id	sid	tid	token	lemma	pos
ap-9131	1	1	acta	acta	PROPN
ap-9131	1	2	polytechnica	polytechnica	PROPN
ap-9131	1	3	https://doi.org/10.14311/ap.2024.64.0336	https://doi.org/10.14311/ap.2024.64.0336	PROPN
ap-9131	1	4	acta	acta	PROPN
ap-9131	1	5	polytechnica	polytechnica	PROPN
ap-9131	1	6	64(4):336–340	64(4):336–340	PROPN
ap-9131	1	7	,	,	PUNCT
ap-9131	1	8	2024	2024	NUM
ap-9131	1	9	©	©	ADP
ap-9131	1	10	2024	2024	NUM
ap-9131	1	11	the	the	DET
ap-9131	1	12	author(s	author(s	NOUN
ap-9131	1	13	)	)	PUNCT
ap-9131	1	14	.	.	PUNCT
ap-9131	2	1	licensed	license	VERB
ap-9131	2	2	under	under	ADP
ap-9131	2	3	a	a	DET
ap-9131	2	4	cc	cc	NOUN
ap-9131	2	5	-	-	PUNCT
ap-9131	2	6	by	by	ADP
ap-9131	2	7	4.0	4.0	NUM
ap-9131	2	8	licence	licence	NOUN
ap-9131	2	9	published	publish	VERB
ap-9131	2	10	by	by	ADP
ap-9131	2	11	the	the	DET
ap-9131	2	12	czech	czech	PROPN
ap-9131	2	13	technical	technical	PROPN
ap-9131	2	14	university	university	PROPN
ap-9131	2	15	in	in	ADP
ap-9131	2	16	prague	prague	PROPN
ap-9131	2	17	so(3	so(3	PROPN
ap-9131	2	18	)	)	PUNCT
ap-9131	3	1	⊂	⊂	PROPN
ap-9131	3	2	su(3	su(3	PROPN
ap-9131	3	3	)	)	PUNCT
ap-9131	3	4	revisited	revisit	VERB
ap-9131	3	5	čestmír	čestmír	NOUN
ap-9131	3	6	burdík	burdík	PROPN
ap-9131	3	7	,	,	PUNCT
ap-9131	3	8	severin	severin	PROPN
ap-9131	3	9	pošta∗	pošta∗	PROPN
ap-9131	3	10	,	,	PUNCT
ap-9131	3	11	erik	erik	PROPN
ap-9131	3	12	rapp	rapp	PROPN
ap-9131	3	13	czech	czech	PROPN
ap-9131	3	14	technical	technical	PROPN
ap-9131	3	15	university	university	PROPN
ap-9131	3	16	in	in	ADP
ap-9131	3	17	prague	prague	PROPN
ap-9131	3	18	,	,	PUNCT
ap-9131	3	19	faculty	faculty	NOUN
ap-9131	3	20	of	of	ADP
ap-9131	3	21	nuclear	nuclear	ADJ
ap-9131	3	22	sciences	science	NOUN
ap-9131	3	23	and	and	CCONJ
ap-9131	3	24	physical	physical	ADJ
ap-9131	3	25	engineering	engineering	NOUN
ap-9131	3	26	,	,	PUNCT
ap-9131	3	27	department	department	NOUN
ap-9131	3	28	of	of	ADP
ap-9131	3	29	mathematics	mathematic	NOUN
ap-9131	3	30	,	,	PUNCT
ap-9131	3	31	trojanova	trojanova	X
ap-9131	3	32	13	13	NUM
ap-9131	3	33	,	,	PUNCT
ap-9131	3	34	120	120	NUM
ap-9131	3	35	00	00	NUM
ap-9131	3	36	prague	prague	PROPN
ap-9131	3	37	,	,	PUNCT
ap-9131	3	38	czech	czech	PROPN
ap-9131	3	39	republic	republic	NOUN
ap-9131	3	40	∗	∗	NOUN
ap-9131	3	41	corresponding	correspond	VERB
ap-9131	3	42	author	author	NOUN
ap-9131	3	43	:	:	PUNCT
ap-9131	3	44	severin.posta@fjfi.cvut.cz	severin.posta@fjfi.cvut.cz	NOUN
ap-9131	3	45	abstract	abstract	NOUN
ap-9131	3	46	.	.	PUNCT
ap-9131	4	1	this	this	DET
ap-9131	4	2	paper	paper	NOUN
ap-9131	4	3	reproduces	reproduce	VERB
ap-9131	4	4	the	the	DET
ap-9131	4	5	result	result	NOUN
ap-9131	4	6	of	of	ADP
ap-9131	4	7	elliot	elliot	NOUN
ap-9131	4	8	,	,	PUNCT
ap-9131	4	9	namely	namely	ADV
ap-9131	4	10	that	that	SCONJ
ap-9131	4	11	the	the	DET
ap-9131	4	12	irreducible	irreducible	ADJ
ap-9131	4	13	finite	finite	ADJ
ap-9131	4	14	dimensional	dimensional	ADJ
ap-9131	4	15	representation	representation	NOUN
ap-9131	4	16	of	of	ADP
ap-9131	4	17	the	the	DET
ap-9131	4	18	lie	lie	NOUN
ap-9131	4	19	algebra	algebra	PROPN
ap-9131	4	20	su(3	su(3	PROPN
ap-9131	4	21	)	)	PUNCT
ap-9131	4	22	of	of	ADP
ap-9131	4	23	highest	high	ADJ
ap-9131	4	24	weight	weight	NOUN
ap-9131	4	25	(	(	PUNCT
ap-9131	4	26	m	m	PROPN
ap-9131	4	27	,	,	PUNCT
ap-9131	4	28	n	n	CCONJ
ap-9131	4	29	)	)	PUNCT
ap-9131	4	30	is	be	AUX
ap-9131	4	31	decomposed	decompose	VERB
ap-9131	4	32	according	accord	VERB
ap-9131	4	33	to	to	ADP
ap-9131	4	34	the	the	DET
ap-9131	4	35	embedding	embed	VERB
ap-9131	4	36	so(3	so(3	NOUN
ap-9131	4	37	)	)	PUNCT
ap-9131	4	38	⊂	⊂	PROPN
ap-9131	4	39	su(3	su(3	PROPN
ap-9131	4	40	)	)	PUNCT
ap-9131	4	41	.	.	PUNCT
ap-9131	5	1	first	first	ADV
ap-9131	5	2	,	,	PUNCT
ap-9131	5	3	a	a	DET
ap-9131	5	4	realisation	realisation	NOUN
ap-9131	5	5	(	(	PUNCT
ap-9131	5	6	a	a	DET
ap-9131	5	7	representation	representation	NOUN
ap-9131	5	8	in	in	ADP
ap-9131	5	9	terms	term	NOUN
ap-9131	5	10	of	of	ADP
ap-9131	5	11	vector	vector	NOUN
ap-9131	5	12	fields	field	NOUN
ap-9131	5	13	)	)	PUNCT
ap-9131	5	14	of	of	ADP
ap-9131	5	15	the	the	DET
ap-9131	5	16	lie	lie	NOUN
ap-9131	5	17	algebra	algebra	PROPN
ap-9131	5	18	su(3	su(3	PROPN
ap-9131	5	19	)	)	PUNCT
ap-9131	5	20	is	be	AUX
ap-9131	5	21	constructed	construct	VERB
ap-9131	5	22	on	on	ADP
ap-9131	5	23	a	a	DET
ap-9131	5	24	space	space	NOUN
ap-9131	5	25	of	of	ADP
ap-9131	5	26	polynomials	polynomial	NOUN
ap-9131	5	27	of	of	ADP
ap-9131	5	28	three	three	NUM
ap-9131	5	29	variables	variable	NOUN
ap-9131	5	30	.	.	PUNCT
ap-9131	6	1	the	the	DET
ap-9131	6	2	special	special	ADJ
ap-9131	6	3	polynomial	polynomial	ADJ
ap-9131	6	4	basis	basis	NOUN
ap-9131	6	5	of	of	ADP
ap-9131	6	6	the	the	DET
ap-9131	6	7	representation	representation	NOUN
ap-9131	6	8	space	space	NOUN
ap-9131	6	9	is	be	AUX
ap-9131	6	10	given	give	VERB
ap-9131	6	11	.	.	PUNCT
ap-9131	7	1	in	in	ADP
ap-9131	7	2	this	this	DET
ap-9131	7	3	basis	basis	NOUN
ap-9131	7	4	,	,	PUNCT
ap-9131	7	5	we	we	PRON
ap-9131	7	6	find	find	VERB
ap-9131	7	7	the	the	DET
ap-9131	7	8	highest	high	ADJ
ap-9131	7	9	weight	weight	NOUN
ap-9131	7	10	vectors	vector	NOUN
ap-9131	7	11	of	of	ADP
ap-9131	7	12	the	the	DET
ap-9131	7	13	representation	representation	NOUN
ap-9131	7	14	of	of	ADP
ap-9131	7	15	the	the	DET
ap-9131	7	16	lie	lie	NOUN
ap-9131	7	17	subalgebra	subalgebra	NOUN
ap-9131	7	18	so(3	so(3	NOUN
ap-9131	7	19	)	)	PUNCT
ap-9131	7	20	and	and	CCONJ
ap-9131	7	21	in	in	ADP
ap-9131	7	22	this	this	DET
ap-9131	7	23	way	way	NOUN
ap-9131	7	24	the	the	DET
ap-9131	7	25	representation	representation	NOUN
ap-9131	7	26	space	space	NOUN
ap-9131	7	27	is	be	AUX
ap-9131	7	28	decomposed	decompose	VERB
ap-9131	7	29	to	to	ADP
ap-9131	7	30	the	the	DET
ap-9131	7	31	direct	direct	ADJ
ap-9131	7	32	sum	sum	NOUN
ap-9131	7	33	of	of	ADP
ap-9131	7	34	invariant	invariant	ADJ
ap-9131	7	35	subspaces	subspace	NOUN
ap-9131	7	36	.	.	PUNCT
ap-9131	8	1	the	the	DET
ap-9131	8	2	process	process	NOUN
ap-9131	8	3	is	be	AUX
ap-9131	8	4	illustrated	illustrate	VERB
ap-9131	8	5	by	by	ADP
ap-9131	8	6	the	the	DET
ap-9131	8	7	example	example	NOUN
ap-9131	8	8	of	of	ADP
ap-9131	8	9	the	the	DET
ap-9131	8	10	decomposition	decomposition	NOUN
ap-9131	8	11	of	of	ADP
ap-9131	8	12	the	the	DET
ap-9131	8	13	representation	representation	NOUN
ap-9131	8	14	of	of	ADP
ap-9131	8	15	highest	high	ADJ
ap-9131	8	16	weight	weight	NOUN
ap-9131	8	17	(	(	PUNCT
ap-9131	8	18	2	2	NUM
ap-9131	8	19	,	,	PUNCT
ap-9131	8	20	2	2	NUM
ap-9131	8	21	)	)	PUNCT
ap-9131	8	22	.	.	PUNCT
ap-9131	9	1	as	as	ADP
ap-9131	9	2	an	an	DET
ap-9131	9	3	additional	additional	ADJ
ap-9131	9	4	result	result	NOUN
ap-9131	9	5	,	,	PUNCT
ap-9131	9	6	the	the	DET
ap-9131	9	7	generating	generate	VERB
ap-9131	9	8	function	function	NOUN
ap-9131	9	9	of	of	ADP
ap-9131	9	10	the	the	DET
ap-9131	9	11	decomposition	decomposition	NOUN
ap-9131	9	12	is	be	AUX
ap-9131	9	13	given	give	VERB
ap-9131	9	14	.	.	PUNCT
ap-9131	10	1	keywords	keyword	NOUN
ap-9131	10	2	:	:	PUNCT
ap-9131	10	3	lie	lie	NOUN
ap-9131	10	4	algebra	algebra	NOUN
ap-9131	10	5	,	,	PUNCT
ap-9131	10	6	realisation	realisation	NOUN
ap-9131	10	7	,	,	PUNCT
ap-9131	10	8	representation	representation	NOUN
ap-9131	10	9	,	,	PUNCT
ap-9131	10	10	decomposition	decomposition	NOUN
ap-9131	10	11	,	,	PUNCT
ap-9131	10	12	embedding	embed	VERB
ap-9131	10	13	.	.	PUNCT
ap-9131	11	1	1	1	X
ap-9131	11	2	.	.	X
ap-9131	11	3	introduction	introduction	NOUN
ap-9131	11	4	in	in	ADP
ap-9131	11	5	the	the	DET
ap-9131	11	6	article	article	NOUN
ap-9131	11	7	by	by	ADP
ap-9131	11	8	elliot	elliot	PROPN
ap-9131	12	1	[	[	X
ap-9131	12	2	1	1	NUM
ap-9131	12	3	]	]	PUNCT
ap-9131	12	4	,	,	PUNCT
ap-9131	12	5	the	the	DET
ap-9131	12	6	plethsym	plethsym	NOUN
ap-9131	12	7	method	method	NOUN
ap-9131	12	8	is	be	AUX
ap-9131	12	9	used	use	VERB
ap-9131	12	10	to	to	PART
ap-9131	12	11	decompose	decompose	VERB
ap-9131	12	12	the	the	DET
ap-9131	12	13	irreducible	irreducible	ADJ
ap-9131	12	14	finite	finite	ADJ
ap-9131	12	15	dimensional	dimensional	ADJ
ap-9131	12	16	representation	representation	NOUN
ap-9131	12	17	of	of	ADP
ap-9131	12	18	lie	lie	NOUN
ap-9131	12	19	algebra	algebra	PROPN
ap-9131	12	20	su(3	su(3	PROPN
ap-9131	12	21	)	)	PUNCT
ap-9131	12	22	,	,	PUNCT
ap-9131	12	23	the	the	DET
ap-9131	12	24	lie	lie	NOUN
ap-9131	12	25	algebra	algebra	NOUN
ap-9131	12	26	of	of	ADP
ap-9131	12	27	antihermitian	antihermitian	ADJ
ap-9131	12	28	3	3	NUM
ap-9131	12	29	×	×	NOUN
ap-9131	12	30	3	3	NUM
ap-9131	12	31	-	-	PUNCT
ap-9131	12	32	matrices	matrix	NOUN
ap-9131	12	33	with	with	ADP
ap-9131	12	34	vanishing	vanish	VERB
ap-9131	12	35	trace	trace	NOUN
ap-9131	12	36	,	,	PUNCT
ap-9131	12	37	with	with	ADP
ap-9131	12	38	the	the	DET
ap-9131	12	39	highest	high	ADJ
ap-9131	12	40	weight	weight	NOUN
ap-9131	12	41	(	(	PUNCT
ap-9131	12	42	m	m	PROPN
ap-9131	12	43	,	,	PUNCT
ap-9131	12	44	n	n	CCONJ
ap-9131	12	45	)	)	PUNCT
ap-9131	12	46	,	,	PUNCT
ap-9131	12	47	where	where	SCONJ
ap-9131	12	48	m	m	VERB
ap-9131	12	49	,	,	PUNCT
ap-9131	12	50	n	n	PRON
ap-9131	12	51	are	be	AUX
ap-9131	12	52	non	non	ADJ
ap-9131	12	53	-	-	ADJ
ap-9131	12	54	negative	negative	ADJ
ap-9131	12	55	integers	integer	NOUN
ap-9131	12	56	,	,	PUNCT
ap-9131	12	57	into	into	ADP
ap-9131	12	58	the	the	DET
ap-9131	12	59	direct	direct	ADJ
ap-9131	12	60	sum	sum	NOUN
ap-9131	12	61	of	of	ADP
ap-9131	12	62	irreducible	irreducible	ADJ
ap-9131	12	63	representations	representation	NOUN
ap-9131	12	64	of	of	ADP
ap-9131	12	65	so(3	so(3	NOUN
ap-9131	12	66	)	)	PUNCT
ap-9131	12	67	,	,	PUNCT
ap-9131	12	68	the	the	DET
ap-9131	12	69	lie	lie	NOUN
ap-9131	12	70	algebra	algebra	NOUN
ap-9131	12	71	of	of	ADP
ap-9131	12	72	3×3	3×3	NUM
ap-9131	12	73	skew	skew	ADJ
ap-9131	12	74	-	-	PUNCT
ap-9131	12	75	symmetric	symmetric	ADJ
ap-9131	12	76	matrices	matrix	NOUN
ap-9131	12	77	,	,	PUNCT
ap-9131	12	78	according	accord	VERB
ap-9131	12	79	to	to	ADP
ap-9131	12	80	the	the	DET
ap-9131	12	81	embedding	embed	VERB
ap-9131	12	82	so(3	so(3	NOUN
ap-9131	12	83	)	)	PUNCT
ap-9131	12	84	⊂	⊂	PROPN
ap-9131	12	85	su(3	su(3	PROPN
ap-9131	12	86	)	)	PUNCT
ap-9131	12	87	.	.	PUNCT
ap-9131	13	1	the	the	DET
ap-9131	13	2	embedding	embed	VERB
ap-9131	13	3	so(3	so(3	NOUN
ap-9131	13	4	)	)	PUNCT
ap-9131	13	5	⊂	⊂	PROPN
ap-9131	13	6	su(3	su(3	PROPN
ap-9131	13	7	)	)	PUNCT
ap-9131	13	8	is	be	AUX
ap-9131	13	9	widely	widely	ADV
ap-9131	13	10	used	use	VERB
ap-9131	13	11	in	in	ADP
ap-9131	13	12	theoretical	theoretical	ADJ
ap-9131	13	13	physics	physics	NOUN
ap-9131	13	14	and	and	CCONJ
ap-9131	13	15	corresponding	corresponding	ADJ
ap-9131	13	16	irreducible	irreducible	ADJ
ap-9131	13	17	bases	basis	NOUN
ap-9131	13	18	,	,	PUNCT
ap-9131	13	19	both	both	DET
ap-9131	13	20	non	non	ADJ
ap-9131	13	21	-	-	ADJ
ap-9131	13	22	orthogonal	orthogonal	ADJ
ap-9131	13	23	and	and	CCONJ
ap-9131	13	24	orthogonal	orthogonal	ADJ
ap-9131	13	25	ones	one	NOUN
ap-9131	13	26	,	,	PUNCT
ap-9131	13	27	have	have	AUX
ap-9131	13	28	been	be	AUX
ap-9131	13	29	intensively	intensively	ADV
ap-9131	13	30	studied	study	VERB
ap-9131	13	31	(	(	PUNCT
ap-9131	13	32	see	see	VERB
ap-9131	13	33	[	[	X
ap-9131	13	34	2–5	2–5	NOUN
ap-9131	13	35	]	]	PUNCT
