpam-5175	89	24	no	no	DET
ejpam-5175	89	25	only	only	ADV
ejpam-5175	89	26	one	one	NUM
ejpam-5175	89	27	way	way	NOUN
ejpam-5175	89	28	to	to	PART
ejpam-5175	89	29	represent	represent	VERB
ejpam-5175	89	30	z2	z2	PROPN
ejpam-5175	89	31	in	in	ADP
ejpam-5175	89	32	a	a	DET
ejpam-5175	89	33	non	non	ADJ
ejpam-5175	89	34	-	-	ADJ
ejpam-5175	89	35	trivial	trivial	ADJ
ejpam-5175	89	36	way	way	NOUN
ejpam-5175	89	37	in	in	ADP
ejpam-5175	89	38	c	c	PROPN
ejpam-5175	89	39	and	and	CCONJ
ejpam-5175	89	40	therefore	therefore	ADV
ejpam-5175	89	41	we	we	PRON
ejpam-5175	89	42	obtain	obtain	VERB
ejpam-5175	89	43	the	the	DET
ejpam-5175	89	44	following	follow	VERB
ejpam-5175	89	45	representations	representation	NOUN
ejpam-5175	89	46	:	:	PUNCT
ejpam-5175	89	47	when	when	SCONJ
ejpam-5175	89	48	kerτ	kerτ	ADJ
ejpam-5175	89	49	=	=	NOUN
ejpam-5175	89	50	i	i	PRON
ejpam-5175	89	51	τ2({±1,±i	τ2({±1,±i	VERB
ejpam-5175	89	52	}	}	PUNCT
ejpam-5175	89	53	)	)	PUNCT
ejpam-5175	90	1	=	=	SYM
ejpam-5175	90	2	1	1	NUM
ejpam-5175	90	3	,	,	PUNCT
ejpam-5175	90	4	τ2({±j,±k	τ2({±j,±k	NOUN
ejpam-5175	90	5	}	}	PUNCT
ejpam-5175	90	6	)	)	PUNCT
ejpam-5175	90	7	=	=	PUNCT
ejpam-5175	91	1	−1	−1	NOUN
ejpam-5175	91	2	when	when	SCONJ
ejpam-5175	91	3	kerτ	kerτ	ADJ
ejpam-5175	91	4	=	=	SYM
ejpam-5175	91	5	j	j	NOUN
ejpam-5175	91	6	τ3({±1,±j	τ3({±1,±j	PROPN
ejpam-5175	91	7	}	}	PUNCT
ejpam-5175	91	8	)	)	PUNCT
ejpam-5175	91	9	=	=	SYM
ejpam-5175	91	10	1	1	NUM
ejpam-5175	91	11	,	,	PUNCT
ejpam-5175	91	12	τ3({±i,±k	τ3({±i,±k	NOUN
ejpam-5175	91	13	}	}	PUNCT
ejpam-5175	91	14	)	)	PUNCT
ejpam-5175	91	15	=	=	PUNCT
ejpam-5175	91	16	−1	−1	NOUN
ejpam-5175	91	17	when	when	SCONJ
ejpam-5175	91	18	kerτ	kerτ	ADJ
ejpam-5175	91	19	=	=	PROPN
ejpam-5175	91	20	k	k	X
ejpam-5175	91	21	τ4({±1,±k	τ4({±1,±k	PROPN
ejpam-5175	91	22	}	}	PUNCT
ejpam-5175	91	23	)	)	PUNCT
ejpam-5175	91	24	=	=	SYM
ejpam-5175	91	25	1	1	NUM
ejpam-5175	91	26	,	,	PUNCT
ejpam-5175	91	27	τ4({±i,±j	τ4({±i,±j	PROPN
ejpam-5175	91	28	}	}	PUNCT
ejpam-5175	91	29	)	)	PUNCT
ejpam-5175	91	30	=	=	PUNCT
ejpam-5175	91	31	−1	−1	NOUN
ejpam-5175	91	32	when	when	SCONJ
ejpam-5175	91	33	kerτ	kerτ	ADJ
ejpam-5175	91	34	=	=	NOUN
ejpam-5175	91	35	z(h	z(h	PROPN
ejpam-5175	91	36	)	)	PUNCT
ejpam-5175	91	37	,	,	PUNCT
ejpam-5175	91	38	the	the	DET
ejpam-5175	91	39	representations	representation	NOUN
ejpam-5175	91	40	obtained	obtain	VERB
ejpam-5175	91	41	by	by	ADP
ejpam-5175	91	42	composing	compose	VERB
ejpam-5175	91	43	the	the	DET
ejpam-5175	91	44	projection	projection	NOUN
ejpam-5175	91	45	on	on	ADP
ejpam-5175	91	46	the	the	DET
ejpam-5175	91	47	quotient	quotient	NOUN
ejpam-5175	91	48	by	by	ADP
ejpam-5175	91	49	a	a	DET
ejpam-5175	91	50	representation	representation	NOUN
ejpam-5175	91	51	of	of	ADP
ejpam-5175	91	52	e	e	PROPN
ejpam-5175	91	53	in	in	ADP
ejpam-5175	91	54	c∗	c∗	PROPN
ejpam-5175	91	55	still	still	ADV
ejpam-5175	91	56	give	give	VERB
ejpam-5175	91	57	the	the	DET
ejpam-5175	91	58	three	three	NUM
ejpam-5175	91	59	representations	representation	NOUN
ejpam-5175	91	60	above	above	ADV
ejpam-5175	91	61	.	.	PUNCT
ejpam-5175	92	1	the	the	DET
ejpam-5175	92	2	four	four	NUM
ejpam-5175	92	3	representations	representation	NOUN
ejpam-5175	92	4	thus	thus	ADV
ejpam-5175	92	5	found	find	VERB
ejpam-5175	92	6	are	be	AUX
ejpam-5175	92	7	not	not	PART
ejpam-5175	92	8	isomorphic	isomorphic	ADJ
ejpam-5175	92	9	with	with	ADP
ejpam-5175	92	10	each	each	DET
ejpam-5175	92	11	other	other	ADJ
ejpam-5175	92	12	.	.	PUNCT
ejpam-5175	93	1	3.2.2	3.2.2	NUM
ejpam-5175	93	2	.	.	PUNCT
ejpam-5175	94	1	realization	realization	NOUN
ejpam-5175	94	2	of	of	ADP
ejpam-5175	94	3	the	the	DET
ejpam-5175	94	4	irreducible	irreducible	ADJ
ejpam-5175	94	5	representation	representation	NOUN
ejpam-5175	94	6	of	of	ADP
ejpam-5175	94	7	degree	degree	NOUN
ejpam-5175	94	8	2	2	NUM
ejpam-5175	94	9	q8	q8	PROPN
ejpam-5175	94	10	operates	operate	VERB
ejpam-5175	94	11	by	by	ADP
ejpam-5175	94	12	left	left	ADJ
ejpam-5175	94	13	multiplication	multiplication	NOUN
ejpam-5175	94	14	on	on	ADP
ejpam-5175	94	15	the	the	DET
ejpam-5175	94	16	space	space	NOUN
ejpam-5175	94	17	h	h	NOUN
ejpam-5175	94	18	of	of	ADP
ejpam-5175	94	19	quaternions	quaternion	NOUN
ejpam-5175	94	20	,	,	PUNCT
ejpam-5175	94	21	which	which	PRON
ejpam-5175	94	22	is	be	AUX
ejpam-5175	94	23	a	a	DET
ejpam-5175	94	24	vector	vector	NOUN
ejpam-5175	94	25	space	space	NOUN
ejpam-5175	94	26	on	on	ADP
ejpam-5175	94	27	the	the	DET
ejpam-5175	94	28	right	right	NOUN
ejpam-5175	94	29	on	on	ADP
ejpam-5175	94	30	c	c	NOUN
ejpam-5175	94	31	=	=	SYM
ejpam-5175	94	32	r	r	PROPN
ejpam-5175	94	33	⊕	⊕	PROPN
ejpam-5175	94	34	ri	ri	PROPN
ejpam-5175	94	35	,	,	PUNCT
ejpam-5175	94	36	of	of	ADP
ejpam-5175	94	37	dimension	dimension	NOUN
ejpam-5175	94	38	2	2	NUM
ejpam-5175	94	39	.	.	PUNCT
ejpam-5175	95	1	in	in	ADP
ejpam-5175	95	2	the	the	DET
ejpam-5175	95	3	basis	basis	NOUN
ejpam-5175	95	4	{	{	PUNCT
ejpam-5175	95	5	1	1	NUM
ejpam-5175	95	6	,	,	PUNCT
ejpam-5175	95	7	j	j	PROPN
ejpam-5175	95	8	}	}	PUNCT
ejpam-5175	95	9	,	,	PUNCT
ejpam-5175	95	10	we	we	PRON
ejpam-5175	95	11	obtain	obtain	VERB
ejpam-5175	95	12	the	the	DET
ejpam-5175	95	13	following	follow	VERB
ejpam-5175	95	14	matrix	matrix	NOUN
ejpam-5175	95	15	representation	representation	NOUN
ejpam-5175	95	16	:	:	PUNCT
ejpam-5175	95	17	τ5(±1	τ5(±1	X
ejpam-5175	95	18	)	)	PUNCT
ejpam-5175	96	1	=	=	SYM
ejpam-5175	96	2	±	±	NOUN
ejpam-5175	96	3	(	(	PUNCT
ejpam-5175	96	4	1	1	NUM
ejpam-5175	96	5	0	0	NUM
ejpam-5175	96	6	0	0	NUM
ejpam-5175	96	7	1	1	NUM
ejpam-5175	96	8	)	)	PUNCT
ejpam-5175	96	9	τ5(±i	τ5(±i	NOUN
ejpam-5175	96	10	)	)	PUNCT
ejpam-5175	96	11	=	=	SYM
ejpam-5175	96	12	±	±	NOUN
ejpam-5175	96	13	(	(	PUNCT
ejpam-5175	96	14	i	i	NOUN
ejpam-5175	96	15	0	0	NUM
ejpam-5175	96	16	0	0	NUM
ejpam-5175	96	17	−i	−i	NOUN
ejpam-5175	96	18	)	)	PUNCT
ejpam-5175	96	19	τ5(±j	τ5(±j	NOUN
ejpam-5175	96	20	)	)	PUNCT
ejpam-5175	96	21	=	=	SYM
ejpam-5175	96	22	±	±	NOUN
ejpam-5175	96	23	(	(	PUNCT
ejpam-5175	96	24	0	0	NUM
ejpam-5175	96	25	−1	−1	NOUN
ejpam-5175	96	26	1	1	NUM
ejpam-5175	96	27	0	0	NUM
ejpam-5175	96	28	)	)	PUNCT
ejpam-5175	96	29	τ5(±k	τ5(±k	NOUN
ejpam-5175	96	30	)	)	PUNCT
ejpam-5175	96	31	=	=	SYM
ejpam-5175	96	32	±	±	NOUN
ejpam-5175	96	33	(	(	PUNCT
ejpam-5175	96	34	0	0	NUM
ejpam-5175	96	35	−i	−i	ADJ
ejpam-5175	96	36	−i	−i	NOUN
ejpam-5175	96	37	0	0	NUM
ejpam-5175	96	38	)	)	PUNCT
ejpam-5175	96	39	a.	a.	NOUN
ejpam-5175	96	40	labsir	labsir	PROPN
ejpam-5175	96	41	,	,	PUNCT
ejpam-5175	96	42	e.	e.	PROPN
ejpam-5175	96	43	fanich	fanich	PROPN
ejpam-5175	96	44	/	/	SYM
ejpam-5175	96	45	eur	eur	PROPN
ejpam-5175	96	46	.	.	PUNCT
ejpam-5175	97	1	j.	j.	PROPN
ejpam-5175	97	2	pure	pure	PROPN
ejpam-5175	97	3	appl	appl	PROPN
ejpam-5175	97	4	.	.	PROPN
ejpam-5175	97	5	math	math	PROPN
ejpam-5175	97	6	,	,	PUNCT
ejpam-5175	97	7	17	17	NUM
ejpam-5175	97	8	(	(	PUNCT
ejpam-5175	97	9	3	3	NUM
ejpam-5175	97	10	)	)	PUNCT
ejpam-5175	97	11	(	(	PUNCT
ejpam-5175	97	12	2024	2024	NUM
ejpam-5175	97	13	)	)	PUNCT
ejpam-5175	97	14	,	,	PUNCT
ejpam-5175	97	15	1717	1717	NUM
ejpam-5175	97	16	-	-	SYM
ejpam-5175	97	17	1726	1726	NUM
ejpam-5175	97	18	1723	1723	NUM
ejpam-5175	97	19	3.3	3.3	NUM
ejpam-5175	97	20	.	.	PUNCT
ejpam-5175	98	1	some	some	DET
ejpam-5175	98	2	representations	representation	NOUN
ejpam-5175	98	3	of	of	ADP
ejpam-5175	98	4	the	the	DET
ejpam-5175	98	5	group	group	NOUN
ejpam-5175	98	6	q8	q8	PROPN
ejpam-5175	98	7	we	we	PRON
ejpam-5175	98	8	know	know	VERB
ejpam-5175	98	9	that	that	SCONJ
ejpam-5175	98	10	any	any	DET
ejpam-5175	98	11	representation	representation	NOUN
ejpam-5175	98	12	is	be	AUX
ejpam-5175	98	13	the	the	DET
ejpam-5175	98	14	sum	sum	NOUN
ejpam-5175	98	15	of	of	ADP
ejpam-5175	98	16	irreducible	irreducible	ADJ
ejpam-5175	98	17	representations	representation	NOUN
ejpam-5175	98	18	,	,	PUNCT
ejpam-5175	98	19	therefore	therefore	ADV
ejpam-5175	98	20	,	,	PUNCT
ejpam-5175	98	21	from	from	ADP
ejpam-5175	98	22	these	these	PRON
ejpam-5175	98	23	we	we	PRON
ejpam-5175	98	24	can	can	AUX
ejpam-5175	98	25	construct	construct	VERB
ejpam-5175	98	26	the	the	DET
ejpam-5175	98	27	desired	desire	VERB
ejpam-5175	98	28	representations	representation	NOUN
ejpam-5175	98	29	.	.	PUNCT
ejpam-5175	99	1	3.3.1	3.3.1	X
ejpam-5175	99	2	.	.	PUNCT
ejpam-5175	100	1	the	the	DET
ejpam-5175	100	2	regular	regular	ADJ
ejpam-5175	100	3	representation	representation	NOUN
ejpam-5175	100	4	of	of	ADP
ejpam-5175	100	5	q8	q8	PROPN
ejpam-5175	100	6	we	we	PRON
ejpam-5175	100	7	have	have	VERB
ejpam-5175	100	8	|q8|	|q8|	ADJ
ejpam-5175	100	9	=	=	SYM
ejpam-5175	100	10	8	8	NUM
ejpam-5175	100	11	,	,	PUNCT
ejpam-5175	100	12	therefore	therefore	ADV
ejpam-5175	100	13	the	the	DET
ejpam-5175	100	14	degree	degree	NOUN
ejpam-5175	100	15	of	of	ADP
ejpam-5175	100	16	the	the	DET
ejpam-5175	100	17	regular	regular	ADJ
ejpam-5175	100	18	representation	representation	NOUN
ejpam-5175	100	19	equal	equal	ADJ
ejpam-5175	100	20	to	to	ADP
ejpam-5175	100	21	8	8	NUM
ejpam-5175	100	22	,	,	PUNCT
ejpam-5175	100	23	and	and	CCONJ
ejpam-5175	100	24	we	we	PRON
ejpam-5175	100	25	know	know	VERB
ejpam-5175	100	26	that	that	SCONJ
ejpam-5175	100	27	every	every	DET
ejpam-5175	100	28	irreducible	irreducible	ADJ
ejpam-5175	100	29	representation	representation	NOUN
ejpam-5175	100	30	is	be	AUX
ejpam-5175	100	31	contained	contain	VERB
ejpam-5175	100	32	in	in	ADP
ejpam-5175	100	33	the	the	DET
ejpam-5175	100	34	regular	regular	ADJ
ejpam-5175	100	35	representation	representation	NOUN
ejpam-5175	100	36	a	a	DET
ejpam-5175	100	37	number	number	NOUN
ejpam-5175	100	38	of	of	ADP
ejpam-5175	100	39	times	time	NOUN
ejpam-5175	100	40	equal	equal	ADJ
ejpam-5175	100	41	to	to	ADP
ejpam-5175	100	42	its	its	PRON
ejpam-5175	100	43	degree	degree	NOUN
ejpam-5175	100	44	,	,	PUNCT
ejpam-5175	100	45	therefore	therefore	ADV
ejpam-5175	100	46	:	:	PUNCT
ejpam-5175	100	47	τreg	τreg	NOUN
ejpam-5175	100	48	=	=	SYM