ap-9131	13	36	)	)	PUNCT
ap-9131	13	37	.	.	PUNCT
ap-9131	14	1	the	the	DET
ap-9131	14	2	formula	formula	NOUN
ap-9131	14	3	(	(	PUNCT
ap-9131	14	4	14	14	NUM
ap-9131	14	5	)	)	PUNCT
ap-9131	14	6	in	in	ADP
ap-9131	14	7	[	[	X
ap-9131	14	8	1	1	X
ap-9131	14	9	]	]	PUNCT
ap-9131	14	10	states	state	VERB
ap-9131	14	11	that	that	SCONJ
ap-9131	14	12	the	the	DET
ap-9131	14	13	representations	representation	NOUN
ap-9131	14	14	(	(	PUNCT
ap-9131	14	15	λ	λ	NOUN
ap-9131	14	16	)	)	PUNCT
ap-9131	14	17	of	of	ADP
ap-9131	14	18	so(3	so(3	NOUN
ap-9131	14	19	)	)	PUNCT
ap-9131	14	20	with	with	ADP
ap-9131	14	21	the	the	DET
ap-9131	14	22	highest	high	ADJ
ap-9131	14	23	weight	weight	NOUN
ap-9131	14	24	λ	λ	PROPN
ap-9131	14	25	,	,	PUNCT
ap-9131	14	26	which	which	PRON
ap-9131	14	27	occur	occur	VERB
ap-9131	14	28	in	in	ADP
ap-9131	14	29	the	the	DET
ap-9131	14	30	representation	representation	NOUN
ap-9131	14	31	(	(	PUNCT
ap-9131	14	32	m	m	PROPN
ap-9131	14	33	,	,	PUNCT
ap-9131	14	34	n	n	CCONJ
ap-9131	14	35	)	)	PUNCT
ap-9131	14	36	of	of	ADP
ap-9131	14	37	su(3	su(3	PROPN
ap-9131	14	38	)	)	PUNCT
ap-9131	14	39	,	,	PUNCT
ap-9131	14	40	are	be	AUX
ap-9131	14	41	given	give	VERB
ap-9131	14	42	by	by	ADP
ap-9131	14	43	:	:	PUNCT
ap-9131	14	44	λ	λ	X
ap-9131	14	45	=	=	SYM
ap-9131	14	46	k	k	PROPN
ap-9131	14	47	,	,	PUNCT
ap-9131	14	48	k	k	PROPN
ap-9131	15	1	+	+	PROPN
ap-9131	15	2	1	1	NUM
ap-9131	15	3	,	,	PUNCT
ap-9131	15	4	k	k	PROPN
ap-9131	15	5	+	+	PROPN
ap-9131	15	6	2	2	NUM
ap-9131	15	7	,	,	PUNCT
ap-9131	15	8	...	...	PUNCT
ap-9131	15	9	,	,	PUNCT
ap-9131	15	10	k	k	PROPN
ap-9131	16	1	+	+	CCONJ
ap-9131	16	2	max{m	max{m	PROPN
ap-9131	16	3	,	,	PUNCT
ap-9131	16	4	n	n	CCONJ
ap-9131	16	5	}	}	PUNCT
ap-9131	16	6	,	,	PUNCT
ap-9131	16	7	where	where	SCONJ
ap-9131	16	8	the	the	DET
ap-9131	16	9	integer	integer	NOUN
ap-9131	16	10	:	:	PUNCT
ap-9131	16	11	k	k	X
ap-9131	16	12	=	=	SYM
ap-9131	16	13	min{m	min{m	PROPN
ap-9131	16	14	,	,	PUNCT
ap-9131	16	15	n	n	CCONJ
ap-9131	16	16	}	}	PUNCT
ap-9131	16	17	,	,	PUNCT
ap-9131	16	18	min{m	min{m	PROPN
ap-9131	16	19	,	,	PUNCT
ap-9131	16	20	n	n	CCONJ
ap-9131	16	21	}	}	PUNCT
ap-9131	16	22	−	−	PROPN
ap-9131	16	23	2	2	NUM
ap-9131	16	24	,	,	PUNCT
ap-9131	16	25	...	...	PUNCT
ap-9131	16	26	,	,	PUNCT
ap-9131	16	27	1	1	NUM
ap-9131	16	28	or	or	CCONJ
ap-9131	16	29	0	0	NUM
ap-9131	16	30	,	,	PUNCT
ap-9131	16	31	(	(	PUNCT
ap-9131	16	32	1	1	X
ap-9131	16	33	)	)	PUNCT
ap-9131	16	34	with	with	ADP
ap-9131	16	35	the	the	DET
ap-9131	16	36	exception	exception	NOUN
ap-9131	16	37	that	that	SCONJ
ap-9131	16	38	if	if	SCONJ
ap-9131	16	39	k	k	PROPN
ap-9131	16	40	=	=	NOUN
ap-9131	16	41	0	0	NUM
ap-9131	16	42	:	:	PUNCT
ap-9131	16	43	λ	λ	X
ap-9131	16	44	=	=	SYM
ap-9131	16	45	max{m	max{m	PROPN
ap-9131	16	46	,	,	PUNCT
ap-9131	16	47	n	n	CCONJ
ap-9131	16	48	}	}	PUNCT
ap-9131	16	49	,	,	PUNCT
ap-9131	16	50	max{m	max{m	PROPN
ap-9131	16	51	,	,	PUNCT
ap-9131	16	52	n	n	CCONJ
ap-9131	16	53	}	}	PUNCT
ap-9131	16	54	−	−	PROPN
ap-9131	16	55	2	2	NUM
ap-9131	16	56	,	,	PUNCT
ap-9131	16	57	...	...	PUNCT
ap-9131	16	58	,	,	PUNCT
ap-9131	16	59	1	1	NUM
ap-9131	16	60	or	or	CCONJ
ap-9131	16	61	0	0	NUM
ap-9131	16	62	.	.	PUNCT
ap-9131	17	1	in	in	ADP
ap-9131	17	2	this	this	DET
ap-9131	17	3	paper	paper	NOUN
ap-9131	17	4	,	,	PUNCT
ap-9131	17	5	we	we	PRON
ap-9131	17	6	reproduce	reproduce	VERB
ap-9131	17	7	this	this	DET
ap-9131	17	8	result	result	NOUN
ap-9131	17	9	using	use	VERB
ap-9131	17	10	differential	differential	ADJ
ap-9131	17	11	operator	operator	NOUN
ap-9131	17	12	realisations	realisation	NOUN
ap-9131	17	13	,	,	PUNCT
ap-9131	17	14	which	which	PRON
ap-9131	17	15	act	act	VERB
ap-9131	17	16	on	on	ADP
ap-9131	17	17	a	a	DET
ap-9131	17	18	space	space	NOUN
ap-9131	17	19	of	of	ADP
ap-9131	17	20	polynomials	polynomial	NOUN
ap-9131	17	21	of	of	ADP
ap-9131	17	22	three	three	NUM
ap-9131	17	23	independent	independent	ADJ
ap-9131	17	24	variables	variable	NOUN
ap-9131	17	25	.	.	PUNCT
ap-9131	18	1	this	this	DET
ap-9131	18	2	tool	tool	NOUN
ap-9131	18	3	is	be	AUX
ap-9131	18	4	used	use	VERB
ap-9131	18	5	in	in	ADP
ap-9131	18	6	various	various	ADJ
ap-9131	18	7	contexts	contexts	NOUN
ap-9131	18	8	,	,	PUNCT
ap-9131	18	9	namely	namely	ADV
ap-9131	18	10	in	in	ADP
ap-9131	18	11	a	a	DET
ap-9131	18	12	modern	modern	ADJ
ap-9131	18	13	group	group	NOUN
ap-9131	18	14	analysis	analysis	NOUN
ap-9131	18	15	of	of	ADP
ap-9131	18	16	differential	differential	ADJ
ap-9131	18	17	equations	equation	NOUN
ap-9131	18	18	[	[	X
ap-9131	18	19	6–9	6–9	NOUN
ap-9131	18	20	]	]	PUNCT
ap-9131	18	21	,	,	PUNCT
ap-9131	18	22	in	in	ADP
ap-9131	18	23	classification	classification	NOUN
ap-9131	18	24	of	of	ADP
ap-9131	18	25	gravity	gravity	NOUN
ap-9131	18	26	fields	field	NOUN
ap-9131	18	27	[	[	X
ap-9131	18	28	10	10	NUM
ap-9131	18	29	]	]	PUNCT
ap-9131	18	30	,	,	PUNCT
ap-9131	18	31	in	in	ADP
ap-9131	18	32	geometric	geometric	ADJ
ap-9131	18	33	control	control	NOUN
ap-9131	18	34	theory	theory	NOUN
ap-9131	18	35	[	[	X
ap-9131	18	36	11	11	NUM
ap-9131	18	37	]	]	PUNCT
ap-9131	18	38	,	,	PUNCT
ap-9131	18	39	in	in	ADP
ap-9131	18	40	difference	difference	NOUN
ap-9131	18	41	schemes	scheme	NOUN
ap-9131	18	42	for	for	ADP
ap-9131	18	43	numerical	numerical	ADJ
ap-9131	18	44	solutions	solution	NOUN
ap-9131	18	45	of	of	ADP
ap-9131	18	46	differential	differential	ADJ
ap-9131	18	47	equations	equation	NOUN
ap-9131	19	1	[	[	X
ap-9131	19	2	12	12	NUM
ap-9131	19	3	]	]	PUNCT
ap-9131	19	4	,	,	PUNCT
ap-9131	19	5	etc	etc	X
ap-9131	19	6	.	.	X
ap-9131	19	7	2	2	X
ap-9131	19	8	.	.	X
ap-9131	19	9	realisation	realisation	NOUN
ap-9131	19	10	of	of	ADP
ap-9131	19	11	su(3	su(3	NOUN
ap-9131	19	12	)	)	PUNCT
ap-9131	19	13	we	we	PRON
ap-9131	19	14	make	make	VERB
ap-9131	19	15	use	use	NOUN
ap-9131	19	16	of	of	ADP
ap-9131	19	17	the	the	DET
ap-9131	19	18	realisation	realisation	NOUN
ap-9131	19	19	of	of	ADP
ap-9131	19	20	the	the	DET
ap-9131	19	21	lie	lie	NOUN
ap-9131	19	22	algebra	algebra	NOUN
ap-9131	19	23	gl(3,c	gl(3,c	NOUN
ap-9131	19	24	)	)	PUNCT
ap-9131	19	25	,	,	PUNCT
ap-9131	19	26	which	which	PRON
ap-9131	19	27	is	be	AUX
ap-9131	19	28	a	a	DET
ap-9131	19	29	complex	complex	ADJ
ap-9131	19	30	lie	lie	NOUN
ap-9131	19	31	algebra	algebra	NOUN
ap-9131	19	32	of	of	ADP
ap-9131	19	33	elements	element	NOUN
ap-9131	19	34	eij	eij	PROPN
ap-9131	19	35	,	,	PUNCT
ap-9131	19	36	i	i	PRON
ap-9131	19	37	,	,	PUNCT
ap-9131	19	38	j	j	PROPN
ap-9131	19	39	=	=	SYM
ap-9131	19	40	1	1	NUM
ap-9131	19	41	,	,	PUNCT
ap-9131	19	42	2	2	NUM
ap-9131	19	43	,	,	PUNCT
ap-9131	19	44	3	3	NUM
ap-9131	19	45	satisfying	satisfy	VERB
ap-9131	19	46	commutation	commutation	NOUN
ap-9131	19	47	relations	relation	NOUN
ap-9131	19	48	:	:	PUNCT
ap-9131	20	1	[	[	X
ap-9131	20	2	eij	eij	X
ap-9131	20	3	,	,	PUNCT
ap-9131	20	4	ekl	ekl	PROPN
ap-9131	20	5	]	]	X
ap-9131	20	6	=	=	SYM
ap-9131	20	7	δjkeil	δjkeil	NOUN
ap-9131	20	8	−	−	PROPN
ap-9131	20	9	δliekj	δliekj	ADJ
ap-9131	20	10	,	,	PUNCT
ap-9131	20	11	on	on	ADP
ap-9131	20	12	a	a	DET
ap-9131	20	13	space	space	NOUN
ap-9131	20	14	of	of	ADP
ap-9131	20	15	polynomials	polynomial	NOUN
ap-9131	20	16	of	of	ADP
ap-9131	20	17	three	three	NUM
ap-9131	20	18	variables	variable	NOUN
ap-9131	20	19	c[x1	c[x1	NOUN
ap-9131	20	20	,	,	PUNCT
ap-9131	20	21	x2	x2	PROPN
ap-9131	20	22	,	,	PUNCT
ap-9131	20	23	x3	x3	ADJ
ap-9131	20	24	]	]	PUNCT
ap-9131	20	25	.	.	PUNCT
ap-9131	21	1	(	(	PUNCT
ap-9131	21	2	for	for	ADP
ap-9131	21	3	an	an	DET
ap-9131	21	4	extensive	extensive	ADJ
ap-9131	21	5	list	list	NOUN
ap-9131	21	6	of	of	ADP
ap-9131	21	7	realisations	realisation	NOUN
ap-9131	21	8	of	of	ADP
ap-9131	21	9	low	low	ADJ
ap-9131	21	10	dimensional	dimensional	ADJ
ap-9131	21	11	lie	lie	NOUN
ap-9131	21	12	algebras	algebra	NOUN
ap-9131	21	13	see	see	VERB
ap-9131	21	14	[	[	X
ap-9131	21	15	13	13	NUM
ap-9131	21	16	]	]	PUNCT
ap-9131	21	17	.	.	PUNCT
ap-9131	22	1	see	see	VERB
ap-9131	22	2	[	[	X
ap-9131	22	3	14	14	NUM
ap-9131	22	4	]	]	X
ap-9131	22	5	how	how	SCONJ
ap-9131	22	6	to	to	PART
ap-9131	22	7	obtain	obtain	VERB
ap-9131	22	8	all	all	DET
ap-9131	22	9	irreducible	irreducible	ADJ
ap-9131	22	10	representations	representation	NOUN
ap-9131	22	11	of	of	ADP
ap-9131	22	12	classical	classical	ADJ
ap-9131	22	13	lie	lie	NOUN
ap-9131	22	14	algebras	algebra	NOUN
ap-9131	22	15	in	in	ADP
ap-9131	22	16	terms	term	NOUN
ap-9131	22	17	of	of	ADP
ap-9131	22	18	polynomial	polynomial	ADJ
ap-9131	22	19	vector	vector	NOUN
ap-9131	22	20	fields	field	NOUN
ap-9131	22	21	.	.	PUNCT
ap-9131	22	22	)	)	PUNCT
ap-9131	23	1	the	the	DET
ap-9131	23	2	realisation	realisation	NOUN
ap-9131	23	3	ρ	ρ	PROPN
ap-9131	23	4	is	be	AUX
ap-9131	23	5	given	give	VERB
ap-9131	23	6	by	by	ADP
ap-9131	23	7	the	the	DET
ap-9131	23	8	formulas	formula	NOUN
ap-9131	23	9	[	[	X
ap-9131	23	10	15	15	NUM
ap-9131	23	11	]	]	SYM
ap-9131	23	12	:	:	PUNCT
ap-9131	23	13	ρ(e11	ρ(e11	NUM
ap-9131	23	14	)	)	PUNCT
ap-9131	23	15	=	=	SYM
ap-9131	24	1	x1∂1	x1∂1	PROPN
ap-9131	24	2	+	+	PROPN
ap-9131	25	1	x3∂3	x3∂3	PROPN
ap-9131	25	2	+	+	CCONJ
ap-9131	25	3	iα1	iα1	PROPN
ap-9131	25	4	+	+	CCONJ
ap-9131	25	5	1	1	NUM
ap-9131	25	6	,	,	PUNCT
ap-9131	25	7	ρ(e12	ρ(e12	NOUN
ap-9131	25	8	)	)	PUNCT
ap-9131	26	1	=	=	PUNCT
ap-9131	27	1	x1∂2	x1∂2	PROPN
ap-9131	28	1	+	+	NUM
ap-9131	28	2	x2	x2	PROPN
ap-9131	28	3	3∂3	3∂3	NUM
ap-9131	28	4	+	+	CCONJ
ap-9131	28	5	(	(	PUNCT
ap-9131	28	6	1	1	NUM
ap-9131	28	7	+	+	NUM
ap-9131	28	8	i(α1	i(α1	NOUN
ap-9131	28	9	−	−	PROPN
ap-9131	28	10	α2))x3	α2))x3	PROPN
ap-9131	28	11	,	,	PUNCT
ap-9131	28	12	ρ(e13	ρ(e13	NUM
ap-9131	28	13	)	)	PUNCT
ap-9131	28	14	=	=	SYM
ap-9131	29	1	x2	x2	PROPN
ap-9131	29	2	1∂1	1∂1	NUM
ap-9131	29	3	+	+	CCONJ
ap-9131	29	4	x1x2∂2	x1x2∂2	PUNCT
ap-9131	30	1	+	+	NUM
ap-9131	30	2	x3(x1	x3(x1	PROPN
ap-9131	30	3	+	+	CCONJ
ap-9131	30	4	x2x3)∂3	x2x3)∂3	PROPN
ap-9131	31	1	+	+	CCONJ
ap-9131	31	2	(	(	PUNCT
ap-9131	31	3	2	2	NUM
ap-9131	31	4	+	+	NUM
ap-9131	31	5	i(α1	i(α1	NOUN
ap-9131	31	6	−	−	VERB
ap-9131	31	7	α3))x1	α3))x1	NOUN
ap-9131	31	8	+	+	CCONJ
ap-9131	31	9	x2x3(1	x2x3(1	ADJ
ap-9131	31	10	+	+	CCONJ
ap-9131	31	11	i(α1	i(α1	NOUN
ap-9131	31	12	−	−	PROPN
ap-9131	31	13	α2	α2	PROPN
ap-9131	31	14	)	)	PUNCT
ap-9131	31	15	)	)	PUNCT
ap-9131	31	16	,	,	PUNCT
ap-9131	31	17	ρ(e21	ρ(e21	NUM
ap-9131	31	18	)	)	PUNCT
ap-9131	31	19	=	=	PUNCT
ap-9131	32	1	x2∂1	x2∂1	PROPN
ap-9131	32	2	−	−	PROPN
ap-9131	32	3	∂3	∂3	NOUN
ap-9131	32	4	,	,	PUNCT
ap-9131	32	5	ρ(e22	ρ(e22	ADV
ap-9131	32	6	)	)	PUNCT
ap-9131	33	1	=	=	PUNCT
ap-9131	34	1	x2∂2	x2∂2	PRON
ap-9131	34	2	−	−	PROPN
ap-9131	35	1	x3∂3	x3∂3	PROPN
ap-9131	35	2	+	+	NUM
ap-9131	35	3	iα2	iα2	PROPN
ap-9131	35	4	,	,	PUNCT
ap-9131	35	5	ρ(e23	ρ(e23	NUM
ap-9131	35	6	)	)	PUNCT
ap-9131	35	7	=	=	PUNCT
ap-9131	36	1	x1x2∂1	x1x2∂1	PROPN
ap-9131	37	1	+	+	CCONJ
ap-9131	37	2	x2	x2	PROPN
ap-9131	37	3	2∂2	2∂2	NUM
ap-9131	37	4	−	−	PROPN
ap-9131	37	5	(	(	PUNCT
ap-9131	37	6	x1	x1	PROPN
ap-9131	37	7	+	+	PROPN
ap-9131	37	8	x2x3)∂3	x2x3)∂3	PROPN
ap-9131	38	1	+	+	CCONJ
ap-9131	38	2	(	(	PUNCT
ap-9131	38	3	1	1	NUM
ap-9131	38	4	+	+	NUM
ap-9131	38	5	i(α2	i(α2	NOUN
ap-9131	38	6	−	−	PROPN
ap-9131	38	7	α3))x2	α3))x2	PROPN
ap-9131	38	8	,	,	PUNCT
ap-9131	38	9	ρ(e31	ρ(e31	NUM
ap-9131	38	10	)	)	PUNCT