ejpam-5175	101	1	τ1	τ1	PROPN
ejpam-5175	101	2	⊕	⊕	PROPN
ejpam-5175	101	3	τ2	τ2	PROPN
ejpam-5175	101	4	⊕	⊕	PROPN
ejpam-5175	101	5	τ3	τ3	PROPN
ejpam-5175	101	6	⊕	⊕	PROPN
ejpam-5175	101	7	τ4	τ4	PROPN
ejpam-5175	101	8	⊕	⊕	PROPN
ejpam-5175	101	9	2τ5	2τ5	NUM
ejpam-5175	102	1	so	so	ADV
ejpam-5175	102	2	:	:	PUNCT
ejpam-5175	102	3	τreg	τreg	NOUN
ejpam-5175	102	4	:	:	PUNCT
ejpam-5175	102	5	q8	q8	PROPN
ejpam-5175	102	6	→	→	SYM
ejpam-5175	102	7	gl8(c	gl8(c	PROPN
ejpam-5175	102	8	)	)	PUNCT
ejpam-5175	102	9	defined	define	VERB
ejpam-5175	102	10	by	by	ADP
ejpam-5175	102	11	:	:	PUNCT
ejpam-5175	102	12	τreg(1	τreg(1	ADJ
ejpam-5175	102	13	)	)	PUNCT
ejpam-5175	103	1	=	=	PUNCT
ejpam-5175	103	2			NOUN
ejpam-5175	103	3	1	1	NUM
ejpam-5175	103	4	0	0	NUM
ejpam-5175	103	5	0	0	NUM
ejpam-5175	103	6	0	0	NUM
ejpam-5175	103	7	0	0	NUM
ejpam-5175	103	8	0	0	NUM
ejpam-5175	103	9	0	0	NUM
ejpam-5175	103	10	0	0	NUM
ejpam-5175	103	11	0	0	NUM
ejpam-5175	103	12	1	1	NUM
ejpam-5175	103	13	0	0	NUM
ejpam-5175	103	14	0	0	NUM
ejpam-5175	103	15	0	0	NUM
ejpam-5175	103	16	0	0	NUM
ejpam-5175	103	17	0	0	NUM
ejpam-5175	103	18	0	0	NUM
ejpam-5175	103	19	0	0	NUM
ejpam-5175	103	20	0	0	NUM
ejpam-5175	103	21	1	1	NUM
ejpam-5175	103	22	0	0	NUM
ejpam-5175	103	23	0	0	NUM
ejpam-5175	103	24	0	0	NUM
ejpam-5175	103	25	0	0	NUM
ejpam-5175	103	26	0	0	NUM
ejpam-5175	103	27	0	0	NUM
ejpam-5175	103	28	0	0	NUM
ejpam-5175	103	29	0	0	NUM
ejpam-5175	103	30	1	1	NUM
ejpam-5175	103	31	0	0	NUM
ejpam-5175	103	32	0	0	NUM
ejpam-5175	103	33	0	0	NUM
ejpam-5175	103	34	0	0	NUM
ejpam-5175	103	35	0	0	NUM
ejpam-5175	103	36	0	0	NUM
ejpam-5175	103	37	0	0	NUM
ejpam-5175	103	38	0	0	NUM
ejpam-5175	103	39	1	1	NUM
ejpam-5175	103	40	0	0	NUM
ejpam-5175	103	41	0	0	NUM
ejpam-5175	103	42	0	0	NUM
ejpam-5175	103	43	0	0	NUM
ejpam-5175	103	44	0	0	NUM
ejpam-5175	103	45	0	0	NUM
ejpam-5175	103	46	0	0	NUM
ejpam-5175	103	47	0	0	NUM
ejpam-5175	103	48	1	1	NUM
ejpam-5175	103	49	0	0	NUM
ejpam-5175	103	50	0	0	NUM
ejpam-5175	103	51	0	0	NUM
ejpam-5175	103	52	0	0	NUM
ejpam-5175	103	53	0	0	NUM
ejpam-5175	103	54	0	0	NUM
ejpam-5175	103	55	0	0	NUM
ejpam-5175	103	56	0	0	NUM
ejpam-5175	103	57	1	1	NUM
ejpam-5175	103	58	0	0	NUM
ejpam-5175	103	59	0	0	NUM
ejpam-5175	103	60	0	0	NUM
ejpam-5175	103	61	0	0	NUM
ejpam-5175	103	62	0	0	NUM
ejpam-5175	103	63	0	0	NUM
ejpam-5175	103	64	0	0	NUM
ejpam-5175	103	65	0	0	NUM
ejpam-5175	103	66	1	1	NUM
ejpam-5175	103	67			NOUN
ejpam-5175	103	68	τreg(−1	τreg(−1	NOUN
ejpam-5175	103	69	)	)	PUNCT
ejpam-5175	103	70	=	=	PUNCT
ejpam-5175	103	71			ADJ
ejpam-5175	103	72	1	1	NUM
ejpam-5175	103	73	0	0	NUM
ejpam-5175	103	74	0	0	NUM
ejpam-5175	103	75	0	0	NUM
ejpam-5175	103	76	0	0	NUM
ejpam-5175	103	77	0	0	NUM
ejpam-5175	103	78	0	0	NUM
ejpam-5175	103	79	0	0	NUM
ejpam-5175	103	80	0	0	NUM
ejpam-5175	103	81	1	1	NUM
ejpam-5175	103	82	0	0	NUM
ejpam-5175	103	83	0	0	NUM
ejpam-5175	103	84	0	0	NUM
ejpam-5175	103	85	0	0	NUM
ejpam-5175	103	86	0	0	NUM
ejpam-5175	103	87	0	0	NUM
ejpam-5175	103	88	0	0	NUM
ejpam-5175	103	89	0	0	NUM
ejpam-5175	103	90	1	1	NUM
ejpam-5175	103	91	0	0	NUM
ejpam-5175	103	92	0	0	NUM
ejpam-5175	103	93	0	0	NUM
ejpam-5175	103	94	0	0	NUM
ejpam-5175	103	95	0	0	NUM
ejpam-5175	103	96	0	0	NUM
ejpam-5175	103	97	0	0	NUM
ejpam-5175	103	98	0	0	NUM
ejpam-5175	103	99	1	1	NUM
ejpam-5175	103	100	0	0	NUM
ejpam-5175	103	101	0	0	NUM
ejpam-5175	103	102	0	0	NUM
ejpam-5175	103	103	0	0	NUM
ejpam-5175	103	104	0	0	NUM
ejpam-5175	103	105	0	0	NUM
ejpam-5175	103	106	0	0	NUM
ejpam-5175	103	107	0	0	NUM
ejpam-5175	103	108	−1	−1	NOUN
ejpam-5175	103	109	0	0	NUM
ejpam-5175	103	110	0	0	NUM
ejpam-5175	103	111	0	0	NUM
ejpam-5175	103	112	0	0	NUM
ejpam-5175	103	113	0	0	NUM
ejpam-5175	103	114	0	0	NUM
ejpam-5175	103	115	0	0	NUM
ejpam-5175	103	116	0	0	NUM
ejpam-5175	103	117	−1	−1	NOUN
ejpam-5175	103	118	0	0	NUM
ejpam-5175	103	119	0	0	NUM
ejpam-5175	103	120	0	0	NUM
ejpam-5175	103	121	0	0	NUM
ejpam-5175	103	122	0	0	NUM
ejpam-5175	103	123	0	0	NUM
ejpam-5175	103	124	0	0	NUM
ejpam-5175	103	125	0	0	NUM
ejpam-5175	103	126	−1	−1	NOUN
ejpam-5175	103	127	0	0	NUM
ejpam-5175	103	128	0	0	NUM
ejpam-5175	103	129	0	0	NUM
ejpam-5175	103	130	0	0	NUM
ejpam-5175	103	131	0	0	NUM
ejpam-5175	103	132	0	0	NUM
ejpam-5175	103	133	0	0	NUM
ejpam-5175	103	134	0	0	NUM
ejpam-5175	103	135	−1	−1	NOUN
ejpam-5175	103	136			PUNCT
ejpam-5175	103	137	τreg(i	τreg(i	PROPN
ejpam-5175	103	138	)	)	PUNCT
ejpam-5175	103	139	=	=	PUNCT
ejpam-5175	103	140			NOUN
ejpam-5175	103	141	1	1	NUM
ejpam-5175	103	142	0	0	NUM
ejpam-5175	103	143	0	0	NUM
ejpam-5175	103	144	0	0	NUM
ejpam-5175	103	145	0	0	NUM
ejpam-5175	103	146	0	0	NUM
ejpam-5175	103	147	0	0	NUM
ejpam-5175	103	148	0	0	NUM
ejpam-5175	103	149	0	0	NUM
ejpam-5175	103	150	1	1	NUM
ejpam-5175	103	151	0	0	NUM
ejpam-5175	103	152	0	0	NUM
ejpam-5175	103	153	0	0	NUM
ejpam-5175	103	154	0	0	NUM
ejpam-5175	103	155	0	0	NUM
ejpam-5175	103	156	0	0	NUM
ejpam-5175	103	157	0	0	NUM
ejpam-5175	103	158	0	0	NUM