ap-9131	39	1	=	=	SYM
ap-9131	39	2	−∂1	−∂1	ADJ
ap-9131	39	3	,	,	PUNCT
ap-9131	39	4	ρ(e32	ρ(e32	NOUN
ap-9131	39	5	)	)	PUNCT
ap-9131	39	6	=	=	PUNCT
ap-9131	40	1	−∂2	−∂2	ADJ
ap-9131	40	2	,	,	PUNCT
ap-9131	40	3	ρ(e33	ρ(e33	NOUN
ap-9131	40	4	)	)	PUNCT
ap-9131	41	1	=	=	PUNCT
ap-9131	41	2	−x1∂1	−x1∂1	PUNCT
ap-9131	41	3	−	−	PROPN
ap-9131	42	1	x2∂2	x2∂2	PROPN
ap-9131	43	1	+	+	CCONJ
ap-9131	43	2	iα3	iα3	PROPN
ap-9131	43	3	−	−	PROPN
ap-9131	43	4	1	1	NUM
ap-9131	43	5	,	,	PUNCT
ap-9131	43	6	(	(	PUNCT
ap-9131	43	7	2	2	X
ap-9131	43	8	)	)	PUNCT
ap-9131	43	9	where	where	SCONJ
ap-9131	43	10	α1	α1	PROPN
ap-9131	43	11	,	,	PUNCT
ap-9131	43	12	α2	α2	ADJ
ap-9131	43	13	,	,	PUNCT
ap-9131	43	14	α3	α3	PROPN
ap-9131	43	15	are	be	AUX
ap-9131	43	16	arbitrary	arbitrary	ADJ
ap-9131	43	17	complex	complex	ADJ
ap-9131	43	18	parameters	parameter	NOUN
ap-9131	43	19	.	.	PUNCT
ap-9131	44	1	introducing	introduce	VERB
ap-9131	44	2	the	the	DET
ap-9131	44	3	generators	generator	NOUN
ap-9131	44	4	:	:	PUNCT
ap-9131	44	5	h1	h1	VERB
ap-9131	44	6	=	=	PUNCT
ap-9131	44	7	e11	e11	ADJ
ap-9131	44	8	−	−	PROPN
ap-9131	44	9	e22	e22	NOUN
ap-9131	44	10	,	,	PUNCT
ap-9131	44	11	h2	h2	NOUN
ap-9131	44	12	=	=	SYM
ap-9131	44	13	e22	e22	PROPN
ap-9131	44	14	−	−	PROPN
ap-9131	44	15	e33	e33	PROPN
ap-9131	44	16	,	,	PUNCT
ap-9131	44	17	and	and	CCONJ
ap-9131	44	18	the	the	DET
ap-9131	44	19	operators	operator	NOUN
ap-9131	44	20	:	:	PUNCT
ap-9131	44	21	ρ(h1	ρ(h1	X
ap-9131	44	22	)	)	PUNCT
ap-9131	44	23	=	=	SYM
ap-9131	44	24	ρ(e11	ρ(e11	X
ap-9131	44	25	)	)	PUNCT
ap-9131	44	26	−	−	NOUN
ap-9131	44	27	ρ(e22	ρ(e22	NOUN
ap-9131	44	28	)	)	PUNCT
ap-9131	45	1	=	=	SYM
ap-9131	46	1	x1∂1	x1∂1	PROPN
ap-9131	46	2	−	−	PROPN
ap-9131	47	1	x2∂2	x2∂2	PROPN
ap-9131	48	1	+	+	CCONJ
ap-9131	48	2	2x3∂3	2x3∂3	NUM
ap-9131	48	3	+	+	CCONJ
ap-9131	48	4	i(α1	i(α1	NOUN
ap-9131	48	5	−	−	PROPN
ap-9131	48	6	α2	α2	ADV
ap-9131	48	7	)	)	PUNCT
ap-9131	49	1	+	+	CCONJ
ap-9131	49	2	1	1	NUM
ap-9131	49	3	,	,	PUNCT
ap-9131	49	4	ρ(h2	ρ(h2	NOUN
ap-9131	49	5	)	)	PUNCT
ap-9131	49	6	=	=	SYM
ap-9131	49	7	ρ(e22	ρ(e22	NOUN
ap-9131	49	8	)	)	PUNCT
ap-9131	49	9	−	−	NOUN
ap-9131	49	10	ρ(e33	ρ(e33	NOUN
ap-9131	49	11	)	)	PUNCT
ap-9131	50	1	=	=	SYM
ap-9131	51	1	x1∂1	x1∂1	PROPN
ap-9131	52	1	+	+	CCONJ
ap-9131	53	1	2x2∂2	2x2∂2	NUM
ap-9131	53	2	−	−	NOUN
ap-9131	53	3	x3∂3	x3∂3	NUM
ap-9131	53	4	+	+	PROPN
ap-9131	53	5	i(α2	i(α2	NOUN
ap-9131	53	6	−	−	PROPN
ap-9131	53	7	α3	α3	NOUN
ap-9131	53	8	)	)	PUNCT
ap-9131	54	1	+	+	CCONJ
ap-9131	54	2	1	1	NUM
ap-9131	54	3	,	,	PUNCT
ap-9131	54	4	we	we	PRON
ap-9131	54	5	obtain	obtain	VERB
ap-9131	54	6	a	a	DET
ap-9131	54	7	realisation	realisation	NOUN
ap-9131	54	8	of	of	ADP
ap-9131	54	9	the	the	DET
ap-9131	54	10	lie	lie	NOUN
ap-9131	54	11	algebra	algebra	NOUN
ap-9131	54	12	sl(3,c	sl(3,c	VERB
ap-9131	54	13	)	)	PUNCT
ap-9131	54	14	≃	≃	PROPN
ap-9131	54	15	su(3)c	su(3)c	PROPN
ap-9131	54	16	,	,	PUNCT
ap-9131	54	17	given	give	VERB
ap-9131	54	18	by	by	ADP
ap-9131	54	19	the	the	DET
ap-9131	54	20	generators	generator	NOUN
ap-9131	54	21	e12	e12	NOUN
ap-9131	54	22	,	,	PUNCT
ap-9131	54	23	e13	e13	PROPN
ap-9131	54	24	,	,	PUNCT
ap-9131	54	25	336	336	NUM
ap-9131	54	26	https://doi.org/10.14311/ap.2024.64.0336	https://doi.org/10.14311/ap.2024.64.0336	NOUN
ap-9131	54	27	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
ap-9131	54	28	https://www.cvut.cz/en	https://www.cvut.cz/en	NUM
ap-9131	54	29	vol	vol	NOUN
ap-9131	54	30	.	.	PROPN
ap-9131	55	1	64	64	NUM
ap-9131	55	2	no	no	NOUN
ap-9131	55	3	.	.	PUNCT
ap-9131	56	1	4/2024	4/2024	NUM
ap-9131	56	2	so(3	so(3	NOUN
ap-9131	56	3	)	)	PUNCT
ap-9131	56	4	⊂	⊂	PROPN
ap-9131	56	5	su(3	su(3	PROPN
ap-9131	56	6	)	)	PUNCT
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ap-9131	56	8	e23	e23	NOUN
ap-9131	56	9	,	,	PUNCT
ap-9131	56	10	e21	e21	PROPN
ap-9131	56	11	,	,	PUNCT
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ap-9131	56	15	,	,	PUNCT
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ap-9131	56	17	,	,	PUNCT
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ap-9131	56	19	h2	h2	NOUN
ap-9131	56	20	and	and	CCONJ
ap-9131	56	21	commutation	commutation	NOUN
ap-9131	56	22	relations	relation	NOUN
ap-9131	56	23	:	:	PUNCT
ap-9131	56	24	[	[	X
ap-9131	56	25	e12	e12	NOUN
ap-9131	56	26	,	,	PUNCT
ap-9131	56	27	e23	e23	NOUN
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ap-9131	56	29	=	=	SYM
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ap-9131	56	39	,	,	PUNCT
ap-9131	56	40	[	[	X
ap-9131	56	41	e31	e31	X
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ap-9131	56	44	]	]	X
ap-9131	56	45	=	=	SYM
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ap-9131	56	47	,	,	PUNCT
ap-9131	56	48	[	[	X
ap-9131	56	49	h1	h1	NOUN
ap-9131	56	50	,	,	PUNCT
ap-9131	56	51	e12	e12	NOUN
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ap-9131	56	53	=	=	SYM
ap-9131	56	54	2e12	2e12	NOUN
ap-9131	56	55	,	,	PUNCT
ap-9131	56	56	[	[	X
ap-9131	56	57	e12	e12	NOUN
ap-9131	56	58	,	,	PUNCT
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ap-9131	56	61	=	=	SYM
ap-9131	56	62	e12	e12	NOUN
ap-9131	56	63	,	,	PUNCT
ap-9131	56	64	[	[	X
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ap-9131	56	67	e13	e13	PROPN
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ap-9131	56	69	=	=	SYM
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ap-9131	56	71	,	,	PUNCT
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ap-9131	56	73	e13	e13	X
ap-9131	56	74	,	,	PUNCT
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ap-9131	56	77	=	=	SYM
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ap-9131	56	82	[	[	X
ap-9131	56	83	e13	e13	NOUN
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ap-9131	56	85	e32	e32	NOUN
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ap-9131	56	87	=	=	SYM
ap-9131	56	88	e12	e12	NOUN
ap-9131	56	89	,	,	PUNCT
ap-9131	56	90	[	[	X
ap-9131	56	91	h1	h1	X
ap-9131	56	92	,	,	PUNCT
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ap-9131	56	94	]	]	X
ap-9131	56	95	=	=	SYM
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ap-9131	56	97	,	,	PUNCT
ap-9131	56	98	[	[	X
ap-9131	56	99	h2	h2	NOUN
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ap-9131	56	103	=	=	SYM
ap-9131	56	104	e13	e13	PROPN
ap-9131	56	105	,	,	PUNCT
ap-9131	56	106	[	[	X
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ap-9131	56	108	,	,	PUNCT
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ap-9131	56	110	]	]	X
ap-9131	56	111	=	=	SYM
ap-9131	56	112	e21	e21	PROPN
ap-9131	56	113	,	,	PUNCT
ap-9131	56	114	[	[	X
ap-9131	56	115	e23	e23	ADJ
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ap-9131	56	117	e32	e32	NOUN
ap-9131	56	118	]	]	X
ap-9131	56	119	=	=	SYM
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ap-9131	56	122	[	[	X
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ap-9131	56	126	]	]	X
ap-9131	56	127	=	=	SYM
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ap-9131	56	129	,	,	PUNCT
ap-9131	56	130	[	[	X
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ap-9131	56	135	=	=	SYM
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ap-9131	56	137	,	,	PUNCT
ap-9131	56	138	[	[	X
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ap-9131	56	140	,	,	PUNCT
ap-9131	56	141	e21	e21	PROPN
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ap-9131	56	143	=	=	PUNCT
ap-9131	56	144	e31	e31	X
ap-9131	56	145	,	,	PUNCT
ap-9131	56	146	[	[	X
ap-9131	56	147	e21	e21	X
ap-9131	56	148	,	,	PUNCT
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ap-9131	56	150	]	]	X
ap-9131	56	151	=	=	PUNCT
ap-9131	56	152	2e21	2e21	NUM
ap-9131	56	153	,	,	PUNCT
ap-9131	56	154	[	[	X
ap-9131	56	155	h2	h2	NOUN
ap-9131	56	156	,	,	PUNCT
ap-9131	56	157	e21	e21	PROPN
ap-9131	56	158	]	]	PUNCT
ap-9131	56	159	=	=	SYM
ap-9131	56	160	e21	e21	PROPN
ap-9131	56	161	,	,	PUNCT
ap-9131	56	162	[	[	X
ap-9131	56	163	e31	e31	X
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ap-9131	56	167	=	=	PUNCT
ap-9131	56	168	e31	e31	X
ap-9131	56	169	,	,	PUNCT
ap-9131	56	170	[	[	X
ap-9131	56	171	e31	e31	X
ap-9131	56	172	,	,	PUNCT
ap-9131	56	173	h2	h2	PROPN
ap-9131	56	174	]	]	X
ap-9131	56	175	=	=	PUNCT
ap-9131	56	176	e31	e31	PROPN
ap-9131	56	177	,	,	PUNCT
ap-9131	56	178	[	[	X
ap-9131	56	179	h1	h1	NOUN
ap-9131	56	180	,	,	PUNCT
ap-9131	56	181	e32	e32	PROPN
ap-9131	56	182	]	]	X
ap-9131	56	183	=	=	SYM
ap-9131	56	184	e32	e32	NOUN
ap-9131	56	185	,	,	PUNCT
ap-9131	56	186	[	[	X
ap-9131	56	187	e32	e32	NOUN
ap-9131	56	188	,	,	PUNCT
ap-9131	56	189	h2	h2	NOUN
ap-9131	56	190	]	]	X
ap-9131	56	191	=	=	SYM
ap-9131	56	192	2e32	2e32	NUM
ap-9131	56	193	,	,	PUNCT
ap-9131	56	194	(	(	PUNCT
ap-9131	56	195	other	other	ADJ
ap-9131	56	196	commutation	commutation	NOUN
ap-9131	56	197	relations	relation	NOUN
ap-9131	56	198	are	be	AUX
ap-9131	56	199	zero	zero	NUM
ap-9131	56	200	)	)	PUNCT
ap-9131	56	201	.	.	PUNCT
ap-9131	57	1	for	for	ADP
ap-9131	57	2	any	any	DET
ap-9131	57	3	m	m	NOUN
ap-9131	57	4	,	,	PUNCT
ap-9131	57	5	n	n	CCONJ
ap-9131	57	6	non	non	ADJ
ap-9131	57	7	-	-	ADJ
ap-9131	57	8	negative	negative	ADJ
ap-9131	57	9	integers	integer	NOUN
ap-9131	57	10	,	,	PUNCT
ap-9131	57	11	let	let	VERB
ap-9131	57	12	us	we	PRON
ap-9131	57	13	take	take	VERB
ap-9131	57	14	:	:	PUNCT
ap-9131	57	15	α1	α1	PROPN
ap-9131	57	16	=	=	SYM
ap-9131	57	17	0	0	NUM
ap-9131	57	18	,	,	PUNCT
ap-9131	57	19	α2	α2	NOUN
ap-9131	57	20	=	=	SYM
ap-9131	57	21	−i(n	−i(n	PROPN
ap-9131	57	22	+	+	PROPN
ap-9131	57	23	1	1	NUM
ap-9131	57	24	)	)	PUNCT
ap-9131	57	25	,	,	PUNCT
ap-9131	57	26	α3	α3	NOUN
ap-9131	57	27	=	=	SYM
ap-9131	57	28	−i(m	−i(m	NOUN
ap-9131	57	29	+	+	CCONJ
ap-9131	57	30	n	n	PROPN
ap-9131	57	31	+	+	NOUN
ap-9131	57	32	2	2	NUM
ap-9131	57	33	)	)	PUNCT
ap-9131	57	34	.	.	PUNCT
ap-9131	58	1	this	this	DET
ap-9131	58	2	way	way	NOUN
ap-9131	58	3	(	(	PUNCT
ap-9131	58	4	2	2	X
ap-9131	58	5	)	)	PUNCT
ap-9131	58	6	becomes	become	VERB
ap-9131	58	7	a	a	DET
ap-9131	58	8	realisation	realisation	NOUN
ap-9131	58	9	of	of	ADP
ap-9131	58	10	su(3)c	su(3)c	NOUN
ap-9131	58	11	,	,	PUNCT
ap-9131	58	12	and	and	CCONJ
ap-9131	58	13	also	also	ADV
ap-9131	58	14	of	of	ADP
ap-9131	58	15	the	the	DET
ap-9131	58	16	real	real	ADJ
ap-9131	58	17	form	form	NOUN
ap-9131	58	18	su(3	su(3	PROPN
ap-9131	58	19	)	)	PUNCT
ap-9131	58	20	,	,	PUNCT
ap-9131	58	21	which	which	PRON
ap-9131	58	22	turns	turn	VERB
ap-9131	58	23	out	out	ADP
ap-9131	58	24	to	to	PART
ap-9131	58	25	be	be	AUX
ap-9131	58	26	reducible	reducible	ADJ
ap-9131	58	27	(	(	PUNCT
ap-9131	58	28	see	see	VERB
ap-9131	58	29	theorem	theorem	NOUN
ap-9131	58	30	1	1	NUM
ap-9131	58	31	)	)	PUNCT
ap-9131	58	32	.	.	PUNCT
ap-9131	59	1	(	(	PUNCT
ap-9131	59	2	we	we	PRON
ap-9131	59	3	denote	denote	VERB
ap-9131	59	4	this	this	DET
ap-9131	59	5	realisation	realisation	NOUN
ap-9131	59	6	by	by	ADP
ap-9131	59	7	the	the	DET
ap-9131	59	8	same	same	ADJ
ap-9131	59	9	symbol	symbol	NOUN
ap-9131	59	10	ρ	ρ	PROPN
ap-9131	59	11	.	.	PUNCT
ap-9131	59	12	)	)	PUNCT
ap-9131	59	13	from	from	ADP
ap-9131	59	14	now	now	ADV
ap-9131	59	15	on	on	ADV
ap-9131	59	16	,	,	PUNCT
ap-9131	59	17	we	we	PRON
ap-9131	59	18	suppose	suppose	VERB
ap-9131	59	19	,	,	PUNCT