ejpam-5175	103	159	−1	−1	NOUN
ejpam-5175	103	160	0	0	NUM
ejpam-5175	103	161	0	0	NUM
ejpam-5175	103	162	0	0	NUM
ejpam-5175	103	163	0	0	NUM
ejpam-5175	103	164	0	0	NUM
ejpam-5175	103	165	0	0	NUM
ejpam-5175	103	166	0	0	NUM
ejpam-5175	103	167	0	0	NUM
ejpam-5175	103	168	−1	−1	NOUN
ejpam-5175	103	169	0	0	NUM
ejpam-5175	103	170	0	0	NUM
ejpam-5175	103	171	0	0	NUM
ejpam-5175	103	172	0	0	NUM
ejpam-5175	103	173	0	0	NUM
ejpam-5175	103	174	0	0	NUM
ejpam-5175	103	175	0	0	NUM
ejpam-5175	103	176	0	0	NUM
ejpam-5175	104	1	i	i	NOUN
ejpam-5175	104	2	0	0	NUM
ejpam-5175	104	3	0	0	NUM
ejpam-5175	104	4	0	0	NUM
ejpam-5175	104	5	0	0	NUM
ejpam-5175	104	6	0	0	NUM
ejpam-5175	104	7	0	0	NUM
ejpam-5175	104	8	0	0	NUM
ejpam-5175	104	9	0	0	NUM
ejpam-5175	105	1	−i	−i	NOUN
ejpam-5175	105	2	0	0	NUM
ejpam-5175	105	3	0	0	NUM
ejpam-5175	105	4	0	0	NUM
ejpam-5175	105	5	0	0	NUM
ejpam-5175	105	6	0	0	NUM
ejpam-5175	105	7	0	0	NUM
ejpam-5175	105	8	0	0	NUM
ejpam-5175	105	9	0	0	NUM
ejpam-5175	106	1	i	i	NOUN
ejpam-5175	106	2	0	0	NUM
ejpam-5175	106	3	0	0	NUM
ejpam-5175	106	4	0	0	NUM
ejpam-5175	106	5	0	0	NUM
ejpam-5175	106	6	0	0	NUM
ejpam-5175	106	7	0	0	NUM
ejpam-5175	106	8	0	0	NUM
ejpam-5175	106	9	0	0	NUM
ejpam-5175	106	10	−i	−i	ADJ
ejpam-5175	106	11			PROPN
ejpam-5175	106	12	a.	a.	NOUN
ejpam-5175	106	13	labsir	labsir	PROPN
ejpam-5175	106	14	,	,	PUNCT
ejpam-5175	106	15	e.	e.	PROPN
ejpam-5175	106	16	fanich	fanich	PROPN
ejpam-5175	106	17	/	/	SYM
ejpam-5175	106	18	eur	eur	PROPN
ejpam-5175	106	19	.	.	PUNCT
ejpam-5175	107	1	j.	j.	PROPN
ejpam-5175	107	2	pure	pure	PROPN
ejpam-5175	107	3	appl	appl	PROPN
ejpam-5175	107	4	.	.	PROPN
ejpam-5175	107	5	math	math	PROPN
ejpam-5175	107	6	,	,	PUNCT
ejpam-5175	107	7	17	17	NUM
ejpam-5175	107	8	(	(	PUNCT
ejpam-5175	107	9	3	3	NUM
ejpam-5175	107	10	)	)	PUNCT
ejpam-5175	107	11	(	(	PUNCT
ejpam-5175	107	12	2024	2024	NUM
ejpam-5175	107	13	)	)	PUNCT
ejpam-5175	107	14	,	,	PUNCT
ejpam-5175	107	15	1717	1717	NUM
ejpam-5175	107	16	-	-	SYM
ejpam-5175	107	17	1726	1726	NUM
ejpam-5175	107	18	1724	1724	NUM
ejpam-5175	107	19	τreg(−i	τreg(−i	NOUN
ejpam-5175	107	20	)	)	PUNCT
ejpam-5175	107	21	=	=	PUNCT
ejpam-5175	108	1			ADJ
ejpam-5175	108	2	1	1	NUM
ejpam-5175	108	3	0	0	NUM
ejpam-5175	108	4	0	0	NUM
ejpam-5175	108	5	0	0	NUM
ejpam-5175	108	6	0	0	NUM
ejpam-5175	108	7	0	0	NUM
ejpam-5175	108	8	0	0	NUM
ejpam-5175	108	9	0	0	NUM
ejpam-5175	108	10	0	0	NUM
ejpam-5175	108	11	1	1	NUM
ejpam-5175	108	12	0	0	NUM
ejpam-5175	108	13	0	0	NUM
ejpam-5175	108	14	0	0	NUM
ejpam-5175	108	15	0	0	NUM
ejpam-5175	108	16	0	0	NUM
ejpam-5175	108	17	0	0	NUM
ejpam-5175	108	18	0	0	NUM
ejpam-5175	108	19	0	0	NUM
ejpam-5175	108	20	−1	−1	NOUN
ejpam-5175	108	21	0	0	NUM
ejpam-5175	108	22	0	0	NUM
ejpam-5175	108	23	0	0	NUM
ejpam-5175	108	24	0	0	NUM
ejpam-5175	108	25	0	0	NUM
ejpam-5175	108	26	0	0	NUM
ejpam-5175	108	27	0	0	NUM
ejpam-5175	108	28	0	0	NUM
ejpam-5175	108	29	−1	−1	NOUN
ejpam-5175	108	30	0	0	NUM
ejpam-5175	108	31	0	0	NUM
ejpam-5175	108	32	0	0	NUM
ejpam-5175	108	33	0	0	NUM
ejpam-5175	108	34	0	0	NUM
ejpam-5175	108	35	0	0	NUM
ejpam-5175	108	36	0	0	NUM
ejpam-5175	108	37	0	0	NUM
ejpam-5175	109	1	−i	−i	NOUN
ejpam-5175	109	2	0	0	NUM
ejpam-5175	109	3	0	0	NUM
ejpam-5175	109	4	0	0	NUM
ejpam-5175	109	5	0	0	NUM
ejpam-5175	109	6	0	0	NUM
ejpam-5175	109	7	0	0	NUM
ejpam-5175	109	8	0	0	NUM
ejpam-5175	109	9	0	0	NUM
ejpam-5175	110	1	i	i	NOUN
ejpam-5175	110	2	0	0	NUM
ejpam-5175	110	3	0	0	NUM
ejpam-5175	110	4	0	0	NUM
ejpam-5175	110	5	0	0	NUM
ejpam-5175	110	6	0	0	NUM
ejpam-5175	110	7	0	0	NUM
ejpam-5175	110	8	0	0	NUM
ejpam-5175	110	9	0	0	NUM
ejpam-5175	111	1	−i	−i	NOUN
ejpam-5175	111	2	0	0	NUM
ejpam-5175	111	3	0	0	NUM
ejpam-5175	111	4	0	0	NUM
ejpam-5175	111	5	0	0	NUM
ejpam-5175	111	6	0	0	NUM
ejpam-5175	111	7	0	0	NUM
ejpam-5175	111	8	0	0	NUM
ejpam-5175	111	9	0	0	NUM
ejpam-5175	112	1	i	i	PRON
ejpam-5175	112	2			NOUN
ejpam-5175	112	3	τreg(j	τreg(j	NOUN
ejpam-5175	112	4	)	)	PUNCT
ejpam-5175	112	5	=	=	PUNCT
ejpam-5175	112	6			NOUN
ejpam-5175	112	7	1	1	NUM
ejpam-5175	112	8	0	0	NUM
ejpam-5175	112	9	0	0	NUM
ejpam-5175	112	10	0	0	NUM
ejpam-5175	112	11	0	0	NUM
ejpam-5175	112	12	0	0	NUM
ejpam-5175	112	13	0	0	NUM
ejpam-5175	112	14	0	0	NUM
ejpam-5175	112	15	0	0	NUM
ejpam-5175	112	16	−1	−1	NOUN
ejpam-5175	112	17	0	0	NUM
ejpam-5175	112	18	0	0	NUM
ejpam-5175	112	19	0	0	NUM
ejpam-5175	112	20	0	0	NUM
ejpam-5175	112	21	0	0	NUM
ejpam-5175	112	22	0	0	NUM
ejpam-5175	112	23	0	0	NUM
ejpam-5175	112	24	0	0	NUM
ejpam-5175	112	25	1	1	NUM
ejpam-5175	112	26	0	0	NUM
ejpam-5175	112	27	0	0	NUM
ejpam-5175	112	28	0	0	NUM
ejpam-5175	112	29	0	0	NUM
ejpam-5175	112	30	0	0	NUM
ejpam-5175	112	31	0	0	NUM
ejpam-5175	112	32	0	0	NUM
ejpam-5175	112	33	0	0	NUM
ejpam-5175	112	34	−1	−1	NOUN
ejpam-5175	112	35	0	0	NUM
ejpam-5175	112	36	0	0	NUM
ejpam-5175	112	37	0	0	NUM
ejpam-5175	112	38	0	0	NUM
ejpam-5175	112	39	0	0	NUM
ejpam-5175	112	40	0	0	NUM
ejpam-5175	112	41	0	0	NUM
ejpam-5175	112	42	0	0	NUM
ejpam-5175	112	43	0	0	NUM