ap-9131	59	20	for	for	ADP
ap-9131	59	21	technical	technical	ADJ
ap-9131	59	22	reasons	reason	NOUN
ap-9131	59	23	,	,	PUNCT
ap-9131	59	24	m	m	PROPN
ap-9131	59	25	,	,	PUNCT
ap-9131	59	26	n	n	CCONJ
ap-9131	59	27	to	to	PART
ap-9131	59	28	be	be	AUX
ap-9131	59	29	even	even	ADV
ap-9131	59	30	integers	integer	NOUN
ap-9131	59	31	such	such	ADJ
ap-9131	59	32	that	that	SCONJ
ap-9131	59	33	m	m	PROPN
ap-9131	59	34	≥	≥	PROPN
ap-9131	59	35	n.	n.	NOUN
ap-9131	59	36	(	(	PUNCT
ap-9131	59	37	the	the	DET
ap-9131	59	38	process	process	NOUN
ap-9131	59	39	would	would	AUX
ap-9131	59	40	differ	differ	VERB
ap-9131	59	41	slightly	slightly	ADV
ap-9131	59	42	for	for	ADP
ap-9131	59	43	the	the	DET
ap-9131	59	44	case	case	NOUN
ap-9131	59	45	of	of	ADP
ap-9131	59	46	m	m	PROPN
ap-9131	59	47	,	,	PUNCT
ap-9131	59	48	n	n	PRON
ap-9131	59	49	being	be	AUX
ap-9131	59	50	odd	odd	ADJ
ap-9131	59	51	,	,	PUNCT
ap-9131	59	52	we	we	PRON
ap-9131	59	53	omit	omit	VERB
ap-9131	59	54	details	detail	NOUN
ap-9131	59	55	here	here	ADV
ap-9131	59	56	for	for	ADP
ap-9131	59	57	brevity	brevity	NOUN
ap-9131	59	58	.	.	PUNCT
ap-9131	59	59	)	)	PUNCT
ap-9131	60	1	let	let	VERB
ap-9131	60	2	us	we	PRON
ap-9131	60	3	now	now	ADV
ap-9131	60	4	denote	denote	VERB
ap-9131	60	5	:	:	PUNCT
ap-9131	61	1	y	y	PROPN
ap-9131	61	2	=	=	PUNCT
ap-9131	61	3	x1	x1	PROPN
ap-9131	62	1	+	+	NUM
ap-9131	62	2	x2x3	x2x3	PROPN
ap-9131	62	3	,	,	PUNCT
ap-9131	62	4	and	and	CCONJ
ap-9131	62	5	let	let	VERB
ap-9131	62	6	us	we	PRON
ap-9131	62	7	take	take	VERB
ap-9131	62	8	the	the	DET
ap-9131	62	9	polynomials	polynomial	NOUN
ap-9131	62	10	from	from	ADP
ap-9131	62	11	the	the	DET
ap-9131	62	12	representation	representation	NOUN
ap-9131	62	13	space	space	NOUN
ap-9131	62	14	c[x1	c[x1	NOUN
ap-9131	62	15	,	,	PUNCT
ap-9131	62	16	x2	x2	PROPN
ap-9131	62	17	,	,	PUNCT
ap-9131	62	18	x3	x3	PROPN
ap-9131	62	19	]	]	PUNCT
ap-9131	62	20	which	which	PRON
ap-9131	62	21	are	be	AUX
ap-9131	62	22	given	give	VERB
ap-9131	62	23	in	in	ADP
ap-9131	62	24	table	table	NOUN
ap-9131	62	25	1	1	NUM
ap-9131	62	26	.	.	PUNCT
ap-9131	63	1	let	let	VERB
ap-9131	63	2	us	we	PRON
ap-9131	63	3	define	define	VERB
ap-9131	63	4	the	the	DET
ap-9131	63	5	subspace	subspace	NOUN
ap-9131	63	6	p	p	PROPN
ap-9131	63	7	⊂	⊂	PROPN
ap-9131	63	8	c[x1	c[x1	PROPN
ap-9131	63	9	,	,	PUNCT
ap-9131	63	10	x2	x2	PROPN
ap-9131	63	11	,	,	PUNCT
ap-9131	63	12	x3	x3	ADJ
ap-9131	63	13	]	]	PUNCT
ap-9131	63	14	as	as	ADP
ap-9131	63	15	a	a	DET
ap-9131	63	16	linear	linear	ADJ
ap-9131	63	17	span	span	NOUN
ap-9131	63	18	of	of	ADP
ap-9131	63	19	all	all	DET
ap-9131	63	20	these	these	DET
ap-9131	63	21	polynomials	polynomial	NOUN
ap-9131	63	22	.	.	PUNCT
ap-9131	64	1	this	this	PRON
ap-9131	64	2	turns	turn	VERB
ap-9131	64	3	out	out	ADP
ap-9131	64	4	to	to	PART
ap-9131	64	5	be	be	AUX
ap-9131	64	6	an	an	DET
ap-9131	64	7	invariant	invariant	ADJ
ap-9131	64	8	subspace	subspace	NOUN
ap-9131	64	9	of	of	ADP
ap-9131	64	10	ρ	ρ	PROPN
ap-9131	64	11	(	(	PUNCT
ap-9131	64	12	see	see	VERB
ap-9131	64	13	lemma	lemma	PROPN
ap-9131	64	14	2	2	NUM
ap-9131	64	15	)	)	PUNCT
ap-9131	64	16	.	.	PUNCT
ap-9131	65	1	to	to	PART
ap-9131	65	2	show	show	VERB
ap-9131	65	3	this	this	PRON
ap-9131	65	4	,	,	PUNCT
ap-9131	65	5	we	we	PRON
ap-9131	65	6	start	start	VERB
ap-9131	65	7	with	with	ADP
ap-9131	65	8	a	a	DET
ap-9131	65	9	finding	finding	NOUN
ap-9131	65	10	of	of	ADP
ap-9131	65	11	a	a	DET
ap-9131	65	12	suitable	suitable	ADJ
ap-9131	65	13	set	set	NOUN
ap-9131	65	14	of	of	ADP
ap-9131	65	15	su(3)c	su(3)c	PROPN
ap-9131	65	16	algebra	algebra	NOUN
ap-9131	65	17	generators	generator	NOUN
ap-9131	65	18	.	.	PUNCT
ap-9131	66	1	lemma	lemma	PROPN
ap-9131	66	2	1	1	NUM
ap-9131	66	3	.	.	PUNCT
ap-9131	67	1	su(3)c	su(3)c	NOUN
ap-9131	67	2	is	be	AUX
ap-9131	67	3	generated	generate	VERB
ap-9131	67	4	(	(	PUNCT
ap-9131	67	5	as	as	ADP
ap-9131	67	6	a	a	DET
ap-9131	67	7	lie	lie	NOUN
ap-9131	67	8	algebra	algebra	NOUN
ap-9131	67	9	)	)	PUNCT
ap-9131	67	10	by	by	ADP
ap-9131	67	11	the	the	DET
ap-9131	67	12	generators	generator	NOUN
ap-9131	67	13	:	:	PUNCT
ap-9131	67	14	e12	e12	NOUN
ap-9131	67	15	,	,	PUNCT
ap-9131	67	16	e23	e23	PROPN
ap-9131	67	17	,	,	PUNCT
ap-9131	67	18	e31	e31	PROPN
ap-9131	67	19	.	.	PUNCT
ap-9131	68	1	proof	proof	NOUN
ap-9131	68	2	.	.	PUNCT
ap-9131	69	1	first	first	ADV
ap-9131	69	2	,	,	PUNCT
ap-9131	69	3	using	use	VERB
ap-9131	69	4	e12	e12	NOUN
ap-9131	69	5	and	and	CCONJ
ap-9131	69	6	e23	e23	NOUN
ap-9131	69	7	,	,	PUNCT
ap-9131	69	8	we	we	PRON
ap-9131	69	9	obtain	obtain	VERB
ap-9131	69	10	the	the	DET
ap-9131	69	11	generator	generator	NOUN
ap-9131	69	12	e13	e13	PROPN
ap-9131	69	13	,	,	PUNCT
ap-9131	69	14	because	because	SCONJ
ap-9131	69	15	:	:	PUNCT
ap-9131	69	16	[	[	X
ap-9131	69	17	e12	e12	NOUN
ap-9131	69	18	,	,	PUNCT
ap-9131	69	19	e23	e23	NOUN
ap-9131	69	20	]	]	X
ap-9131	69	21	=	=	SYM
ap-9131	69	22	e13	e13	PROPN
ap-9131	69	23	.	.	PUNCT
ap-9131	70	1	then	then	ADV
ap-9131	70	2	,	,	PUNCT
ap-9131	70	3	using	use	VERB
ap-9131	70	4	e23	e23	NOUN
ap-9131	70	5	and	and	CCONJ
ap-9131	70	6	e31	e31	PROPN
ap-9131	70	7	,	,	PUNCT
ap-9131	70	8	we	we	PRON
ap-9131	70	9	obtain	obtain	VERB
ap-9131	70	10	e21	e21	NUM
ap-9131	70	11	:	:	PUNCT
ap-9131	70	12	[	[	X
ap-9131	70	13	e23	e23	X
ap-9131	70	14	,	,	PUNCT
ap-9131	70	15	e31	e31	PROPN
ap-9131	70	16	]	]	X
ap-9131	70	17	=	=	SYM
ap-9131	70	18	e21	e21	PROPN
ap-9131	70	19	.	.	PUNCT
ap-9131	71	1	similarly	similarly	ADV
ap-9131	71	2	,	,	PUNCT
ap-9131	71	3	we	we	PRON
ap-9131	71	4	get	get	VERB
ap-9131	71	5	h1	h1	ADJ
ap-9131	71	6	by	by	ADP
ap-9131	71	7	:	:	PUNCT
ap-9131	71	8	[	[	X
ap-9131	71	9	e12	e12	NOUN
ap-9131	71	10	,	,	PUNCT
ap-9131	71	11	e21	e21	PROPN
ap-9131	71	12	]	]	PUNCT
ap-9131	71	13	=	=	SYM
ap-9131	71	14	h1	h1	PROPN
ap-9131	71	15	,	,	PUNCT
ap-9131	71	16	and	and	CCONJ
ap-9131	71	17	e32	e32	ADJ
ap-9131	71	18	by	by	ADP
ap-9131	71	19	:	:	PUNCT
ap-9131	72	1	[	[	X
ap-9131	72	2	e31	e31	X
ap-9131	72	3	,	,	PUNCT
ap-9131	72	4	e12	e12	NOUN
ap-9131	72	5	]	]	X
ap-9131	72	6	=	=	SYM
ap-9131	72	7	e32	e32	NOUN
ap-9131	72	8	.	.	PUNCT
ap-9131	73	1	finally	finally	ADV
ap-9131	73	2	,	,	PUNCT
ap-9131	73	3	we	we	PRON
ap-9131	73	4	obtain	obtain	VERB
ap-9131	73	5	h2	h2	NOUN
ap-9131	73	6	using	use	VERB
ap-9131	73	7	:	:	PUNCT
ap-9131	74	1	[	[	X
ap-9131	74	2	e23	e23	ADJ
ap-9131	74	3	,	,	PUNCT
ap-9131	74	4	e32	e32	NOUN
ap-9131	74	5	]	]	X
ap-9131	74	6	=	=	SYM
ap-9131	74	7	h2	h2	NOUN
ap-9131	74	8	.	.	PROPN
ap-9131	74	9	1	1	NUM
ap-9131	74	10	)	)	PUNCT
ap-9131	74	11	xm−j	xm−j	NOUN
ap-9131	74	12	1	1	NUM
ap-9131	74	13	xn−b−j	xn−b−j	PROPN
ap-9131	74	14	3	3	NUM
ap-9131	74	15	ybxk	ybxk	NOUN
ap-9131	74	16	1(x2x3)j−k	1(x2x3)j−k	NUM
ap-9131	74	17	,	,	PUNCT
ap-9131	74	18	0	0	NUM
ap-9131	74	19	≤	≤	NUM
ap-9131	74	20	b	b	X
ap-9131	74	21	≤	≤	NUM
ap-9131	74	22	n	n	CCONJ
ap-9131	74	23	,	,	PUNCT
ap-9131	74	24	0	0	NUM
ap-9131	74	25	≤	≤	NUM
ap-9131	74	26	j	j	PROPN
ap-9131	74	27	≤	≤	PROPN
ap-9131	74	28	n	n	CCONJ
ap-9131	74	29	−	−	PROPN
ap-9131	74	30	b	b	PROPN
ap-9131	74	31	,	,	PUNCT
ap-9131	74	32	0	0	NUM
ap-9131	74	33	≤	≤	NUM
ap-9131	74	34	k	k	X
ap-9131	74	35	≤	≤	PROPN
ap-9131	74	36	j	j	PROPN
ap-9131	74	37	,	,	PUNCT
ap-9131	74	38	2	2	NUM
ap-9131	74	39	)	)	PUNCT
ap-9131	74	40	xm−j	xm−j	NOUN
ap-9131	74	41	1	1	NUM
ap-9131	74	42	x	x	SYM
ap-9131	74	43	j−(n−b	j−(n−b	PROPN
ap-9131	74	44	)	)	PUNCT
ap-9131	74	45	2	2	NUM
ap-9131	74	46	ybxk	ybxk	NOUN
ap-9131	74	47	1(x2x3)n−b−k	1(x2x3)n−b−k	NUM
ap-9131	74	48	,	,	PUNCT
ap-9131	74	49	0	0	NUM
ap-9131	74	50	≤	≤	NUM
ap-9131	74	51	b	b	X
ap-9131	74	52	≤	≤	NUM
ap-9131	74	53	n	n	CCONJ
ap-9131	74	54	,	,	PUNCT
ap-9131	74	55	n	n	CCONJ
ap-9131	74	56	−	−	PROPN
ap-9131	74	57	b	b	NOUN
ap-9131	74	58	+	+	CCONJ
ap-9131	74	59	1	1	NUM
ap-9131	74	60	≤	≤	NUM
ap-9131	74	61	j	j	PROPN
ap-9131	74	62	≤	≤	PROPN
ap-9131	74	63	m	m	PROPN
ap-9131	74	64	,	,	PUNCT
ap-9131	74	65	0	0	NUM
ap-9131	74	66	≤	≤	NUM
ap-9131	74	67	k	k	NOUN
ap-9131	74	68	≤	≤	NUM
ap-9131	74	69	n	n	CCONJ
ap-9131	74	70	−	−	PROPN
ap-9131	74	71	b	b	PROPN
ap-9131	74	72	,	,	PUNCT
ap-9131	74	73	3	3	NUM
ap-9131	74	74	)	)	PUNCT
ap-9131	74	75	x	x	SYM
ap-9131	74	76	j−(n−b	j−(n−b	PROPN
ap-9131	74	77	)	)	PUNCT
ap-9131	74	78	2	2	NUM
ap-9131	74	79	ybxk	ybxk	NOUN
ap-9131	74	80	1(x2x3)m+n−b−j−k	1(x2x3)m+n−b−j−k	NOUN
ap-9131	74	81	,	,	PUNCT
ap-9131	74	82	0	0	NUM
ap-9131	74	83	≤	≤	NUM
ap-9131	74	84	b	b	X
ap-9131	74	85	≤	≤	NUM
ap-9131	74	86	n	n	CCONJ
ap-9131	74	87	,	,	PUNCT
ap-9131	74	88	m	m	VERB
ap-9131	74	89	+	+	ADJ
ap-9131	74	90	1	1	NUM
ap-9131	74	91	≤	≤	NUM
ap-9131	74	92	j	j	PROPN
ap-9131	74	93	≤	≤	NUM
ap-9131	74	94	m	m	VERB
ap-9131	74	95	+	+	NOUN
ap-9131	74	96	n	n	CCONJ
ap-9131	74	97	−	−	PROPN
ap-9131	74	98	b	b	NOUN
ap-9131	74	99	,	,	PUNCT
ap-9131	74	100	0	0	NUM
ap-9131	74	101	≤	≤	NUM
ap-9131	74	102	k	k	X
ap-9131	75	1	≤	≤	NUM
ap-9131	75	2	m	m	VERB
ap-9131	75	3	+	+	PUNCT
ap-9131	75	4	(	(	PUNCT
ap-9131	75	5	n	n	CCONJ
ap-9131	75	6	−	−	PROPN
ap-9131	75	7	b	b	NOUN
ap-9131	75	8	)	)	PUNCT
ap-9131	75	9	−	−	PROPN
ap-9131	75	10	j	j	PROPN
ap-9131	75	11	,	,	PUNCT
ap-9131	75	12	4	4	NUM
ap-9131	75	13	)	)	PUNCT
ap-9131	75	14	xm−j	xm−j	NOUN
ap-9131	75	15	1	1	NUM
ap-9131	75	16	xn−k	xn−k	PROPN
ap-9131	75	17	3	3	NUM
ap-9131	75	18	xl	xl	PROPN
ap-9131	75	19	1(x2x3)k−l	1(x2x3)k−l	PROPN
ap-9131	75	20	,	,	PUNCT
ap-9131	75	21	1	1	NUM
ap-9131	75	22	≤	≤	NUM
ap-9131	75	23	j	j	PROPN
ap-9131	75	24	≤	≤	NUM
ap-9131	75	25	n	n	CCONJ
ap-9131	75	26	,	,	PUNCT
ap-9131	75	27	0	0	NUM
ap-9131	75	28	≤	≤	NUM
ap-9131	76	1	k	k	X
ap-9131	76	2	≤	≤	PROPN
ap-9131	76	3	j	j	PROPN
ap-9131	77	1	−	−	PROPN
ap-9131	77	2	1	1	NUM
ap-9131	77	3	,	,	PUNCT
ap-9131	77	4	0	0	NUM
ap-9131	77	5	≤	≤	NUM
ap-9131	77	6	l	l	NOUN
ap-9131	77	7	≤	≤	NOUN
ap-9131	78	1	k	k	NOUN
ap-9131	78	2	,	,	PUNCT
ap-9131	78	3	5	5	NUM
ap-9131	78	4	)	)	PUNCT
ap-9131	78	5	xm−j	xm−j	PROPN
ap-9131	78	6	1	1	NUM
ap-9131	78	7	xn−k	xn−k	PROPN
ap-9131	78	8	3	3	NUM
ap-9131	78	9	xl	xl	PROPN
ap-9131	78	10	1(x2x3)k−l	1(x2x3)k−l	PROPN
ap-9131	78	11	,	,	PUNCT
ap-9131	78	12	n	n	PROPN
ap-9131	78	13	+	+	CCONJ
ap-9131	78	14	1	1	NUM
ap-9131	78	15	≤	≤	NUM
ap-9131	78	16	j	j	PROPN
ap-9131	78	17	≤	≤	PROPN
ap-9131	78	18	m	m	PROPN
ap-9131	78	19	,	,	PUNCT
ap-9131	78	20	0	0	NUM
ap-9131	78	21	≤	≤	NUM
ap-9131	78	22	k	k	X
ap-9131	78	23	≤	≤	NUM
ap-9131	78	24	n	n	CCONJ
ap-9131	78	25	,	,	PUNCT
ap-9131	78	26	0	0	NUM
ap-9131	78	27	≤	≤	NUM
ap-9131	78	28	l	l	NOUN
ap-9131	78	29	≤	≤	NOUN
ap-9131	79	1	k	k	NOUN
ap-9131	79	2	,	,	PUNCT
ap-9131	79	3	6	6	NUM
ap-9131	79	4	)	)	PUNCT
ap-9131	79	5	xm−j	xm−j	PROPN
ap-9131	79	6	1	1	NUM
ap-9131	79	7	xk−n	xk−n	PROPN
ap-9131	79	8	2	2	NUM
ap-9131	79	9	xl	xl	PROPN
ap-9131	79	10	1(x2x3)n−l	1(x2x3)n−l	NUM
ap-9131	79	11	,	,	PUNCT
ap-9131	79	12	n	n	PROPN
ap-9131	79	13	+	+	CCONJ
ap-9131	79	14	2	2	NUM
ap-9131	79	15	≤	≤	NUM
ap-9131	79	16	j	j	PROPN
ap-9131	79	17	≤	≤	NUM
ap-9131	79	18	m	m	PROPN
ap-9131	79	19	,	,	PUNCT
ap-9131	79	20	n	n	PROPN
ap-9131	79	21	+	+	CCONJ
ap-9131	79	22	1	1	NUM
ap-9131	79	23	≤	≤	NUM
ap-9131	79	24	k	k	PROPN
ap-9131	79	25	≤	≤	PROPN
ap-9131	79	26	j	j	PROPN
ap-9131	80	1	−	−	PROPN
ap-9131	80	2	1	1	NUM
ap-9131	80	3	,	,	PUNCT
ap-9131	80	4	0	0	NUM
ap-9131	80	5	≤	≤	NUM
ap-9131	80	6	l	l	NOUN