ejpam-5175	112	44	−1	−1	NOUN
ejpam-5175	112	45	0	0	NUM
ejpam-5175	112	46	0	0	NUM
ejpam-5175	112	47	0	0	NUM
ejpam-5175	112	48	0	0	NUM
ejpam-5175	112	49	0	0	NUM
ejpam-5175	112	50	0	0	NUM
ejpam-5175	112	51	1	1	NUM
ejpam-5175	112	52	0	0	NUM
ejpam-5175	112	53	0	0	NUM
ejpam-5175	112	54	0	0	NUM
ejpam-5175	112	55	0	0	NUM
ejpam-5175	112	56	0	0	NUM
ejpam-5175	112	57	0	0	NUM
ejpam-5175	112	58	0	0	NUM
ejpam-5175	112	59	0	0	NUM
ejpam-5175	112	60	0	0	NUM
ejpam-5175	112	61	0	0	NUM
ejpam-5175	112	62	−1	−1	NOUN
ejpam-5175	112	63	0	0	NUM
ejpam-5175	112	64	0	0	NUM
ejpam-5175	112	65	0	0	NUM
ejpam-5175	112	66	0	0	NUM
ejpam-5175	112	67	0	0	NUM
ejpam-5175	112	68	0	0	NUM
ejpam-5175	112	69	1	1	NUM
ejpam-5175	112	70	0	0	NUM
ejpam-5175	112	71			NOUN
ejpam-5175	112	72	τreg(−j	τreg(−j	ADJ
ejpam-5175	112	73	)	)	PUNCT
ejpam-5175	113	1	=	=	PUNCT
ejpam-5175	113	2			ADJ
ejpam-5175	114	1	1	1	NUM
ejpam-5175	114	2	0	0	NUM
ejpam-5175	114	3	0	0	NUM
ejpam-5175	114	4	0	0	NUM
ejpam-5175	114	5	0	0	NUM
ejpam-5175	114	6	0	0	NUM
ejpam-5175	114	7	0	0	NUM
ejpam-5175	114	8	0	0	NUM
ejpam-5175	114	9	0	0	NUM
ejpam-5175	114	10	−1	−1	NOUN
ejpam-5175	114	11	0	0	NUM
ejpam-5175	114	12	0	0	NUM
ejpam-5175	114	13	0	0	NUM
ejpam-5175	114	14	0	0	NUM
ejpam-5175	114	15	0	0	NUM
ejpam-5175	114	16	0	0	NUM
ejpam-5175	114	17	0	0	NUM
ejpam-5175	114	18	0	0	NUM
ejpam-5175	114	19	1	1	NUM
ejpam-5175	114	20	0	0	NUM
ejpam-5175	114	21	0	0	NUM
ejpam-5175	114	22	0	0	NUM
ejpam-5175	114	23	0	0	NUM
ejpam-5175	114	24	0	0	NUM
ejpam-5175	114	25	0	0	NUM
ejpam-5175	114	26	0	0	NUM
ejpam-5175	114	27	0	0	NUM
ejpam-5175	114	28	−1	−1	NOUN
ejpam-5175	114	29	0	0	NUM
ejpam-5175	114	30	0	0	NUM
ejpam-5175	114	31	0	0	NUM
ejpam-5175	114	32	0	0	NUM
ejpam-5175	114	33	0	0	NUM
ejpam-5175	114	34	0	0	NUM
ejpam-5175	114	35	0	0	NUM
ejpam-5175	114	36	0	0	NUM
ejpam-5175	114	37	0	0	NUM
ejpam-5175	114	38	1	1	NUM
ejpam-5175	114	39	0	0	NUM
ejpam-5175	114	40	0	0	NUM
ejpam-5175	114	41	0	0	NUM
ejpam-5175	114	42	0	0	NUM
ejpam-5175	114	43	0	0	NUM
ejpam-5175	114	44	0	0	NUM
ejpam-5175	114	45	−1	−1	NOUN
ejpam-5175	114	46	0	0	NUM
ejpam-5175	114	47	0	0	NUM
ejpam-5175	114	48	0	0	NUM
ejpam-5175	114	49	0	0	NUM
ejpam-5175	114	50	0	0	NUM
ejpam-5175	114	51	0	0	NUM
ejpam-5175	114	52	0	0	NUM
ejpam-5175	114	53	0	0	NUM
ejpam-5175	114	54	0	0	NUM
ejpam-5175	114	55	0	0	NUM
ejpam-5175	114	56	1	1	NUM
ejpam-5175	114	57	0	0	NUM
ejpam-5175	114	58	0	0	NUM
ejpam-5175	114	59	0	0	NUM
ejpam-5175	114	60	0	0	NUM
ejpam-5175	114	61	0	0	NUM
ejpam-5175	114	62	0	0	NUM
ejpam-5175	114	63	−1	−1	NOUN
ejpam-5175	114	64	0	0	NUM
ejpam-5175	114	65			NOUN
ejpam-5175	114	66	τreg(k	τreg(k	NOUN
ejpam-5175	114	67	)	)	PUNCT
ejpam-5175	115	1	=	=	PUNCT
ejpam-5175	115	2			ADJ
ejpam-5175	116	1	1	1	NUM
ejpam-5175	116	2	0	0	NUM
ejpam-5175	116	3	0	0	NUM
ejpam-5175	116	4	0	0	NUM
ejpam-5175	116	5	0	0	NUM
ejpam-5175	116	6	0	0	NUM
ejpam-5175	116	7	0	0	NUM
ejpam-5175	116	8	0	0	NUM
ejpam-5175	116	9	0	0	NUM
ejpam-5175	116	10	−1	−1	NOUN
ejpam-5175	116	11	0	0	NUM
ejpam-5175	116	12	0	0	NUM
ejpam-5175	116	13	0	0	NUM
ejpam-5175	116	14	0	0	NUM
ejpam-5175	116	15	0	0	NUM
ejpam-5175	116	16	0	0	NUM
ejpam-5175	116	17	0	0	NUM
ejpam-5175	116	18	0	0	NUM
ejpam-5175	116	19	−1	−1	NOUN
ejpam-5175	116	20	0	0	NUM
ejpam-5175	116	21	0	0	NUM
ejpam-5175	116	22	0	0	NUM
ejpam-5175	116	23	0	0	NUM
ejpam-5175	116	24	0	0	NUM
ejpam-5175	116	25	0	0	NUM
ejpam-5175	116	26	0	0	NUM
ejpam-5175	116	27	0	0	NUM
ejpam-5175	116	28	1	1	NUM
ejpam-5175	116	29	0	0	NUM
ejpam-5175	116	30	0	0	NUM
ejpam-5175	116	31	0	0	NUM
ejpam-5175	116	32	0	0	NUM
ejpam-5175	116	33	0	0	NUM
ejpam-5175	116	34	0	0	NUM
ejpam-5175	116	35	0	0	NUM
ejpam-5175	116	36	0	0	NUM
ejpam-5175	116	37	0	0	NUM
ejpam-5175	117	1	−i	−i	NOUN
ejpam-5175	117	2	0	0	NUM
ejpam-5175	117	3	0	0	NUM
ejpam-5175	117	4	0	0	NUM
ejpam-5175	117	5	0	0	NUM
ejpam-5175	117	6	0	0	NUM
ejpam-5175	117	7	0	0	NUM
ejpam-5175	118	1	−i	−i	NOUN
ejpam-5175	118	2	0	0	NUM
ejpam-5175	118	3	0	0	NUM
ejpam-5175	118	4	0	0	NUM
ejpam-5175	118	5	0	0	NUM
ejpam-5175	118	6	0	0	NUM
ejpam-5175	118	7	0	0	NUM
ejpam-5175	118	8	0	0	NUM
ejpam-5175	118	9	0	0	NUM
ejpam-5175	118	10	0	0	NUM
ejpam-5175	118	11	0	0	NUM
ejpam-5175	119	1	−i	−i	NOUN
ejpam-5175	119	2	0	0	NUM
ejpam-5175	119	3	0	0	NUM
ejpam-5175	119	4	0	0	NUM
ejpam-5175	119	5	0	0	NUM
ejpam-5175	119	6	0	0	NUM
ejpam-5175	119	7	0	0	NUM
ejpam-5175	120	1	−i	−i	ADJ
ejpam-5175	120	2	0	0	NUM
ejpam-5175	121	1			NOUN
ejpam-5175	121	2	τreg(−k	τreg(−k	NOUN
ejpam-5175	121	3	)	)	PUNCT
ejpam-5175	121	4	=	=	PUNCT
ejpam-5175	122	1			NOUN
ejpam-5175	122	2	1	1	NUM
ejpam-5175	122	3	0	0	NUM
ejpam-5175	122	4	0	0	NUM
ejpam-5175	122	5	0	0	NUM
ejpam-5175	122	6	0	0	NUM
ejpam-5175	122	7	0	0	NUM
ejpam-5175	122	8	0	0	NUM
ejpam-5175	122	9	0	0	NUM
ejpam-5175	122	10	0	0	NUM
ejpam-5175	122	11	−1	−1	NOUN
ejpam-5175	122	12	0	0	NUM
ejpam-5175	122	13	0	0	NUM
ejpam-5175	122	14	0	0	NUM
ejpam-5175	122	15	0	0	NUM
ejpam-5175	122	16	0	0	NUM
ejpam-5175	122	17	0	0	NUM
ejpam-5175	122	18	0	0	NUM
ejpam-5175	122	19	0	0	NUM
ejpam-5175	122	20	−1	−1	NOUN
ejpam-5175	122	21	0	0	NUM
ejpam-5175	122	22	0	0	NUM
ejpam-5175	122	23	0	0	NUM
ejpam-5175	122	24	0	0	NUM
ejpam-5175	122	25	0	0	NUM
ejpam-5175	122	26	0	0	NUM
ejpam-5175	122	27	0	0	NUM
ejpam-5175	122	28	0	0	NUM
ejpam-5175	122	29	1	1	NUM
ejpam-5175	122	30	0	0	NUM
ejpam-5175	122	31	0	0	NUM
ejpam-5175	122	32	0	0	NUM
ejpam-5175	122	33	0	0	NUM
ejpam-5175	122	34	0	0	NUM
ejpam-5175	122	35	0	0	NUM
ejpam-5175	122	36	0	0	NUM
ejpam-5175	122	37	0	0	NUM
ejpam-5175	122	38	0	0	NUM
ejpam-5175	123	1	i	i	NOUN
ejpam-5175	123	2	0	0	NUM
ejpam-5175	123	3	0	0	NUM
ejpam-5175	123	4	0	0	NUM
ejpam-5175	123	5	0	0	NUM
ejpam-5175	123	6	0	0	NUM
ejpam-5175	123	7	0	0	NUM
ejpam-5175	124	1	i	i	NOUN
ejpam-5175	124	2	0	0	NUM
ejpam-5175	124	3	0	0	NUM
ejpam-5175	124	4	0	0	NUM
ejpam-5175	124	5	0	0	NUM
ejpam-5175	124	6	0	0	NUM
ejpam-5175	124	7	0	0	NUM
ejpam-5175	124	8	0	0	NUM
ejpam-5175	124	9	0	0	NUM
ejpam-5175	124	10	0	0	NUM
ejpam-5175	124	11	0	0	NUM
ejpam-5175	125	1	i	i	NOUN
ejpam-5175	125	2	0	0	NUM
ejpam-5175	125	3	0	0	NUM
ejpam-5175	125	4	0	0	NUM
ejpam-5175	125	5	0	0	NUM
ejpam-5175	125	6	0	0	NUM
ejpam-5175	125	7	0	0	NUM
ejpam-5175	126	1	i	i	NOUN
ejpam-5175	126	2	0	0	NUM
ejpam-5175	126	3			NOUN
ejpam-5175	126	4	references	reference	VERB
ejpam-5175	126	5	1725	1725	NUM
ejpam-5175	126	6	3.3.2	3.3.2	NUM
ejpam-5175	126	7	.	.	PUNCT
ejpam-5175	127	1	the	the	DET
ejpam-5175	127	2	representation	representation	NOUN
ejpam-5175	127	3	of	of	ADP
ejpam-5175	127	4	degree	degree	NOUN
ejpam-5175	127	5	6	6	NUM
ejpam-5175	127	6	of	of	ADP
ejpam-5175	127	7	q8	q8	PROPN
ejpam-5175	127	8	let	let	VERB
ejpam-5175	127	9	θ	θ	NOUN
ejpam-5175	127	10	be	be	AUX
ejpam-5175	127	11	the	the	DET
ejpam-5175	127	12	representation	representation	NOUN
ejpam-5175	127	13	of	of	ADP
ejpam-5175	127	14	degree	degree	NOUN
ejpam-5175	127	15	6	6	NUM
ejpam-5175	127	16	of	of	ADP
ejpam-5175	127	17	q8	q8	PROPN
ejpam-5175	127	18	,	,	PUNCT
ejpam-5175	127	19	then	then	ADV
ejpam-5175	127	20	:	:	PUNCT
ejpam-5175	127	21	θ	θ	PROPN
ejpam-5175	127	22	=	=	SYM
ejpam-5175	127	23	τ1	τ1	PROPN
ejpam-5175	127	24	⊕	⊕	PROPN
ejpam-5175	127	25	τ2	τ2	PROPN
ejpam-5175	127	26	⊕	⊕	PROPN
ejpam-5175	127	27	τ3	τ3	PROPN
ejpam-5175	127	28	⊕	⊕	PROPN
ejpam-5175	127	29	τ4	τ4	PROPN
ejpam-5175	127	30	⊕	⊕	PROPN
ejpam-5175	127	31	τ5	τ5	VERB
ejpam-5175	128	1	so	so	ADV
ejpam-5175	128	2	:	:	PUNCT
ejpam-5175	128	3	θ	θ	NOUN
ejpam-5175	128	4	:	:	PUNCT
ejpam-5175	128	5	q8	q8	PROPN
ejpam-5175	128	6	→	→	SYM
ejpam-5175	128	7	gl6(c	gl6(c	PROPN
ejpam-5175	128	8	)	)	PUNCT
ejpam-5175	128	9	defined	define	VERB
ejpam-5175	128	10	by	by	ADP
ejpam-5175	128	11	:	:	PUNCT
ejpam-5175	128	12	θ(1	θ(1	X
ejpam-5175	128	13	)	)	PUNCT
ejpam-5175	129	1	=	=	PRON
ejpam-5175	129	2			VERB
ejpam-5175	129	3	1	1	NUM
ejpam-5175	129	4	0	0	NUM
ejpam-5175	129	5	0	0	NUM
ejpam-5175	129	6	0	0	NUM
ejpam-5175	129	7	0	0	NUM
ejpam-5175	129	8	0	0	NUM
ejpam-5175	129	9	0	0	NUM
ejpam-5175	129	10	1	1	NUM
ejpam-5175	129	11	0	0	NUM
ejpam-5175	129	12	0	0	NUM
ejpam-5175	129	13	0	0	NUM
ejpam-5175	129	14	0	0	NUM
ejpam-5175	129	15	0	0	NUM
ejpam-5175	129	16	0	0	NUM
ejpam-5175	129	17	1	1	NUM
ejpam-5175	129	18	0	0	NUM
ejpam-5175	129	19	0	0	NUM
ejpam-5175	129	20	0	0	NUM
ejpam-5175	129	21	0	0	NUM
ejpam-5175	129	22	0	0	NUM
ejpam-5175	129	23	0	0	NUM
ejpam-5175	129	24	1	1	NUM
ejpam-5175	129	25	0	0	NUM
ejpam-5175	129	26	0	0	NUM
ejpam-5175	129	27	0	0	NUM
ejpam-5175	129	28	0	0	NUM
ejpam-5175	129	29	0	0	NUM
ejpam-5175	129	30	0	0	NUM
ejpam-5175	129	31	1	1	NUM
ejpam-5175	129	32	0	0	NUM
ejpam-5175	129	33	0	0	NUM
ejpam-5175	129	34	0	0	NUM
ejpam-5175	129	35	0	0	NUM
ejpam-5175	129	36	0	0	NUM
ejpam-5175	129	37	0	0	NUM
ejpam-5175	129	38	1	1	NUM
ejpam-5175	129	39			PROPN
ejpam-5175	129	40	;	;	PUNCT
ejpam-5175	129	41	θ(−1	θ(−1	X
ejpam-5175	129	42	)	)	PUNCT
ejpam-5175	130	1	=	=	PRON
ejpam-5175	130	2			VERB
ejpam-5175	130	3	1	1	NUM
ejpam-5175	130	4	0	0	NUM
ejpam-5175	130	5	0	0	NUM
ejpam-5175	130	6	0	0	NUM
ejpam-5175	130	7	0	0	NUM
ejpam-5175	130	8	0	0	NUM
ejpam-5175	130	9	0	0	NUM
ejpam-5175	130	10	1	1	NUM
ejpam-5175	130	11	0	0	NUM
ejpam-5175	130	12	0	0	NUM
ejpam-5175	130	13	0	0	NUM
ejpam-5175	130	14	0	0	NUM
ejpam-5175	130	15	0	0	NUM
ejpam-5175	130	16	0	0	NUM
ejpam-5175	130	17	1	1	NUM
ejpam-5175	130	18	0	0	NUM
ejpam-5175	130	19	0	0	NUM
ejpam-5175	130	20	0	0	NUM
ejpam-5175	130	21	0	0	NUM
ejpam-5175	130	22	0	0	NUM
ejpam-5175	130	23	0	0	NUM
ejpam-5175	130	24	1	1	NUM
ejpam-5175	130	25	0	0	NUM
ejpam-5175	130	26	0	0	NUM
ejpam-5175	130	27	0	0	NUM
ejpam-5175	130	28	0	0	NUM
ejpam-5175	130	29	0	0	NUM
ejpam-5175	130	30	0	0	NUM
ejpam-5175	130	31	−1	−1	NOUN
ejpam-5175	130	32	0	0	NUM
ejpam-5175	130	33	0	0	NUM
ejpam-5175	130	34	0	0	NUM
ejpam-5175	130	35	0	0	NUM
ejpam-5175	130	36	0	0	NUM
ejpam-5175	130	37	0	0	NUM
ejpam-5175	130	38	−1	−1	NOUN
ejpam-5175	130	39			SCONJ
ejpam-5175	130	40	θ(i	θ(i	X