ap-9131	80	7	≤	≤	NOUN
ap-9131	80	8	n	n	CCONJ
ap-9131	80	9	,	,	PUNCT
ap-9131	80	10	7	7	NUM
ap-9131	80	11	)	)	PUNCT
ap-9131	80	12	xm−j	xm−j	PROPN
ap-9131	80	13	2	2	NUM
ap-9131	80	14	xl	xl	PROPN
ap-9131	80	15	1(x2x3)k−l	1(x2x3)k−l	PROPN
ap-9131	80	16	,	,	PUNCT
ap-9131	80	17	1	1	NUM
ap-9131	80	18	≤	≤	NUM
ap-9131	80	19	j	j	PROPN
ap-9131	80	20	≤	≤	NUM
ap-9131	80	21	n	n	CCONJ
ap-9131	80	22	,	,	PUNCT
ap-9131	80	23	0	0	NUM
ap-9131	80	24	≤	≤	NUM
ap-9131	81	1	k	k	X
ap-9131	81	2	≤	≤	PROPN
ap-9131	81	3	j	j	PROPN
ap-9131	82	1	−	−	PROPN
ap-9131	82	2	1	1	NUM
ap-9131	82	3	,	,	PUNCT
ap-9131	82	4	0	0	NUM
ap-9131	82	5	≤	≤	NUM
ap-9131	82	6	l	l	NOUN
ap-9131	82	7	≤	≤	NOUN
ap-9131	82	8	k	k	X
ap-9131	82	9	,	,	PUNCT
ap-9131	82	10	8)	8)	NUM
ap-9131	82	11	xm−j	xm−j	NOUN
ap-9131	82	12	2	2	NUM
ap-9131	82	13	xl	xl	PROPN
ap-9131	82	14	1(x2x3)k−l	1(x2x3)k−l	PROPN
ap-9131	82	15	,	,	PUNCT
ap-9131	82	16	n	n	PROPN
ap-9131	82	17	+	+	CCONJ
ap-9131	82	18	1	1	NUM
ap-9131	82	19	≤	≤	NUM
ap-9131	82	20	j	j	PROPN
ap-9131	82	21	≤	≤	PROPN
ap-9131	82	22	m	m	PROPN
ap-9131	82	23	,	,	PUNCT
ap-9131	82	24	0	0	NUM
ap-9131	82	25	≤	≤	NUM
ap-9131	82	26	k	k	NOUN
ap-9131	82	27	≤	≤	NUM
ap-9131	82	28	n	n	CCONJ
ap-9131	82	29	−	−	PROPN
ap-9131	82	30	1	1	NUM
ap-9131	82	31	,	,	PUNCT
ap-9131	82	32	0	0	NUM
ap-9131	82	33	≤	≤	NUM
ap-9131	82	34	l	l	NOUN
ap-9131	82	35	≤	≤	NOUN
ap-9131	83	1	k	k	NOUN
ap-9131	83	2	,	,	PUNCT
ap-9131	83	3	9	9	X
ap-9131	83	4	)	)	PUNCT
ap-9131	83	5	xn−j	xn−j	NOUN
ap-9131	83	6	3	3	NUM
ap-9131	83	7	xl	xl	PROPN
ap-9131	83	8	1(x2x3)k−l	1(x2x3)k−l	PROPN
ap-9131	83	9	,	,	PUNCT
ap-9131	83	10	1	1	NUM
ap-9131	83	11	≤	≤	NUM
ap-9131	83	12	j	j	PROPN
ap-9131	83	13	≤	≤	PROPN
ap-9131	83	14	n	n	CCONJ
ap-9131	83	15	−	−	PROPN
ap-9131	83	16	1	1	NUM
ap-9131	83	17	,	,	PUNCT
ap-9131	83	18	0	0	NUM
ap-9131	83	19	≤	≤	NUM
ap-9131	83	20	k	k	X
ap-9131	83	21	≤	≤	PROPN
ap-9131	83	22	j	j	PROPN
ap-9131	84	1	−	−	PROPN
ap-9131	84	2	1	1	NUM
ap-9131	84	3	,	,	PUNCT
ap-9131	84	4	0	0	NUM
ap-9131	84	5	≤	≤	NUM
ap-9131	84	6	l	l	NOUN
ap-9131	84	7	≤	≤	PROPN
ap-9131	84	8	k.	k.	NOUN
ap-9131	84	9	table	table	PROPN
ap-9131	84	10	1	1	NUM
ap-9131	84	11	.	.	PUNCT
ap-9131	85	1	p	p	NOUN
ap-9131	85	2	.	.	PUNCT
ap-9131	86	1	note	note	NOUN
ap-9131	86	2	1	1	NUM
ap-9131	86	3	.	.	PUNCT
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ap-9131	87	2	,	,	PUNCT
ap-9131	87	3	one	one	PRON
ap-9131	87	4	can	can	AUX
ap-9131	87	5	show	show	VERB
ap-9131	87	6	that	that	SCONJ
ap-9131	87	7	su(3)c	su(3)c	PROPN
ap-9131	87	8	is	be	AUX
ap-9131	87	9	generated	generate	VERB
ap-9131	87	10	by	by	ADP
ap-9131	87	11	the	the	DET
ap-9131	87	12	triplet	triplet	NOUN
ap-9131	87	13	:	:	PUNCT
ap-9131	87	14	e13	e13	PROPN
ap-9131	87	15	,	,	PUNCT
ap-9131	87	16	e21	e21	NUM
ap-9131	87	17	,	,	PUNCT
ap-9131	87	18	e32	e32	PROPN
ap-9131	87	19	.	.	PUNCT
ap-9131	88	1	lemma	lemma	PROPN
ap-9131	88	2	2	2	NUM
ap-9131	88	3	.	.	X
ap-9131	89	1	p	p	NOUN
ap-9131	89	2	is	be	AUX
ap-9131	89	3	an	an	DET
ap-9131	89	4	invariant	invariant	ADJ
ap-9131	89	5	subspace	subspace	NOUN
ap-9131	89	6	of	of	ADP
ap-9131	89	7	the	the	DET
ap-9131	89	8	realisation	realisation	NOUN
ap-9131	89	9	ρ	ρ	NOUN
ap-9131	89	10	of	of	ADP
ap-9131	89	11	su(3)c	su(3)c	NOUN
ap-9131	89	12	given	give	VERB
ap-9131	89	13	by	by	ADP
ap-9131	89	14	(	(	PUNCT
ap-9131	89	15	2	2	NUM
ap-9131	89	16	)	)	PUNCT
ap-9131	89	17	.	.	PUNCT
ap-9131	90	1	proof	proof	NOUN
ap-9131	90	2	.	.	PUNCT
ap-9131	91	1	due	due	ADP
ap-9131	91	2	to	to	ADP
ap-9131	91	3	lemma	lemma	PROPN
ap-9131	91	4	1	1	NUM
ap-9131	91	5	,	,	PUNCT
ap-9131	91	6	it	it	PRON
ap-9131	91	7	is	be	AUX
ap-9131	91	8	sufficient	sufficient	ADJ
ap-9131	91	9	to	to	PART
ap-9131	91	10	show	show	VERB
ap-9131	91	11	that	that	SCONJ
ap-9131	91	12	p	p	NOUN
ap-9131	91	13	is	be	AUX
ap-9131	91	14	invariant	invariant	ADJ
ap-9131	91	15	with	with	ADP
ap-9131	91	16	respect	respect	NOUN
ap-9131	91	17	to	to	ADP
ap-9131	91	18	ρ(e12	ρ(e12	NOUN
ap-9131	91	19	)	)	PUNCT
ap-9131	91	20	,	,	PUNCT
ap-9131	91	21	ρ(e23	ρ(e23	NUM
ap-9131	91	22	)	)	PUNCT
ap-9131	91	23	,	,	PUNCT
ap-9131	91	24	and	and	CCONJ
ap-9131	91	25	ρ(e31	ρ(e31	NUM
ap-9131	91	26	)	)	PUNCT
ap-9131	91	27	.	.	PUNCT
ap-9131	92	1	let	let	VERB
ap-9131	92	2	us	we	PRON
ap-9131	92	3	start	start	VERB
ap-9131	92	4	with	with	ADP
ap-9131	92	5	ρ(e31	ρ(e31	NUM
ap-9131	92	6	)	)	PUNCT
ap-9131	93	1	=	=	SYM
ap-9131	93	2	−∂1	−∂1	PROPN
ap-9131	93	3	.	.	PUNCT
ap-9131	94	1	first	first	ADV
ap-9131	94	2	,	,	PUNCT
ap-9131	94	3	let	let	VERB
ap-9131	94	4	us	we	PRON
ap-9131	94	5	apply	apply	VERB
ap-9131	94	6	ρ(e31	ρ(e31	NOUN
ap-9131	94	7	)	)	PUNCT
ap-9131	94	8	to	to	ADP
ap-9131	94	9	polynomial	polynomial	ADJ
ap-9131	94	10	of	of	ADP
ap-9131	94	11	type	type	NOUN
ap-9131	94	12	1	1	NUM
ap-9131	94	13	)	)	PUNCT
ap-9131	94	14	from	from	ADP
ap-9131	94	15	table	table	NOUN
ap-9131	94	16	1	1	NUM
ap-9131	94	17	.	.	PUNCT
ap-9131	95	1	we	we	PRON
ap-9131	95	2	obtain	obtain	VERB
ap-9131	95	3	:	:	PUNCT
ap-9131	95	4	ρ(e31)(xm−j	ρ(e31)(xm−j	PROPN
ap-9131	95	5	1	1	NUM
ap-9131	95	6	xn−b−j	xn−b−j	PROPN
ap-9131	95	7	3	3	NUM
ap-9131	95	8	ybxk	ybxk	NOUN
ap-9131	95	9	1(x2x3)j−k	1(x2x3)j−k	NUM
ap-9131	95	10	)	)	PUNCT
ap-9131	95	11	=	=	SYM
ap-9131	95	12	−	−	PROPN
ap-9131	96	1	bxm−j	bxm−j	ADP
ap-9131	96	2	1	1	NUM
ap-9131	96	3	xn−b−j	xn−b−j	PROPN
ap-9131	96	4	3	3	NUM
ap-9131	96	5	xk	xk	PROPN
ap-9131	96	6	1(x2x3)j−kyb−1−	1(x2x3)j−kyb−1−	NUM
ap-9131	96	7	(	(	PUNCT
ap-9131	96	8	m	m	PROPN
ap-9131	96	9	−	−	PROPN
ap-9131	96	10	j	j	PROPN
ap-9131	97	1	+	+	CCONJ
ap-9131	97	2	k)xm−j−1	k)xm−j−1	PROPN
ap-9131	97	3	1	1	NUM
ap-9131	97	4	xn−b−j	xn−b−j	PROPN
ap-9131	97	5	3	3	NUM
ap-9131	97	6	xk	xk	PROPN
ap-9131	97	7	1(x2x3)j−kyb	1(x2x3)j−kyb	NUM
ap-9131	97	8	.	.	PUNCT
ap-9131	98	1	when	when	SCONJ
ap-9131	98	2	b	b	X
ap-9131	98	3	>	>	X
ap-9131	98	4	0	0	PROPN
ap-9131	98	5	,	,	PUNCT
ap-9131	98	6	this	this	DET
ap-9131	98	7	result	result	NOUN
ap-9131	98	8	falls	fall	VERB
ap-9131	98	9	into	into	ADP
ap-9131	98	10	the	the	DET
ap-9131	98	11	group	group	NOUN
ap-9131	98	12	1	1	NUM
ap-9131	98	13	)	)	PUNCT
ap-9131	98	14	in	in	ADP
ap-9131	98	15	table	table	NOUN
ap-9131	98	16	1	1	NUM
ap-9131	98	17	.	.	PUNCT
ap-9131	99	1	when	when	SCONJ
ap-9131	99	2	b	b	X
ap-9131	99	3	>	>	X
ap-9131	99	4	0	0	PUNCT
ap-9131	100	1	and	and	CCONJ
ap-9131	100	2	j	j	PROPN
ap-9131	100	3	<	<	X
ap-9131	100	4	n	n	CCONJ
ap-9131	100	5	,	,	PUNCT
ap-9131	100	6	this	this	DET
ap-9131	100	7	result	result	NOUN
ap-9131	100	8	falls	fall	VERB
ap-9131	100	9	into	into	ADP
ap-9131	100	10	the	the	DET
ap-9131	100	11	group	group	NOUN
ap-9131	100	12	4	4	NUM
ap-9131	100	13	)	)	PUNCT
ap-9131	100	14	.	.	PUNCT
ap-9131	101	1	finally	finally	ADV
ap-9131	101	2	,	,	PUNCT
ap-9131	101	3	when	when	SCONJ
ap-9131	101	4	b	b	X
ap-9131	101	5	>	>	X
ap-9131	101	6	0	0	PROPN
ap-9131	101	7	and	and	CCONJ
ap-9131	101	8	j	j	PROPN
ap-9131	101	9	=	=	SYM
ap-9131	101	10	n	n	CCONJ
ap-9131	101	11	,	,	PUNCT
ap-9131	101	12	this	this	DET
ap-9131	101	13	result	result	NOUN
ap-9131	101	14	falls	fall	VERB
ap-9131	101	15	into	into	ADP
ap-9131	101	16	the	the	DET
ap-9131	101	17	group	group	NOUN
ap-9131	101	18	5	5	NUM
ap-9131	101	19	)	)	PUNCT
ap-9131	101	20	.	.	PUNCT
ap-9131	102	1	for	for	ADP
ap-9131	102	2	other	other	ADJ
ap-9131	102	3	types	type	NOUN
ap-9131	102	4	2)–9	2)–9	NUM
ap-9131	102	5	)	)	PUNCT
ap-9131	102	6	,	,	PUNCT
ap-9131	102	7	we	we	PRON
ap-9131	102	8	get	get	VERB
ap-9131	102	9	similar	similar	ADJ
ap-9131	102	10	results	result	NOUN
ap-9131	102	11	.	.	PUNCT
ap-9131	103	1	for	for	ADP
ap-9131	103	2	the	the	DET
ap-9131	103	3	operators	operator	NOUN
ap-9131	103	4	ρ(e23	ρ(e23	NUM
ap-9131	103	5	)	)	PUNCT
ap-9131	103	6	and	and	CCONJ
ap-9131	103	7	ρ(e31	ρ(e31	NUM
ap-9131	103	8	)	)	PUNCT
ap-9131	103	9	,	,	PUNCT
ap-9131	103	10	we	we	PRON
ap-9131	103	11	proceed	proceed	VERB
ap-9131	103	12	similarly	similarly	ADV
ap-9131	103	13	.	.	PUNCT
ap-9131	104	1	we	we	PRON
ap-9131	104	2	will	will	AUX
ap-9131	104	3	denote	denote	VERB
ap-9131	104	4	the	the	DET
ap-9131	104	5	restriction	restriction	NOUN
ap-9131	104	6	of	of	ADP
ap-9131	104	7	ρ	ρ	PROPN
ap-9131	104	8	on	on	ADP
ap-9131	104	9	the	the	DET
ap-9131	104	10	subspace	subspace	NOUN
ap-9131	104	11	p	p	NOUN
ap-9131	104	12	by	by	ADP
ap-9131	104	13	the	the	DET
ap-9131	104	14	same	same	ADJ
ap-9131	104	15	symbol	symbol	NOUN
ap-9131	104	16	ρ	ρ	NOUN
ap-9131	104	17	.	.	PUNCT
ap-9131	105	1	in	in	ADP
ap-9131	105	2	this	this	DET
ap-9131	105	3	way	way	NOUN
ap-9131	105	4	,	,	PUNCT
ap-9131	105	5	ρ	ρ	PROPN
ap-9131	105	6	becomes	become	VERB
ap-9131	105	7	finite	finite	ADJ
ap-9131	105	8	dimensional	dimensional	ADJ
ap-9131	105	9	representation	representation	NOUN
ap-9131	105	10	on	on	ADP
ap-9131	105	11	p	p	PROPN
ap-9131	105	12	.	.	PUNCT
ap-9131	106	1	theorem	theorem	NOUN
ap-9131	106	2	1	1	NUM
ap-9131	106	3	.	.	PUNCT
ap-9131	107	1	the	the	DET
ap-9131	107	2	polynomials	polynomial	NOUN
ap-9131	107	3	in	in	ADP
ap-9131	107	4	table	table	NOUN
ap-9131	107	5	1	1	NUM
ap-9131	107	6	form	form	NOUN
ap-9131	107	7	a	a	DET
ap-9131	107	8	basis	basis	NOUN
ap-9131	107	9	of	of	ADP
ap-9131	107	10	p	p	NOUN
ap-9131	107	11	.	.	PUNCT
ap-9131	108	1	337	337	NUM
ap-9131	108	2	č	č	NOUN
ap-9131	108	3	.	.	PUNCT
ap-9131	108	4	burdík	burdík	PROPN
ap-9131	108	5	,	,	PUNCT
ap-9131	108	6	s.	s.	PROPN
ap-9131	108	7	pošta	pošta	PROPN
ap-9131	108	8	,	,	PUNCT
ap-9131	108	9	e.	e.	PROPN
ap-9131	108	10	rapp	rapp	PROPN
ap-9131	108	11	acta	acta	PROPN
ap-9131	108	12	polytechnica	polytechnica	PROPN
ap-9131	108	13	proof	proof	NOUN
ap-9131	108	14	.	.	PUNCT
ap-9131	109	1	the	the	DET
ap-9131	109	2	group	group	NOUN
ap-9131	109	3	1	1	NUM
ap-9131	109	4	)	)	PUNCT
ap-9131	109	5	in	in	ADP
ap-9131	109	6	table	table	NOUN
ap-9131	109	7	1	1	NUM
ap-9131	109	8	contains	contain	VERB
ap-9131	109	9	a	a	DET
ap-9131	109	10	polynomial	polynomial	ADJ
ap-9131	109	11	:	:	PUNCT
ap-9131	109	12	v	v	NOUN
ap-9131	109	13	=	=	SYM
ap-9131	109	14	xm	xm	PROPN
ap-9131	109	15	1	1	NUM
ap-9131	109	16	yn	yn	PROPN
ap-9131	109	17	.	.	PUNCT
ap-9131	110	1	(	(	PUNCT
ap-9131	110	2	3	3	X
ap-9131	110	3	)	)	PUNCT
ap-9131	110	4	this	this	DET
ap-9131	110	5	vector	vector	NOUN
ap-9131	110	6	v	v	NOUN
ap-9131	110	7	satisfies	satisfie	NOUN
ap-9131	110	8	:	:	PUNCT
ap-9131	110	9	ρ(h1)v	ρ(h1)v	PROPN
ap-9131	110	10	=	=	SYM
ap-9131	110	11	mv	mv	PROPN
ap-9131	110	12	,	,	PUNCT
ap-9131	110	13	ρ(e12)v	ρ(e12)v	VERB
ap-9131	110	14	=	=	SYM
ap-9131	110	15	0	0	NUM
ap-9131	110	16	,	,	PUNCT
ap-9131	110	17	ρ(h2)v	ρ(h2)v	PROPN
ap-9131	110	18	=	=	SYM
ap-9131	110	19	nv	nv	PROPN
ap-9131	110	20	,	,	PUNCT
ap-9131	110	21	ρ(e23)v	ρ(e23)v	NOUN
ap-9131	110	22	=	=	SYM
ap-9131	110	23	0	0	NUM
ap-9131	110	24	,	,	PUNCT
ap-9131	110	25	i.	i.	PROPN
ap-9131	110	26	e.	e.	PROPN
ap-9131	111	1	it	it	PRON
ap-9131	111	2	is	be	AUX
ap-9131	111	3	the	the	DET
ap-9131	111	4	highest	high	ADJ
ap-9131	111	5	weight	weight	NOUN
ap-9131	111	6	vector	vector	NOUN
ap-9131	111	7	of	of	ADP
ap-9131	111	8	the	the	DET
ap-9131	111	9	representation	representation	NOUN
ap-9131	111	10	ρ	ρ	PROPN
ap-9131	111	11	.	.	PUNCT
ap-9131	112	1	therefore	therefore	ADV
ap-9131	112	2	,	,	PUNCT
ap-9131	112	3	ρ	ρ	PROPN
ap-9131	112	4	contains	contain	VERB