ejpam-5175	130	41	)	)	PUNCT
ejpam-5175	130	42	=	=	PUNCT
ejpam-5175	130	43			VERB
ejpam-5175	130	44	1	1	NUM
ejpam-5175	130	45	0	0	NUM
ejpam-5175	130	46	0	0	NUM
ejpam-5175	130	47	0	0	NUM
ejpam-5175	130	48	0	0	NUM
ejpam-5175	130	49	0	0	NUM
ejpam-5175	130	50	0	0	NUM
ejpam-5175	130	51	1	1	NUM
ejpam-5175	130	52	0	0	NUM
ejpam-5175	130	53	0	0	NUM
ejpam-5175	130	54	0	0	NUM
ejpam-5175	130	55	0	0	NUM
ejpam-5175	130	56	0	0	NUM
ejpam-5175	130	57	0	0	NUM
ejpam-5175	130	58	−1	−1	NOUN
ejpam-5175	130	59	0	0	NUM
ejpam-5175	130	60	0	0	NUM
ejpam-5175	130	61	0	0	NUM
ejpam-5175	130	62	0	0	NUM
ejpam-5175	130	63	0	0	NUM
ejpam-5175	130	64	0	0	NUM
ejpam-5175	130	65	−1	−1	NOUN
ejpam-5175	130	66	0	0	NUM
ejpam-5175	130	67	0	0	NUM
ejpam-5175	130	68	0	0	NUM
ejpam-5175	130	69	0	0	NUM
ejpam-5175	130	70	0	0	NUM
ejpam-5175	130	71	0	0	NUM
ejpam-5175	131	1	i	i	NOUN
ejpam-5175	131	2	0	0	NUM
ejpam-5175	131	3	0	0	NUM
ejpam-5175	131	4	0	0	NUM
ejpam-5175	131	5	0	0	NUM
ejpam-5175	131	6	0	0	NUM
ejpam-5175	131	7	0	0	NUM
ejpam-5175	131	8	−i	−i	PROPN
ejpam-5175	131	9			PROPN
ejpam-5175	131	10	;	;	PUNCT
ejpam-5175	131	11	θ(−i	θ(−i	X
ejpam-5175	131	12	)	)	PUNCT
ejpam-5175	131	13	=	=	PRON
ejpam-5175	131	14			VERB
ejpam-5175	131	15	1	1	NUM
ejpam-5175	131	16	0	0	NUM
ejpam-5175	131	17	0	0	NUM
ejpam-5175	131	18	0	0	NUM
ejpam-5175	131	19	0	0	NUM
ejpam-5175	131	20	0	0	NUM
ejpam-5175	131	21	0	0	NUM
ejpam-5175	131	22	1	1	NUM
ejpam-5175	131	23	0	0	NUM
ejpam-5175	131	24	0	0	NUM
ejpam-5175	131	25	0	0	NUM
ejpam-5175	131	26	0	0	NUM
ejpam-5175	131	27	0	0	NUM
ejpam-5175	131	28	0	0	NUM
ejpam-5175	131	29	−1	−1	NOUN
ejpam-5175	131	30	0	0	NUM
ejpam-5175	131	31	0	0	NUM
ejpam-5175	131	32	0	0	NUM
ejpam-5175	131	33	0	0	NUM
ejpam-5175	131	34	0	0	NUM
ejpam-5175	131	35	0	0	NUM
ejpam-5175	131	36	−1	−1	NOUN
ejpam-5175	131	37	0	0	NUM
ejpam-5175	131	38	0	0	NUM
ejpam-5175	131	39	0	0	NUM
ejpam-5175	131	40	0	0	NUM
ejpam-5175	131	41	0	0	NUM
ejpam-5175	131	42	0	0	NUM
ejpam-5175	132	1	−i	−i	NOUN
ejpam-5175	132	2	0	0	NUM
ejpam-5175	132	3	0	0	NUM
ejpam-5175	132	4	0	0	NUM
ejpam-5175	132	5	0	0	NUM
ejpam-5175	132	6	0	0	NUM
ejpam-5175	132	7	0	0	NUM
ejpam-5175	133	1	i	i	PRON
ejpam-5175	133	2			SCONJ
ejpam-5175	133	3	θ(j	θ(j	NOUN
ejpam-5175	133	4	)	)	PUNCT
ejpam-5175	133	5	=	=	PRON
ejpam-5175	133	6			VERB
ejpam-5175	133	7	1	1	NUM
ejpam-5175	133	8	0	0	NUM
ejpam-5175	133	9	0	0	NUM
ejpam-5175	133	10	0	0	NUM
ejpam-5175	133	11	0	0	NUM
ejpam-5175	133	12	0	0	NUM
ejpam-5175	133	13	0	0	NUM
ejpam-5175	133	14	−1	−1	NOUN
ejpam-5175	133	15	0	0	NUM
ejpam-5175	133	16	0	0	NUM
ejpam-5175	133	17	0	0	NUM
ejpam-5175	133	18	0	0	NUM
ejpam-5175	133	19	0	0	NUM
ejpam-5175	133	20	0	0	NUM
ejpam-5175	133	21	1	1	NUM
ejpam-5175	133	22	0	0	NUM
ejpam-5175	133	23	0	0	NUM
ejpam-5175	133	24	0	0	NUM
ejpam-5175	133	25	0	0	NUM
ejpam-5175	133	26	0	0	NUM
ejpam-5175	133	27	0	0	NUM
ejpam-5175	133	28	−1	−1	NOUN
ejpam-5175	133	29	0	0	NUM
ejpam-5175	133	30	0	0	NUM
ejpam-5175	133	31	0	0	NUM
ejpam-5175	133	32	0	0	NUM
ejpam-5175	133	33	0	0	NUM
ejpam-5175	133	34	0	0	NUM
ejpam-5175	133	35	0	0	NUM
ejpam-5175	133	36	−1	−1	NOUN
ejpam-5175	133	37	0	0	NUM
ejpam-5175	133	38	0	0	NUM
ejpam-5175	133	39	0	0	NUM
ejpam-5175	133	40	0	0	NUM
ejpam-5175	133	41	1	1	NUM
ejpam-5175	133	42	0	0	NUM
ejpam-5175	133	43			ADP
ejpam-5175	133	44	;	;	PUNCT
ejpam-5175	133	45	θ(−j	θ(−j	X
ejpam-5175	133	46	)	)	PUNCT
ejpam-5175	133	47	=	=	SYM
ejpam-5175	133	48			VERB
ejpam-5175	133	49	1	1	NUM
ejpam-5175	133	50	0	0	NUM
ejpam-5175	133	51	0	0	NUM
ejpam-5175	133	52	0	0	NUM
ejpam-5175	133	53	0	0	NUM
ejpam-5175	133	54	0	0	NUM
ejpam-5175	133	55	0	0	NUM
ejpam-5175	133	56	−1	−1	NOUN
ejpam-5175	133	57	0	0	NUM
ejpam-5175	133	58	0	0	NUM
ejpam-5175	133	59	0	0	NUM
ejpam-5175	133	60	0	0	NUM
ejpam-5175	133	61	0	0	NUM
ejpam-5175	133	62	0	0	NUM
ejpam-5175	133	63	1	1	NUM
ejpam-5175	133	64	0	0	NUM
ejpam-5175	133	65	0	0	NUM
ejpam-5175	133	66	0	0	NUM
ejpam-5175	133	67	0	0	NUM
ejpam-5175	133	68	0	0	NUM
ejpam-5175	133	69	0	0	NUM
ejpam-5175	133	70	−1	−1	NOUN
ejpam-5175	133	71	0	0	NUM
ejpam-5175	133	72	0	0	NUM
ejpam-5175	133	73	0	0	NUM
ejpam-5175	133	74	0	0	NUM
ejpam-5175	133	75	0	0	NUM
ejpam-5175	133	76	0	0	NUM
ejpam-5175	133	77	0	0	NUM
ejpam-5175	133	78	1	1	NUM
ejpam-5175	133	79	0	0	NUM
ejpam-5175	133	80	0	0	NUM
ejpam-5175	133	81	0	0	NUM
ejpam-5175	133	82	0	0	NUM
ejpam-5175	133	83	−1	−1	NOUN
ejpam-5175	133	84	0	0	PUNCT
ejpam-5175	133	85			ADP
ejpam-5175	133	86	θ(k	θ(k	ADJ
ejpam-5175	133	87	)	)	PUNCT
ejpam-5175	133	88	=	=	PRON
ejpam-5175	133	89			VERB
ejpam-5175	133	90	1	1	NUM
ejpam-5175	133	91	0	0	NUM
ejpam-5175	133	92	0	0	NUM
ejpam-5175	133	93	0	0	NUM
ejpam-5175	133	94	0	0	NUM
ejpam-5175	133	95	0	0	NUM
ejpam-5175	133	96	0	0	NUM
ejpam-5175	133	97	−1	−1	NOUN
ejpam-5175	133	98	0	0	NUM
ejpam-5175	133	99	0	0	NUM
ejpam-5175	133	100	0	0	NUM
ejpam-5175	133	101	0	0	NUM
ejpam-5175	133	102	0	0	NUM
ejpam-5175	133	103	0	0	NUM
ejpam-5175	133	104	−1	−1	NOUN
ejpam-5175	134	1	0	0	NUM
ejpam-5175	134	2	0	0	NUM
ejpam-5175	134	3	0	0	NUM
ejpam-5175	134	4	0	0	NUM
ejpam-5175	134	5	0	0	NUM
ejpam-5175	134	6	0	0	NUM
ejpam-5175	134	7	1	1	NUM
ejpam-5175	134	8	0	0	NUM
ejpam-5175	134	9	0	0	NUM
ejpam-5175	134	10	0	0	NUM
ejpam-5175	134	11	0	0	NUM
ejpam-5175	134	12	0	0	NUM
ejpam-5175	134	13	0	0	NUM
ejpam-5175	134	14	0	0	NUM
ejpam-5175	135	1	−i	−i	NOUN
ejpam-5175	135	2	0	0	NUM
ejpam-5175	135	3	0	0	NUM
ejpam-5175	135	4	0	0	NUM
ejpam-5175	135	5	0	0	NUM
ejpam-5175	135	6	−i	−i	NOUN
ejpam-5175	135	7	0	0	NUM
ejpam-5175	136	1			ADP
ejpam-5175	136	2	;	;	PUNCT
ejpam-5175	136	3	θ(−k	θ(−k	NOUN
ejpam-5175	136	4	)	)	PUNCT
ejpam-5175	136	5	=	=	SYM
ejpam-5175	136	6			VERB
ejpam-5175	136	7	1	1	NUM
ejpam-5175	136	8	0	0	NUM
ejpam-5175	136	9	0	0	NUM
ejpam-5175	136	10	0	0	NUM
ejpam-5175	136	11	0	0	NUM
ejpam-5175	136	12	0	0	NUM
ejpam-5175	136	13	0	0	NUM
ejpam-5175	136	14	−1	−1	NOUN
ejpam-5175	136	15	0	0	NUM
ejpam-5175	136	16	0	0	NUM
ejpam-5175	136	17	0	0	NUM
ejpam-5175	136	18	0	0	NUM
ejpam-5175	136	19	0	0	NUM
ejpam-5175	136	20	0	0	NUM
ejpam-5175	136	21	−1	−1	NOUN
ejpam-5175	136	22	0	0	NUM
ejpam-5175	136	23	0	0	NUM
ejpam-5175	136	24	0	0	NUM
ejpam-5175	136	25	0	0	NUM
ejpam-5175	136	26	0	0	NUM
ejpam-5175	136	27	0	0	NUM
ejpam-5175	136	28	1	1	NUM
ejpam-5175	136	29	0	0	NUM
ejpam-5175	136	30	0	0	NUM
ejpam-5175	136	31	0	0	NUM
ejpam-5175	136	32	0	0	NUM
ejpam-5175	136	33	0	0	NUM
ejpam-5175	136	34	0	0	NUM
ejpam-5175	136	35	0	0	NUM
ejpam-5175	137	1	i	i	NOUN
ejpam-5175	137	2	0	0	NUM
ejpam-5175	137	3	0	0	NUM
ejpam-5175	137	4	0	0	NUM
ejpam-5175	137	5	0	0	NUM
ejpam-5175	138	1	i	i	NOUN
ejpam-5175	138	2	0	0	NUM
ejpam-5175	139	1			ADP
ejpam-5175	139	2	references	reference	NOUN
ejpam-5175	139	3	[	[	X
ejpam-5175	139	4	1	1	NUM
ejpam-5175	139	5	]	]	X
ejpam-5175	139	6	yvette	yvette	PROPN
ejpam-5175	139	7	kosmann	kosmann	PROPN
ejpam-5175	139	8	-	-	PUNCT
ejpam-5175	139	9	schwarzbach	schwarzbach	NOUN
ejpam-5175	139	10	.	.	PUNCT
ejpam-5175	140	1	groups	group	NOUN
ejpam-5175	140	2	and	and	CCONJ
ejpam-5175	140	3	symmetries	symmetry	NOUN
ejpam-5175	140	4	.	.	PUNCT
ejpam-5175	141	1	springer	springer	NOUN
ejpam-5175	141	2	science	science	PROPN
ejpam-5175	141	3	and	and	CCONJ
ejpam-5175	141	4	business	business	NOUN
ejpam-5175	141	5	media	medium	NOUN
ejpam-5175	141	6	,	,	PUNCT
ejpam-5175	141	7	2009	2009	NUM
ejpam-5175	141	8	.	.	PUNCT
ejpam-5175	142	1	[	[	X
ejpam-5175	142	2	2	2	NUM
ejpam-5175	142	3	]	]	X
ejpam-5175	142	4	david	david	PROPN
ejpam-5175	142	5	renard	renard	PROPN
ejpam-5175	142	6	.	.	PUNCT
ejpam-5175	143	1	groups	group	NOUN
ejpam-5175	143	2	and	and	CCONJ
ejpam-5175	143	3	representation	representation	NOUN
ejpam-5175	143	4	.	.	PUNCT
ejpam-5175	144	1	ecole	ecole	PROPN
ejpam-5175	144	2	polytechnique	polytechnique	PROPN
ejpam-5175	144	3	,	,	PUNCT
ejpam-5175	144	4	2010	2010	NUM
ejpam-5175	144	5	.	.	PUNCT
ejpam-5175	145	1	references	reference	NOUN
ejpam-5175	145	2	1726	1726	NUM
ejpam-5175	145	3	[	[	X
ejpam-5175	145	4	3	3	NUM
ejpam-5175	145	5	]	]	X
ejpam-5175	145	6	jean	jean	PROPN
ejpam-5175	145	7	-	-	PUNCT
ejpam-5175	145	8	pierre	pierre	PROPN
ejpam-5175	145	9	serre	serre	X
ejpam-5175	145	10	.	.	PUNCT
ejpam-5175	146	1	linear	linear	ADJ
ejpam-5175	146	2	representations	representation	NOUN
ejpam-5175	146	3	of	of	ADP
ejpam-5175	146	4	finite	finite	ADJ
ejpam-5175	146	5	groups	group	NOUN
ejpam-5175	146	6	.	.	PUNCT
ejpam-5175	147	1	herman	herman	PROPN
ejpam-5175	147	2	collections	collection	NOUN
ejpam-5175	147	3	methods	method	NOUN
ejpam-5175	147	4	,	,	PUNCT
ejpam-5175	147	5	paris	paris	PROPN
ejpam-5175	147	6	,	,	PUNCT
ejpam-5175	147	7	1998	1998	NUM
ejpam-5175	147	8	.	.	PUNCT
ejpam-5175	148	1	[	[	X
ejpam-5175	148	2	4	4	X
ejpam-5175	148	3	]	]	X
ejpam-5175	148	4	benjamin	benjamin	PROPN
ejpam-5175	148	5	steinberg	steinberg	PROPN
ejpam-5175	148	6	.	.	PUNCT
ejpam-5175	149	1	representation	representation	PROPN
ejpam-5175	149	2	theory	theory	NOUN
ejpam-5175	149	3	of	of	ADP
ejpam-5175	149	4	finite	finite	ADJ
ejpam-5175	149	5	groups	group	NOUN
ejpam-5175	149	6	an	an	DET
ejpam-5175	149	7	introductory	introductory	ADJ
ejpam-5175	149	8	approach	approach	NOUN
ejpam-5175	149	9	.	.	PUNCT
ejpam-5175	150	1	2011	2011	NUM
ejpam-5175	150	2	.	.	PUNCT
ejpam-5175	151	1	[	[	X
ejpam-5175	151	2	5	5	NUM
ejpam-5175	151	3	]	]	PUNCT
ejpam-5175	151	4	w.fulton	w.fulton	NOUN
ejpam-5175	151	5	and	and	CCONJ
ejpam-5175	151	6	j.harris	j.harris	NOUN
ejpam-5175	151	7	.	.	PUNCT
ejpam-5175	151	8	representation	representation	NOUN
ejpam-5175	151	9	theory	theory	NOUN
ejpam-5175	151	10	,	,	PUNCT
ejpam-5175	151	11	graduate	graduate	NOUN
ejpam-5175	151	12	text	text	NOUN
ejpam-5175	151	13	in	in	ADP
ejpam-5175	151	14	mathematics	mathematics	PROPN
ejpam-5175	151	15	.	.	PUNCT
ejpam-5175	152	1	springer	springer	PROPN
ejpam-5175	152	2	,	,	PUNCT
ejpam-5175	152	3	paris	paris	PROPN
ejpam-5175	152	4	,	,	PUNCT
ejpam-5175	152	5	1991	1991	NUM
ejpam-5175	152	6	.	.	PUNCT