ap-9131	112	5	,	,	PUNCT
ap-9131	112	6	as	as	ADP
ap-9131	112	7	a	a	DET
ap-9131	112	8	subrepresentation	subrepresentation	NOUN
ap-9131	112	9	,	,	PUNCT
ap-9131	112	10	the	the	DET
ap-9131	112	11	representation	representation	NOUN
ap-9131	112	12	of	of	ADP
ap-9131	112	13	the	the	DET
ap-9131	112	14	highest	high	ADJ
ap-9131	112	15	weight	weight	NOUN
ap-9131	112	16	(	(	PUNCT
ap-9131	112	17	m	m	NOUN
ap-9131	112	18	,	,	PUNCT
ap-9131	112	19	n	n	CCONJ
ap-9131	112	20	)	)	PUNCT
ap-9131	112	21	and	and	CCONJ
ap-9131	112	22	the	the	DET
ap-9131	112	23	dimension	dimension	NOUN
ap-9131	112	24	of	of	ADP
ap-9131	112	25	p	p	PROPN
ap-9131	112	26	has	have	VERB
ap-9131	112	27	to	to	PART
ap-9131	112	28	be	be	AUX
ap-9131	112	29	greater	great	ADJ
ap-9131	112	30	or	or	CCONJ
ap-9131	112	31	equal	equal	ADJ
ap-9131	112	32	to	to	ADP
ap-9131	112	33	:	:	PUNCT
ap-9131	112	34	1	1	NUM
ap-9131	112	35	2(m	2(m	NUM
ap-9131	113	1	+	+	CCONJ
ap-9131	113	2	1)(n	1)(n	NUM
ap-9131	113	3	+	+	CCONJ
ap-9131	113	4	1)(m	1)(m	NUM
ap-9131	113	5	+	+	CCONJ
ap-9131	113	6	n	n	NOUN
ap-9131	113	7	+	+	NOUN
ap-9131	113	8	2	2	NUM
ap-9131	113	9	)	)	PUNCT
ap-9131	113	10	,	,	PUNCT
ap-9131	113	11	(	(	PUNCT
ap-9131	113	12	4	4	NUM
ap-9131	113	13	)	)	PUNCT
ap-9131	113	14	(	(	PUNCT
ap-9131	113	15	for	for	ADP
ap-9131	113	16	what	what	PRON
ap-9131	113	17	is	be	AUX
ap-9131	113	18	a	a	DET
ap-9131	113	19	well	well	ADV
ap-9131	113	20	-	-	PUNCT
ap-9131	113	21	known	know	VERB
ap-9131	113	22	formula	formula	NOUN
ap-9131	113	23	for	for	ADP
ap-9131	113	24	the	the	DET
ap-9131	113	25	dimension	dimension	NOUN
ap-9131	113	26	of	of	ADP
ap-9131	113	27	the	the	DET
ap-9131	113	28	representation	representation	NOUN
ap-9131	113	29	of	of	ADP
ap-9131	113	30	the	the	DET
ap-9131	113	31	highest	high	ADJ
ap-9131	113	32	weight	weight	NOUN
ap-9131	113	33	(	(	PUNCT
ap-9131	113	34	m	m	PROPN
ap-9131	113	35	,	,	PUNCT
ap-9131	113	36	n	n	CCONJ
ap-9131	113	37	)	)	PUNCT
ap-9131	113	38	,	,	PUNCT
ap-9131	113	39	see	see	VERB
ap-9131	113	40	[	[	X
ap-9131	113	41	16	16	NUM
ap-9131	113	42	]	]	PUNCT
ap-9131	113	43	,	,	PUNCT
ap-9131	113	44	§	§	PROPN
ap-9131	113	45	24.3	24.3	NUM
ap-9131	113	46	)	)	PUNCT
ap-9131	113	47	.	.	PUNCT
ap-9131	114	1	the	the	DET
ap-9131	114	2	numbers	number	NOUN
ap-9131	114	3	of	of	ADP
ap-9131	114	4	vectors	vector	NOUN
ap-9131	114	5	given	give	VERB
ap-9131	114	6	in	in	ADP
ap-9131	114	7	table	table	NOUN
ap-9131	114	8	1	1	NUM
ap-9131	114	9	are	be	AUX
ap-9131	114	10	given	give	VERB
ap-9131	114	11	in	in	ADP
ap-9131	114	12	table	table	NOUN
ap-9131	114	13	2	2	NUM
ap-9131	114	14	.	.	PUNCT
ap-9131	114	15	because	because	SCONJ
ap-9131	114	16	their	their	PRON
ap-9131	114	17	total	total	ADJ
ap-9131	114	18	count	count	NOUN
ap-9131	114	19	agrees	agree	VERB
ap-9131	114	20	with	with	ADP
ap-9131	114	21	(	(	PUNCT
ap-9131	114	22	4	4	NUM
ap-9131	114	23	)	)	PUNCT
ap-9131	114	24	,	,	PUNCT
ap-9131	114	25	the	the	DET
ap-9131	114	26	dimension	dimension	NOUN
ap-9131	114	27	of	of	ADP
ap-9131	114	28	p	p	NOUN
ap-9131	114	29	is	be	AUX
ap-9131	114	30	equal	equal	ADJ
ap-9131	114	31	to	to	ADP
ap-9131	114	32	(	(	PUNCT
ap-9131	114	33	4	4	NUM
ap-9131	114	34	)	)	PUNCT
ap-9131	114	35	and	and	CCONJ
ap-9131	114	36	the	the	DET
ap-9131	114	37	vectors	vector	NOUN
ap-9131	114	38	in	in	ADP
ap-9131	114	39	table	table	NOUN
ap-9131	114	40	1	1	NUM
ap-9131	114	41	are	be	AUX
ap-9131	114	42	linearly	linearly	ADV
ap-9131	114	43	independent	independent	ADJ
ap-9131	114	44	and	and	CCONJ
ap-9131	114	45	form	form	VERB
ap-9131	114	46	a	a	DET
ap-9131	114	47	basis	basis	NOUN
ap-9131	114	48	of	of	ADP
ap-9131	114	49	p	p	PROPN
ap-9131	114	50	.	.	PUNCT
ap-9131	114	51	example	example	NOUN
ap-9131	115	1	1	1	NUM
ap-9131	115	2	.	.	PUNCT
ap-9131	115	3	an	an	DET
ap-9131	115	4	example	example	NOUN
ap-9131	115	5	of	of	ADP
ap-9131	115	6	the	the	DET
ap-9131	115	7	space	space	NOUN
ap-9131	115	8	p	p	NOUN
ap-9131	115	9	together	together	ADV
ap-9131	115	10	with	with	ADP
ap-9131	115	11	the	the	DET
ap-9131	115	12	weights	weight	NOUN
ap-9131	115	13	of	of	ADP
ap-9131	115	14	the	the	DET
ap-9131	115	15	27	27	NUM
ap-9131	115	16	basis	basis	NOUN
ap-9131	115	17	vectors	vector	NOUN
ap-9131	115	18	for	for	ADP
ap-9131	115	19	the	the	DET
ap-9131	115	20	case	case	NOUN
ap-9131	115	21	of	of	ADP
ap-9131	115	22	the	the	DET
ap-9131	115	23	highest	high	ADJ
ap-9131	115	24	weight	weight	NOUN
ap-9131	115	25	(	(	PUNCT
ap-9131	115	26	2	2	NUM
ap-9131	115	27	,	,	PUNCT
ap-9131	115	28	2	2	NUM
ap-9131	115	29	)	)	PUNCT
ap-9131	115	30	is	be	AUX
ap-9131	115	31	shown	show	VERB
ap-9131	115	32	in	in	ADP
ap-9131	115	33	figure	figure	NOUN
ap-9131	115	34	1	1	NUM
ap-9131	115	35	.	.	PUNCT
ap-9131	116	1	let	let	VERB
ap-9131	116	2	us	we	PRON
ap-9131	116	3	denote	denote	VERB
ap-9131	116	4	:	:	PUNCT
ap-9131	116	5	i0	i0	PROPN
ap-9131	116	6	=	=	PROPN
ap-9131	116	7	i(e21	i(e21	ADJ
ap-9131	116	8	−	−	PROPN
ap-9131	116	9	e12	e12	NOUN
ap-9131	116	10	)	)	PUNCT
ap-9131	116	11	,	,	PUNCT
ap-9131	116	12	i±	i±	NOUN
ap-9131	116	13	=	=	SYM
ap-9131	116	14	i(e31	i(e31	ADJ
ap-9131	116	15	−	−	PROPN
ap-9131	116	16	e13	e13	PROPN
ap-9131	116	17	)	)	PUNCT
ap-9131	116	18	±	±	PROPN
ap-9131	116	19	(	(	PUNCT
ap-9131	116	20	e23	e23	NOUN
ap-9131	116	21	−	−	PROPN
ap-9131	116	22	e32	e32	NOUN
ap-9131	116	23	)	)	PUNCT
ap-9131	116	24	.	.	PUNCT
ap-9131	117	1	then	then	ADV
ap-9131	117	2	:	:	PUNCT
ap-9131	117	3	[	[	X
ap-9131	117	4	i0	i0	PROPN
ap-9131	117	5	,	,	PUNCT
ap-9131	117	6	i±	i±	PROPN
ap-9131	117	7	]	]	X
ap-9131	117	8	=	=	SYM
ap-9131	117	9	±i±	±i±	PROPN
ap-9131	117	10	,	,	PUNCT
ap-9131	117	11	[	[	X
ap-9131	117	12	i+	i+	X
ap-9131	117	13	,	,	PUNCT
ap-9131	117	14	i−	i−	PROPN
ap-9131	117	15	]	]	X
ap-9131	117	16	=	=	SYM
ap-9131	117	17	2i0	2i0	NUM
ap-9131	117	18	,	,	PUNCT
ap-9131	117	19	i.	i.	PROPN
ap-9131	117	20	e.	e.	PROPN
ap-9131	118	1	the	the	DET
ap-9131	118	2	generators	generator	NOUN
ap-9131	118	3	i0	i0	PROPN
ap-9131	118	4	,	,	PUNCT
ap-9131	118	5	i+	i+	NUM
ap-9131	118	6	,	,	PUNCT
ap-9131	118	7	and	and	CCONJ
ap-9131	118	8	i−	i−	PROPN
ap-9131	118	9	form	form	VERB
ap-9131	118	10	a	a	DET
ap-9131	118	11	su(2	su(2	NOUN
ap-9131	118	12	)	)	PUNCT
ap-9131	118	13	≃	≃	ADJ
ap-9131	118	14	so(3	so(3	NOUN
ap-9131	118	15	)	)	PUNCT
ap-9131	118	16	subalgebra	subalgebra	NOUN
ap-9131	118	17	of	of	ADP
ap-9131	118	18	su(3	su(3	PROPN
ap-9131	118	19	)	)	PUNCT
ap-9131	118	20	.	.	PUNCT
ap-9131	119	1	let	let	VERB
ap-9131	119	2	us	we	PRON
ap-9131	119	3	now	now	ADV
ap-9131	119	4	denote	denote	VERB
ap-9131	119	5	:	:	PUNCT
ap-9131	120	1	z	z	NOUN
ap-9131	120	2	=	=	SYM
ap-9131	120	3	1	1	NUM
ap-9131	120	4	+	+	CCONJ
ap-9131	120	5	ix3	ix3	PROPN
ap-9131	120	6	,	,	PUNCT
ap-9131	120	7	χ	χ	PROPN
ap-9131	120	8	=	=	SYM
ap-9131	120	9	x2	x2	PROPN
ap-9131	120	10	−	−	PROPN
ap-9131	120	11	ix1	ix1	NOUN
ap-9131	120	12	,	,	PUNCT
ap-9131	120	13	r	r	NOUN
ap-9131	120	14	=	=	SYM
ap-9131	120	15	2z	2z	NUM
ap-9131	121	1	−	−	PROPN
ap-9131	121	2	z2	z2	PROPN
ap-9131	121	3	+	+	CCONJ
ap-9131	121	4	y2	y2	PROPN
ap-9131	121	5	,	,	PUNCT
ap-9131	121	6	w	w	NOUN
ap-9131	121	7	=	=	SYM
ap-9131	121	8	z	z	PROPN
ap-9131	121	9	+	+	CCONJ
ap-9131	121	10	iyχ	iyχ	ADJ
ap-9131	121	11	,	,	PUNCT
ap-9131	121	12	ξ	ξ	X
ap-9131	121	13	=	=	SYM
ap-9131	121	14	1	1	NUM
ap-9131	121	15	+	+	NUM
ap-9131	121	16	x2	x2	NOUN
ap-9131	121	17	1	1	NUM
ap-9131	121	18	+	+	NUM
ap-9131	121	19	x2	x2	PROPN
ap-9131	121	20	2	2	NUM
ap-9131	121	21	,	,	PUNCT
ap-9131	121	22	and	and	CCONJ
ap-9131	121	23	consider	consider	VERB
ap-9131	121	24	the	the	DET
ap-9131	121	25	polynomials	polynomial	NOUN
ap-9131	121	26	given	give	VERB
ap-9131	121	27	in	in	ADP
ap-9131	121	28	the	the	DET
ap-9131	121	29	table	table	NOUN
ap-9131	121	30	3	3	NUM
ap-9131	121	31	(	(	PUNCT
ap-9131	121	32	we	we	PRON
ap-9131	121	33	call	call	VERB
ap-9131	121	34	them	they	PRON
ap-9131	121	35	“	"	PUNCT
ap-9131	121	36	maximal	maximal	ADJ
ap-9131	121	37	vectors	vector	NOUN
ap-9131	121	38	”	"	PUNCT
ap-9131	121	39	)	)	PUNCT
ap-9131	121	40	.	.	PUNCT
ap-9131	122	1	lemma	lemma	PROPN
ap-9131	122	2	3	3	X
ap-9131	122	3	.	.	PUNCT
ap-9131	122	4	maximal	maximal	ADJ
ap-9131	122	5	vectors	vector	NOUN
ap-9131	122	6	sab	sab	VERB
ap-9131	122	7	and	and	CCONJ
ap-9131	122	8	tka	tka	NOUN
ap-9131	122	9	belong	belong	VERB
ap-9131	122	10	to	to	ADP
ap-9131	122	11	p	p	NOUN
ap-9131	122	12	.	.	PUNCT
ap-9131	123	1	proof	proof	NOUN
ap-9131	123	2	.	.	PUNCT
ap-9131	124	1	this	this	DET
ap-9131	124	2	fact	fact	NOUN
ap-9131	124	3	can	can	AUX
ap-9131	124	4	be	be	AUX
ap-9131	124	5	directly	directly	ADV
ap-9131	124	6	verified	verify	VERB
ap-9131	124	7	from	from	ADP
ap-9131	124	8	the	the	DET
ap-9131	124	9	expanded	expand	VERB
ap-9131	124	10	form	form	NOUN
ap-9131	124	11	of	of	ADP
ap-9131	124	12	the	the	DET
ap-9131	124	13	maximal	maximal	ADJ
ap-9131	124	14	vectors	vector	NOUN
ap-9131	124	15	.	.	PUNCT
ap-9131	125	1	lemma	lemma	PROPN
ap-9131	125	2	4	4	X
ap-9131	125	3	.	.	PUNCT
ap-9131	125	4	maximal	maximal	ADJ
ap-9131	125	5	vectors	vector	NOUN
ap-9131	125	6	sab	sab	VERB
ap-9131	125	7	and	and	CCONJ
ap-9131	125	8	tka	tka	NOUN
ap-9131	125	9	are	be	AUX
ap-9131	125	10	the	the	DET
ap-9131	125	11	highest	high	ADJ
ap-9131	125	12	weight	weight	NOUN
ap-9131	125	13	vectors	vector	NOUN
ap-9131	125	14	for	for	ADP
ap-9131	125	15	the	the	DET
ap-9131	125	16	so(3	so(3	NOUN
ap-9131	125	17	)	)	PUNCT
ap-9131	125	18	triple	triple	NOUN
ap-9131	125	19	(	(	PUNCT
ap-9131	125	20	i0	i0	PROPN
ap-9131	125	21	,	,	PUNCT
ap-9131	125	22	i±	i±	PROPN
ap-9131	125	23	)	)	PUNCT
ap-9131	125	24	,	,	PUNCT
ap-9131	125	25	i.	i.	PROPN
ap-9131	125	26	e.	e.	PROPN
ap-9131	126	1	ρ(i0)sab	ρ(i0)sab	PROPN
ap-9131	126	2	=	=	PRON
ap-9131	127	1	(	(	PUNCT
ap-9131	127	2	b	b	NOUN
ap-9131	127	3	+	+	CCONJ
ap-9131	127	4	m)sab	m)sab	ADJ
ap-9131	127	5	,	,	PUNCT
ap-9131	127	6	ρ(i+)sab	ρ(i+)sab	NUM
ap-9131	127	7	=	=	SYM
ap-9131	127	8	0	0	NUM
ap-9131	127	9	,	,	PUNCT
ap-9131	127	10	ρ(i0)tka	ρ(i0)tka	NOUN
ap-9131	127	11	=	=	PUNCT
ap-9131	127	12	(	(	PUNCT
ap-9131	127	13	m	m	VERB
ap-9131	127	14	−	−	NOUN
ap-9131	127	15	2k	2k	NOUN
ap-9131	127	16	+	+	CCONJ
ap-9131	127	17	a	a	DET
ap-9131	127	18	mod	mod	ADJ
ap-9131	127	19	2)tak	2)tak	NUM
ap-9131	127	20	,	,	PUNCT
ap-9131	127	21	ρ(i+)tka	ρ(i+)tka	PROPN
ap-9131	127	22	=	=	SYM
ap-9131	127	23	0	0	NUM
ap-9131	127	24	.	.	NOUN
ap-9131	127	25	1	1	NUM
ap-9131	127	26	)	)	SYM
ap-9131	127	27	1	1	NUM
ap-9131	127	28	6	6	NUM
ap-9131	127	29	(	(	PUNCT
ap-9131	127	30	n	n	PROPN
ap-9131	127	31	+	+	CCONJ
ap-9131	127	32	1)(n2	1)(n2	NUM
ap-9131	128	1	+	+	NUM
ap-9131	128	2	5n	5n	NUM
ap-9131	128	3	+	+	CCONJ
ap-9131	128	4	6	6	NUM
ap-9131	128	5	)	)	PUNCT
ap-9131	128	6	,	,	PUNCT
ap-9131	128	7	2	2	X
ap-9131	128	8	)	)	PUNCT
ap-9131	128	9	1	1	NUM
ap-9131	128	10	6	6	NUM
ap-9131	128	11	(	(	PUNCT
ap-9131	128	12	n	n	NOUN
ap-9131	128	13	+	+	NOUN
ap-9131	128	14	1)(n	1)(n	NUM
ap-9131	128	15	+	+	NUM
ap-9131	128	16	2)(3	2)(3	NUM
ap-9131	128	17	m	m	NUM
ap-9131	128	18	−	−	NOUN
ap-9131	128	19	2n	2n	NUM
ap-9131	128	20	)	)	PUNCT
ap-9131	128	21	,	,	PUNCT
ap-9131	128	22	3	3	X
ap-9131	128	23	)	)	PUNCT
ap-9131	128	24	1	1	NUM
ap-9131	128	25	6	6	NUM
ap-9131	128	26	n(n	n(n	NOUN
ap-9131	128	27	+	+	CCONJ
ap-9131	128	28	1)(n	1)(n	NUM
ap-9131	128	29	+	+	CCONJ
ap-9131	128	30	2	2	NUM
ap-9131	128	31	)	)	PUNCT
ap-9131	128	32	,	,	PUNCT
ap-9131	128	33	4	4	X
ap-9131	128	34	)	)	PUNCT
ap-9131	128	35	1	1	NUM
ap-9131	128	36	6	6	NUM
ap-9131	128	37	n(n	n(n	NOUN
ap-9131	128	38	+	+	CCONJ
ap-9131	128	39	1)(n	1)(n	NUM
ap-9131	128	40	+	+	CCONJ
ap-9131	128	41	2	2	NUM
ap-9131	128	42	)	)	PUNCT
ap-9131	128	43	,	,	PUNCT
ap-9131	128	44	5	5	X
ap-9131	128	45	)	)	PUNCT
ap-9131	128	46	1	1	NUM
ap-9131	128	47	2	2	NUM
ap-9131	128	48	(	(	PUNCT
ap-9131	128	49	n	n	X
ap-9131	128	50	+	+	NOUN
ap-9131	128	51	1)(n	1)(n	NUM
ap-9131	129	1	+	+	CCONJ
ap-9131	129	2	2)(m	2)(m	NUM
ap-9131	129	3	−	−	NOUN
ap-9131	129	4	n	n	CCONJ
ap-9131	129	5	)	)	PUNCT
ap-9131	129	6	,	,	PUNCT
ap-9131	129	7	6	6	X
ap-9131	129	8	)	)	SYM
ap-9131	129	9	1	1	NUM
ap-9131	129	10	2	2	NUM
ap-9131	129	11	(	(	PUNCT
ap-9131	129	12	n	n	NOUN
ap-9131	129	13	+	+	CCONJ
ap-9131	129	14	1)(m	1)(m	NUM
ap-9131	129	15	−	−	NOUN
ap-9131	129	16	n	n	CCONJ
ap-9131	129	17	−	−	PROPN
ap-9131	129	18	1)(m	1)(m	NUM
ap-9131	129	19	−	−	PROPN
ap-9131	129	20	n	n	CCONJ
ap-9131	129	21	)	)	PUNCT
ap-9131	129	22	,	,	PUNCT
ap-9131	129	23	7	7	X
ap-9131	129	24	)	)	PUNCT
ap-9131	129	25	1	1	NUM
ap-9131	129	26	6	6	NUM
ap-9131	129	27	n(n	n(n	NOUN
ap-9131	129	28	+	+	CCONJ
ap-9131	129	29	1)(n	1)(n	NUM
ap-9131	129	30	+	+	CCONJ
ap-9131	129	31	2	2	NUM
ap-9131	129	32	)	)	PUNCT
ap-9131	129	33	,	,	PUNCT
ap-9131	129	34	8)	8)	NUM
ap-9131	129	35	1	1	NUM
ap-9131	129	36	2	2	NUM
ap-9131	129	37	n(n	n(n	NOUN
ap-9131	129	38	+	+	CCONJ
ap-9131	129	39	1)(m	1)(m	NUM
ap-9131	129	40	−	−	NOUN
ap-9131	129	41	n	n	CCONJ
ap-9131	129	42	)	)	PUNCT
ap-9131	129	43	,	,	PUNCT
ap-9131	129	44	9	9	X
ap-9131	129	45	)	)	PUNCT
ap-9131	129	46	1	1	NUM
ap-9131	129	47	6	6	NUM
ap-9131	129	48	(	(	PUNCT
ap-9131	129	49	n	n	CCONJ
ap-9131	129	50	−	−	PROPN
ap-9131	129	51	1)n(n	1)n(n	NUM
ap-9131	129	52	+	+	CCONJ
ap-9131	129	53	1	1	NUM
ap-9131	129	54	)	)	PUNCT
ap-9131	129	55	,	,	PUNCT
ap-9131	129	56	total	total	ADJ
ap-9131	129	57	1	1	NUM
ap-9131	129	58	2	2	NUM
ap-9131	129	59	(	(	PUNCT
ap-9131	129	60	m	m	VERB
ap-9131	129	61	+	+	NOUN
ap-9131	129	62	1)(n	1)(n	NUM
ap-9131	129	63	+	+	CCONJ
ap-9131	129	64	1)(m	1)(m	NUM
ap-9131	129	65	+	+	CCONJ
ap-9131	129	66	n	n	NOUN
ap-9131	129	67	+	+	NOUN
ap-9131	129	68	2	2	NUM
ap-9131	129	69	)	)	PUNCT
ap-9131	129	70	.	.	PUNCT
ap-9131	130	1	table	table	NOUN
ap-9131	130	2	2	2	NUM
ap-9131	130	3	.	.	PUNCT
ap-9131	130	4	vector	vector	NOUN
ap-9131	130	5	counts	count	NOUN
ap-9131	130	6	.	.	PUNCT
ap-9131	131	1	proof	proof	NOUN
ap-9131	131	2	.	.	PUNCT
ap-9131	132	1	this	this	PRON
ap-9131	132	2	is	be	AUX
ap-9131	132	3	verified	verify	VERB
ap-9131	132	4	by	by	ADP
ap-9131	132	5	the	the	DET
ap-9131	132	6	direct	direct	ADJ
ap-9131	132	7	computation	computation	NOUN
ap-9131	132	8	.	.	PUNCT
ap-9131	133	1	lemma	lemma	PROPN
ap-9131	133	2	5	5	NUM
ap-9131	133	3	.	.	PUNCT
ap-9131	133	4	maximal	maximal	ADJ
ap-9131	133	5	vectors	vector	NOUN
ap-9131	133	6	sab	sab	VERB
ap-9131	133	7	and	and	CCONJ
ap-9131	133	8	tka	tka	NOUN
ap-9131	133	9	are	be	AUX
ap-9131	133	10	linearly	linearly	ADV
ap-9131	133	11	independent	independent	ADJ
ap-9131	133	12	.	.	PUNCT
ap-9131	134	1	proof	proof	NOUN
ap-9131	134	2	.	.	PUNCT
ap-9131	135	1	as	as	SCONJ
ap-9131	135	2	the	the	DET
ap-9131	135	3	linear	linear	ADJ
ap-9131	135	4	independence	independence	NOUN
ap-9131	135	5	of	of	ADP
ap-9131	135	6	maximal	maximal	ADJ
ap-9131	135	7	vectors	vector	NOUN
ap-9131	135	8	having	have	VERB
ap-9131	135	9	different	different	ADJ
ap-9131	135	10	eigenvalues	eigenvalue	NOUN
ap-9131	135	11	of	of	ADP
ap-9131	135	12	ρ(i0	ρ(i0	NOUN
ap-9131	135	13	)	)	PUNCT
ap-9131	135	14	is	be	AUX
ap-9131	135	15	clear	clear	ADJ
ap-9131	135	16	,	,	PUNCT
ap-9131	135	17	it	it	PRON
ap-9131	135	18	remans	reman	VERB
ap-9131	135	19	to	to	PART
ap-9131	135	20	check	check	VERB
ap-9131	135	21	the	the	DET
ap-9131	135	22	linear	linear	ADJ
ap-9131	135	23	independence	independence	NOUN
ap-9131	135	24	of	of	ADP
ap-9131	135	25	maximal	maximal	ADJ
ap-9131	135	26	vectors	vector	NOUN
ap-9131	135	27	having	have	VERB
ap-9131	135	28	the	the	DET
ap-9131	135	29	same	same	ADJ
ap-9131	135	30	eigenvalues	eigenvalue	NOUN
ap-9131	135	31	.	.	PUNCT
ap-9131	136	1	but	but	CCONJ
ap-9131	136	2	this	this	PRON
ap-9131	136	3	is	be	AUX
ap-9131	136	4	clear	clear	ADJ
ap-9131	136	5	from	from	ADP
ap-9131	136	6	the	the	DET
ap-9131	136	7	form	form	NOUN
ap-9131	136	8	of	of	ADP
ap-9131	136	9	the	the	DET
ap-9131	136	10	maximal	maximal	ADJ
ap-9131	136	11	vectors	vector	NOUN
ap-9131	136	12	.	.	PUNCT
ap-9131	137	1	we	we	PRON
ap-9131	137	2	are	be	AUX
ap-9131	137	3	now	now	ADV
ap-9131	137	4	ready	ready	ADJ
ap-9131	137	5	to	to	PART
ap-9131	137	6	formulate	formulate	VERB
ap-9131	137	7	the	the	DET
ap-9131	137	8	main	main	ADJ
ap-9131	137	9	theorem	theorem	NOUN
ap-9131	137	10	.	.	PUNCT
ap-9131	137	11	theorem	theorem	NOUN
ap-9131	137	12	2	2	NUM
ap-9131	137	13	.	.	PUNCT
ap-9131	138	1	the	the	DET
ap-9131	138	2	representation	representation	NOUN
ap-9131	138	3	space	space	NOUN
ap-9131	138	4	p	p	NOUN
ap-9131	138	5	is	be	AUX
ap-9131	138	6	a	a	DET
ap-9131	138	7	direct	direct	ADJ
ap-9131	138	8	sum	sum	NOUN
ap-9131	138	9	of	of	ADP
ap-9131	138	10	linear	linear	ADJ
ap-9131	138	11	spans	span	NOUN
ap-9131	138	12	of	of	ADP
ap-9131	138	13	mutually	mutually	ADV
ap-9131	138	14	linearly	linearly	ADV
ap-9131	138	15	independent	independent	ADJ
ap-9131	138	16	vectors	vector	NOUN
ap-9131	138	17	ρ(i−)jsab	ρ(i−)jsab	VERB
ap-9131	138	18	,	,	PUNCT
ap-9131	138	19	0	0	NUM
ap-9131	138	20	≤	≤	NUM
ap-9131	139	1	j	j	PROPN
ap-9131	139	2	≤	≤	ADV
ap-9131	139	3	2(b	2(b	NUM
ap-9131	139	4	+	+	CCONJ
ap-9131	139	5	m	m	NOUN
ap-9131	139	6	)	)	PUNCT
ap-9131	139	7	,	,	PUNCT
ap-9131	139	8	(	(	PUNCT
ap-9131	139	9	5	5	NUM
ap-9131	139	10	)	)	PUNCT
ap-9131	139	11	and	and	CCONJ
ap-9131	139	12	ρ(i−)jtka	ρ(i−)jtka	NOUN
ap-9131	139	13	,	,	PUNCT
ap-9131	139	14	0	0	NUM
ap-9131	139	15	≤	≤	NUM
ap-9131	139	16	j	j	PROPN
ap-9131	139	17	≤	≤	NUM
ap-9131	139	18	2(m	2(m	NUM
ap-9131	139	19	−	−	NOUN
ap-9131	139	20	2k	2k	NOUN
ap-9131	139	21	+	+	CCONJ
ap-9131	139	22	a	a	DET
ap-9131	139	23	mod	mod	ADJ
ap-9131	139	24	2	2	NUM
ap-9131	139	25	)	)	PUNCT
ap-9131	139	26	,	,	PUNCT
ap-9131	139	27	(	(	PUNCT
ap-9131	139	28	6	6	NUM
ap-9131	139	29	)	)	PUNCT
ap-9131	139	30	where	where	SCONJ
ap-9131	139	31	sab	sab	PROPN
ap-9131	139	32	and	and	CCONJ
ap-9131	139	33	tka	tka	NOUN
ap-9131	139	34	and	and	CCONJ
ap-9131	139	35	indices	indice	VERB
ap-9131	139	36	a	a	DET
ap-9131	139	37	,	,	PUNCT
ap-9131	139	38	b	b	NOUN
ap-9131	139	39	,	,	PUNCT
ap-9131	139	40	k	k	PROPN
ap-9131	139	41	are	be	AUX
ap-9131	139	42	given	give	VERB
ap-9131	139	43	in	in	ADP
ap-9131	139	44	the	the	DET
ap-9131	139	45	table	table	NOUN
ap-9131	139	46	3	3	X
ap-9131	139	47	.	.	PUNCT
ap-9131	140	1	the	the	DET
ap-9131	140	2	linear	linear	ADJ
ap-9131	140	3	spans	span	NOUN
ap-9131	140	4	(	(	PUNCT
ap-9131	140	5	5	5	NUM
ap-9131	140	6	)	)	PUNCT
ap-9131	140	7	and	and	CCONJ
ap-9131	140	8	(	(	PUNCT
ap-9131	140	9	6	6	NUM
ap-9131	140	10	)	)	PUNCT
ap-9131	140	11	are	be	AUX
ap-9131	140	12	minimal	minimal	ADJ
ap-9131	140	13	invariant	invariant	ADJ
ap-9131	140	14	subspaces	subspace	NOUN
ap-9131	140	15	of	of	ADP
ap-9131	140	16	representation	representation	NOUN
ap-9131	140	17	ρ	ρ	PROPN
ap-9131	140	18	of	of	ADP
ap-9131	140	19	su(3	su(3	PROPN
ap-9131	140	20	)	)	PUNCT
ap-9131	140	21	of	of	ADP
ap-9131	140	22	highest	high	ADJ
ap-9131	140	23	weight	weight	NOUN
ap-9131	140	24	(	(	PUNCT
ap-9131	140	25	m	m	PROPN
ap-9131	140	26	,	,	PUNCT
ap-9131	140	27	n	n	CCONJ
ap-9131	140	28	)	)	PUNCT
ap-9131	140	29	viewed	view	VERB
ap-9131	140	30	as	as	ADP
ap-9131	140	31	a	a	DET
ap-9131	140	32	(	(	PUNCT
ap-9131	140	33	completely	completely	ADV
ap-9131	140	34	reducible	reducible	ADJ
ap-9131	140	35	)	)	PUNCT
ap-9131	140	36	representation	representation	NOUN
ap-9131	140	37	of	of	ADP
ap-9131	140	38	so(3	so(3	NOUN
ap-9131	140	39	)	)	PUNCT
ap-9131	140	40	,	,	PUNCT
ap-9131	140	41	having	have	VERB
ap-9131	140	42	highest	high	ADJ
ap-9131	140	43	weights	weight	NOUN
ap-9131	140	44	(	(	PUNCT
ap-9131	140	45	b	b	NOUN
ap-9131	140	46	+	+	CCONJ
ap-9131	140	47	n	n	CCONJ
ap-9131	140	48	)	)	PUNCT
ap-9131	140	49	resp	resp	NOUN
ap-9131	140	50	.	.	PUNCT
ap-9131	141	1	(	(	PUNCT
ap-9131	141	2	n	n	CCONJ
ap-9131	141	3	−	−	PROPN
ap-9131	141	4	2k	2k	NOUN
ap-9131	142	1	+	+	CCONJ
ap-9131	142	2	a	a	DET
ap-9131	142	3	mod	mod	ADJ
ap-9131	142	4	2	2	NUM
ap-9131	142	5	)	)	PUNCT
ap-9131	142	6	.	.	PUNCT
ap-9131	143	1	proof	proof	NOUN
ap-9131	143	2	.	.	PUNCT
ap-9131	144	1	the	the	DET
ap-9131	144	2	linear	linear	ADJ
ap-9131	144	3	independence	independence	NOUN
ap-9131	144	4	of	of	ADP
ap-9131	144	5	vectors	vector	NOUN
ap-9131	144	6	(	(	PUNCT
ap-9131	144	7	5	5	NUM
ap-9131	144	8	)	)	PUNCT
ap-9131	144	9	resp	resp	NOUN
ap-9131	144	10	.	.	PUNCT
ap-9131	145	1	(	(	PUNCT
ap-9131	145	2	6	6	NUM
ap-9131	145	3	)	)	PUNCT
ap-9131	145	4	is	be	AUX
ap-9131	145	5	clear	clear	ADJ
ap-9131	145	6	from	from	ADP
ap-9131	145	7	the	the	DET
ap-9131	145	8	linear	linear	ADJ
ap-9131	145	9	independence	independence	NOUN
ap-9131	145	10	of	of	ADP
ap-9131	145	11	vectors	vector	NOUN
ap-9131	145	12	sab	sab	ADJ
ap-9131	145	13	and	and	CCONJ
ap-9131	145	14	tka	tka	ADJ
ap-9131	145	15	,	,	PUNCT
ap-9131	145	16	because	because	SCONJ
ap-9131	145	17	we	we	PRON
ap-9131	145	18	can	can	AUX
ap-9131	145	19	make	make	VERB
ap-9131	145	20	use	use	NOUN
ap-9131	145	21	of	of	ADP
ap-9131	145	22	the	the	DET
ap-9131	145	23	operator	operator	NOUN
ap-9131	145	24	ρ(i+)j	ρ(i+)j	VERB
ap-9131	145	25	to	to	PART
ap-9131	145	26	“	"	PUNCT
ap-9131	145	27	come	come	VERB
ap-9131	145	28	back	back	ADV
ap-9131	145	29	”	"	PUNCT
ap-9131	145	30	from	from	ADP
ap-9131	145	31	ρ(i−)jsab	ρ(i−)jsab	NUM
ap-9131	145	32	to	to	ADP
ap-9131	145	33	the	the	DET
ap-9131	145	34	scalar	scalar	ADJ
ap-9131	145	35	multiple	multiple	NOUN
ap-9131	145	36	of	of	ADP
ap-9131	145	37	the	the	DET
ap-9131	145	38	highest	high	ADJ
ap-9131	145	39	weight	weight	NOUN
ap-9131	145	40	vector	vector	NOUN
ap-9131	145	41	sab	sab	PROPN
ap-9131	145	42	.	.	PUNCT
ap-9131	146	1	the	the	DET
ap-9131	146	2	proof	proof	NOUN
ap-9131	146	3	is	be	AUX
ap-9131	146	4	thus	thus	ADV
ap-9131	146	5	reduced	reduce	VERB
ap-9131	146	6	to	to	ADP
ap-9131	146	7	verifying	verify	VERB
ap-9131	146	8	the	the	DET
ap-9131	146	9	fact	fact	NOUN
ap-9131	146	10	that	that	SCONJ
ap-9131	146	11	the	the	DET
ap-9131	146	12	number	number	NOUN
ap-9131	146	13	of	of	ADP
ap-9131	146	14	vectors	vector	NOUN
ap-9131	146	15	is	be	AUX
ap-9131	146	16	equal	equal	ADJ
ap-9131	146	17	to	to	ADP
ap-9131	146	18	the	the	DET
ap-9131	146	19	dimension	dimension	NOUN
ap-9131	146	20	of	of	ADP
ap-9131	146	21	p	p	NOUN
ap-9131	146	22	,	,	PUNCT
ap-9131	146	23	namely	namely	ADV
ap-9131	146	24	(	(	PUNCT
ap-9131	146	25	4	4	NUM
ap-9131	146	26	)	)	PUNCT
ap-9131	146	27	.	.	PUNCT
ap-9131	147	1	corollary	corollary	ADJ
ap-9131	147	2	1	1	NUM
ap-9131	147	3	.	.	PUNCT
ap-9131	148	1	elliot	elliot	PROPN
ap-9131	148	2	’s	’s	PART
ap-9131	148	3	result	result	NOUN
ap-9131	148	4	(	(	PUNCT
ap-9131	148	5	1	1	X
ap-9131	148	6	)	)	PUNCT
ap-9131	148	7	is	be	AUX
ap-9131	148	8	a	a	DET
ap-9131	148	9	direct	direct	ADJ
ap-9131	148	10	consequence	consequence	NOUN
ap-9131	148	11	of	of	ADP
ap-9131	148	12	the	the	DET
ap-9131	148	13	theorem	theorem	ADJ
ap-9131	148	14	2	2	NUM
ap-9131	148	15	.	.	NOUN
ap-9131	148	16	example	example	NOUN
ap-9131	149	1	2	2	NUM
ap-9131	149	2	.	.	PUNCT
ap-9131	150	1	the	the	DET
ap-9131	150	2	list	list	NOUN
ap-9131	150	3	of	of	ADP
ap-9131	150	4	maximal	maximal	ADJ
ap-9131	150	5	vectors	vector	NOUN
ap-9131	150	6	for	for	ADP
ap-9131	150	7	the	the	DET
ap-9131	150	8	case	case	NOUN
ap-9131	150	9	of	of	ADP
ap-9131	150	10	highest	high	ADJ
ap-9131	150	11	weigth	weigth	NOUN
ap-9131	150	12	(	(	PUNCT
ap-9131	150	13	2	2	NUM
ap-9131	150	14	,	,	PUNCT
ap-9131	150	15	2	2	NUM
ap-9131	150	16	)	)	PUNCT
ap-9131	150	17	(	(	PUNCT
ap-9131	150	18	i.	i.	PROPN
ap-9131	150	19	e.	e.	PROPN
ap-9131	150	20	m	m	PROPN
ap-9131	151	1	=	=	PROPN
ap-9131	151	2	2	2	NUM
ap-9131	151	3	,	,	PUNCT
ap-9131	151	4	n	n	NOUN
ap-9131	151	5	=	=	SYM
ap-9131	151	6	2	2	NUM
ap-9131	151	7	,	,	PUNCT
ap-9131	151	8	see	see	VERB
ap-9131	151	9	the	the	DET
ap-9131	151	10	figure	figure	NOUN
ap-9131	151	11	1	1	NUM
ap-9131	151	12	contains	contain	VERB
ap-9131	151	13	the	the	DET
ap-9131	151	14	vectors	vector	NOUN
ap-9131	151	15	:	:	PUNCT
ap-9131	151	16	z2χ2	z2χ2	PROPN
ap-9131	151	17	,	,	PUNCT
ap-9131	151	18	wzχ	wzχ	PROPN
ap-9131	151	19	,	,	PUNCT
ap-9131	151	20	w2	w2	NOUN
ap-9131	151	21	,	,	PUNCT
ap-9131	151	22	rχ2	rχ2	PROPN
ap-9131	151	23	,	,	PUNCT
ap-9131	151	24	rξ	rξ	PROPN
ap-9131	151	25	,	,	PUNCT
ap-9131	151	26	338	338	NUM
ap-9131	151	27	vol	vol	NOUN
ap-9131	151	28	.	.	PUNCT
ap-9131	152	1	64	64	NUM
ap-9131	152	2	no	no	NOUN
ap-9131	152	3	.	.	PUNCT
ap-9131	153	1	4/2024	4/2024	NUM
ap-9131	153	2	so(3	so(3	NOUN
ap-9131	153	3	)	)	PUNCT
ap-9131	153	4	⊂	⊂	PROPN
ap-9131	153	5	su(3	su(3	PROPN
ap-9131	153	6	)	)	PUNCT
ap-9131	153	7	revisited	revisit	VERB
ap-9131	153	8	1	1	NUM
ap-9131	153	9	2	2	NUM
ap-9131	153	10	3	3	NUM
ap-9131	153	11	figure	figure	NOUN
ap-9131	153	12	1	1	NUM
ap-9131	153	13	.	.	PUNCT
ap-9131	154	1	an	an	DET
ap-9131	154	2	example	example	NOUN
ap-9131	154	3	of	of	ADP
ap-9131	154	4	p	p	PROPN
ap-9131	154	5	.	.	PUNCT
ap-9131	155	1	of	of	ADP
ap-9131	155	2	highest	high	ADJ
ap-9131	155	3	weights	weight	NOUN
ap-9131	155	4	4	4	NUM
ap-9131	155	5	,	,	PUNCT
ap-9131	155	6	3	3	NUM
ap-9131	155	7	,	,	PUNCT
ap-9131	155	8	2	2	NUM
ap-9131	155	9	,	,	PUNCT
ap-9131	155	10	2	2	NUM
ap-9131	155	11	,	,	PUNCT
ap-9131	155	12	0	0	NUM
ap-9131	155	13	.	.	PUNCT
ap-9131	156	1	this	this	PRON
ap-9131	156	2	indicates	indicate	VERB
ap-9131	156	3	the	the	DET
ap-9131	156	4	following	follow	VERB
ap-9131	156	5	decomposition	decomposition	NOUN
ap-9131	156	6	of	of	ADP
ap-9131	156	7	the	the	DET
ap-9131	156	8	representation	representation	NOUN
ap-9131	156	9	(	(	PUNCT
ap-9131	156	10	2	2	NUM
ap-9131	156	11	,	,	PUNCT
ap-9131	156	12	2	2	NUM
ap-9131	156	13	):	):	PUNCT
ap-9131	156	14	(	(	PUNCT
ap-9131	156	15	2	2	NUM
ap-9131	156	16	,	,	PUNCT
ap-9131	156	17	2	2	NUM
ap-9131	156	18	)	)	PUNCT
ap-9131	156	19	≃	≃	NOUN
ap-9131	156	20	(	(	PUNCT
ap-9131	156	21	4	4	NUM
ap-9131	156	22	)	)	PUNCT
ap-9131	156	23	⊕	⊕	PROPN
ap-9131	156	24	(	(	PUNCT
ap-9131	156	25	3	3	X
ap-9131	156	26	)	)	PUNCT
ap-9131	156	27	⊕	⊕	PROPN
ap-9131	156	28	2(2	2(2	NUM
ap-9131	156	29	)	)	PUNCT
ap-9131	157	1	⊕	⊕	PROPN
ap-9131	157	2	(	(	PUNCT
ap-9131	157	3	0	0	NUM
ap-9131	157	4	)	)	PUNCT
ap-9131	157	5	,	,	PUNCT
ap-9131	157	6	(	(	PUNCT
ap-9131	157	7	7	7	X
ap-9131	157	8	)	)	PUNCT
ap-9131	157	9	or	or	CCONJ
ap-9131	157	10	,	,	PUNCT
ap-9131	157	11	in	in	ADP
ap-9131	157	12	the	the	DET
ap-9131	157	13	dimensions	dimension	NOUN
ap-9131	157	14	of	of	ADP
ap-9131	157	15	individual	individual	ADJ
ap-9131	157	16	representations	representation	NOUN
ap-9131	157	17	:	:	PUNCT
ap-9131	157	18	27	27	NUM
ap-9131	157	19	=	=	SYM
ap-9131	157	20	9	9	NUM
ap-9131	157	21	+	+	CCONJ
ap-9131	157	22	7	7	NUM
ap-9131	157	23	+	+	SYM
ap-9131	157	24	2	2	NUM
ap-9131	157	25	×	×	NOUN
ap-9131	157	26	5	5	NUM
ap-9131	157	27	+	+	CCONJ
ap-9131	157	28	1	1	X
ap-9131	157	29	.	.	X
ap-9131	157	30	note	note	NOUN
ap-9131	157	31	2	2	NUM
ap-9131	157	32	.	.	PUNCT
ap-9131	157	33	using	use	VERB
ap-9131	157	34	the	the	DET
ap-9131	157	35	explicit	explicit	ADJ
ap-9131	157	36	decomposition	decomposition	NOUN
ap-9131	157	37	formula	formula	NOUN
ap-9131	157	38	(	(	PUNCT
ap-9131	157	39	1	1	NUM
ap-9131	157	40	)	)	PUNCT
ap-9131	157	41	,	,	PUNCT
ap-9131	157	42	it	it	PRON
ap-9131	157	43	is	be	AUX
ap-9131	157	44	easy	easy	ADJ
ap-9131	157	45	to	to	PART
ap-9131	157	46	obtain	obtain	VERB
ap-9131	157	47	the	the	DET
ap-9131	157	48	generating	generate	VERB
ap-9131	157	49	function	function	NOUN
ap-9131	157	50	f	f	PROPN
ap-9131	157	51	(	(	PUNCT
ap-9131	157	52	p	p	X
ap-9131	157	53	,	,	PUNCT
ap-9131	157	54	q	q	ADJ
ap-9131	157	55	,	,	PUNCT
ap-9131	157	56	x	x	NOUN
ap-9131	157	57	)	)	PUNCT
ap-9131	157	58	for	for	ADP
ap-9131	157	59	the	the	DET
ap-9131	157	60	so(3	so(3	NOUN
ap-9131	157	61	)	)	PUNCT
ap-9131	157	62	⊂	⊂	PROPN
ap-9131	157	63	su(3	su(3	NOUN
ap-9131	157	64	)	)	PUNCT
ap-9131	157	65	decomposition	decomposition	NOUN
ap-9131	157	66	.	.	PUNCT
ap-9131	158	1	it	it	PRON
ap-9131	158	2	reads	read	VERB
ap-9131	158	3	1	1	NUM
ap-9131	158	4	+	+	NUM
ap-9131	158	5	pqx	pqx	NOUN
ap-9131	158	6	(	(	PUNCT
ap-9131	158	7	1	1	NUM
ap-9131	158	8	−	−	PROPN
ap-9131	158	9	p	p	NOUN
ap-9131	158	10	2)(1	2)(1	NUM
ap-9131	158	11	−	−	NOUN
ap-9131	158	12	q2)(1	q2)(1	ADP
ap-9131	158	13	−	−	PROPN
ap-9131	158	14	px)(1	px)(1	NOUN
ap-9131	158	15	−	−	PROPN
ap-9131	158	16	qx	qx	PROPN
ap-9131	158	17	)	)	PUNCT
ap-9131	158	18	.	.	PUNCT
ap-9131	159	1	(	(	PUNCT
ap-9131	159	2	8)	8)	NUM
ap-9131	159	3	for	for	ADP
ap-9131	159	4	example	example	NOUN
ap-9131	159	5	,	,	PUNCT
ap-9131	159	6	the	the	DET
ap-9131	159	7	result	result	NOUN
ap-9131	159	8	(	(	PUNCT
ap-9131	159	9	7	7	X
ap-9131	159	10	)	)	PUNCT
ap-9131	159	11	can	can	AUX
ap-9131	159	12	be	be	AUX
ap-9131	159	13	quickly	quickly	ADV
ap-9131	159	14	rediscovered	rediscover	VERB
ap-9131	159	15	using	use	VERB
ap-9131	159	16	the	the	DET
ap-9131	159	17	generating	generate	VERB
ap-9131	159	18	function	function	NOUN
ap-9131	159	19	(	(	PUNCT
ap-9131	159	20	8)	8)	NUM
ap-9131	159	21	by	by	ADP
ap-9131	159	22	computing	compute	VERB
ap-9131	159	23	:	:	PUNCT
ap-9131	159	24	1	1	NUM
ap-9131	159	25	2	2	NUM
ap-9131	159	26	!	!	SYM
ap-9131	159	27	1	1	NUM
ap-9131	159	28	2	2	X
ap-9131	159	29	!	!	PUNCT
ap-9131	160	1	d2	d2	PROPN
ap-9131	160	2	dp	dp	NOUN
ap-9131	160	3	2	2	NUM
ap-9131	160	4	d2	d2	PROPN
ap-9131	160	5	dq2	dq2	PROPN
ap-9131	160	6	f	f	PROPN
ap-9131	160	7	(	(	PUNCT
ap-9131	160	8	p	p	X
ap-9131	160	9	,	,	PUNCT
ap-9131	160	10	q	q	ADJ
ap-9131	160	11	,	,	PUNCT
ap-9131	160	12	x	x	NOUN
ap-9131	160	13	)	)	PUNCT
ap-9131	160	14	∣∣∣∣p	∣∣∣∣p	PUNCT
ap-9131	161	1	=	=	NOUN
ap-9131	161	2	0	0	X
ap-9131	161	3	q=0	q=0	NOUN
ap-9131	161	4	=	=	SYM
ap-9131	161	5	x4	x4	PROPN
ap-9131	162	1	+	+	CCONJ
ap-9131	162	2	x3	x3	ADJ
ap-9131	162	3	+	+	CCONJ
ap-9131	162	4	2x2	2x2	NUM
ap-9131	162	5	+	+	SYM
ap-9131	162	6	1	1	NUM
ap-9131	162	7	.	.	X
ap-9131	162	8	3	3	X
ap-9131	162	9	.	.	X
ap-9131	162	10	conclusion	conclusion	VERB
ap-9131	162	11	the	the	DET
ap-9131	162	12	differential	differential	ADJ
ap-9131	162	13	realisation	realisation	NOUN
ap-9131	162	14	method	method	NOUN
ap-9131	162	15	for	for	ADP
ap-9131	162	16	obtaining	obtain	VERB
ap-9131	162	17	the	the	DET
ap-9131	162	18	decomposition	decomposition	NOUN
ap-9131	162	19	of	of	ADP
ap-9131	162	20	a	a	DET
ap-9131	162	21	finite	finite	ADJ
ap-9131	162	22	dimensional	dimensional	ADJ
ap-9131	162	23	representation	representation	NOUN
ap-9131	162	24	of	of	ADP
ap-9131	162	25	the	the	DET
ap-9131	162	26	lie	lie	NOUN
ap-9131	162	27	algebra	algebra	PROPN
ap-9131	162	28	su(3	su(3	PROPN
ap-9131	162	29	)	)	PUNCT
ap-9131	162	30	according	accord	VERB
ap-9131	162	31	to	to	ADP
ap-9131	162	32	the	the	DET
ap-9131	162	33	embedding	embed	VERB
ap-9131	162	34	1	1	NUM
ap-9131	162	35	)	)	PUNCT
ap-9131	162	36	sab	sab	NOUN
ap-9131	162	37	=	=	SYM
ap-9131	162	38	wazbχm−ar	wazbχm−ar	X
ap-9131	162	39	n−(b+a	n−(b+a	PROPN
ap-9131	162	40	)	)	PUNCT
ap-9131	162	41	2	2	NUM
ap-9131	162	42	,	,	PUNCT
ap-9131	162	43	0	0	NUM
ap-9131	162	44	≤	≤	NOUN
ap-9131	162	45	a	a	DET
ap-9131	162	46	≤	≤	NUM
ap-9131	162	47	m	m	PROPN
ap-9131	162	48	,	,	PUNCT
ap-9131	163	1	0	0	NUM
ap-9131	163	2	≤	≤	NUM
ap-9131	163	3	b	b	X
ap-9131	163	4	≤	≤	NUM
ap-9131	164	1	n	n	CCONJ
ap-9131	164	2	−	−	PROPN
ap-9131	164	3	a	a	PROPN
ap-9131	164	4	,	,	PUNCT
ap-9131	164	5	a	a	DET
ap-9131	164	6	+	+	X
ap-9131	164	7	b	b	NOUN
ap-9131	164	8	even	even	ADV
ap-9131	164	9	,	,	PUNCT
ap-9131	164	10	2	2	X
ap-9131	164	11	)	)	PUNCT
ap-9131	164	12	tka	tka	NOUN
ap-9131	164	13	=	=	SYM
ap-9131	164	14	r	r	NOUN
ap-9131	164	15	[	[	PUNCT
ap-9131	164	16	n−a	n−a	NOUN
ap-9131	164	17	2	2	NUM
ap-9131	164	18	]	]	SYM
ap-9131	164	19	ξ	ξ	X
ap-9131	164	20	[	[	PUNCT
ap-9131	164	21	a	a	DET
ap-9131	164	22	2	2	NUM
ap-9131	164	23	]	]	PUNCT
ap-9131	164	24	+	+	ADJ
ap-9131	164	25	kwa	kwa	PROPN
ap-9131	164	26	mod	mod	PROPN
ap-9131	164	27	2zaχm−2k−a	2zaχm−2k−a	PROPN
ap-9131	164	28	,	,	PUNCT
ap-9131	164	29	1	1	NUM
ap-9131	164	30	≤	≤	NUM
ap-9131	164	31	k	k	X
ap-9131	164	32	≤	≤	NUM
ap-9131	164	33	m	m	VERB
ap-9131	164	34	2	2	NUM
ap-9131	164	35	,	,	PUNCT
ap-9131	164	36	0	0	NUM
ap-9131	164	37	≤	≤	NOUN
ap-9131	164	38	a	a	DET
ap-9131	164	39	≤	≤	NUM
ap-9131	164	40	m	m	NOUN
ap-9131	164	41	−	−	PROPN
ap-9131	164	42	2k	2k	NUM
ap-9131	164	43	,	,	PUNCT
ap-9131	164	44	a	a	DET
ap-9131	164	45	≤	≤	NUM
ap-9131	164	46	n.	n.	NOUN
ap-9131	164	47	table	table	NOUN
ap-9131	164	48	3	3	NUM
ap-9131	164	49	.	.	PUNCT
ap-9131	164	50	maximal	maximal	ADJ
ap-9131	164	51	vectors	vector	NOUN
ap-9131	164	52	.	.	PUNCT
ap-9131	165	1	so(3	so(3	NOUN
ap-9131	165	2	)	)	PUNCT
ap-9131	165	3	⊂	⊂	PROPN
ap-9131	166	1	su(3	su(3	PROPN
ap-9131	166	2	)	)	PUNCT
ap-9131	166	3	was	be	AUX
ap-9131	166	4	presented	present	VERB
ap-9131	166	5	.	.	PUNCT
ap-9131	167	1	the	the	DET
ap-9131	167	2	parametrisation	parametrisation	NOUN
ap-9131	167	3	of	of	ADP
ap-9131	167	4	the	the	DET
ap-9131	167	5	submodules	submodules	NOUN
ap-9131	167	6	is	be	AUX
ap-9131	167	7	a	a	DET
ap-9131	167	8	convenient	convenient	ADJ
ap-9131	167	9	for	for	ADP
ap-9131	167	10	the	the	DET
ap-9131	167	11	application	application	NOUN
ap-9131	167	12	in	in	ADP
ap-9131	167	13	particle	particle	NOUN
ap-9131	167	14	physics	physics	NOUN
ap-9131	167	15	and	and	CCONJ
ap-9131	167	16	in	in	ADP
ap-9131	167	17	general	general	ADJ
ap-9131	167	18	for	for	ADP
ap-9131	167	19	systems	system	NOUN
ap-9131	167	20	with	with	ADP
ap-9131	167	21	the	the	DET
ap-9131	167	22	appropriate	appropriate	ADJ
ap-9131	167	23	symmetries	symmetry	NOUN
ap-9131	167	24	.	.	PUNCT
ap-9131	168	1	the	the	DET
ap-9131	168	2	realisation	realisation	NOUN
ap-9131	168	3	way	way	NOUN
ap-9131	168	4	is	be	AUX
ap-9131	168	5	shown	show	VERB
ap-9131	168	6	to	to	PART
ap-9131	168	7	be	be	AUX
ap-9131	168	8	convenient	convenient	ADJ
ap-9131	168	9	tool	tool	NOUN
ap-9131	168	10	for	for	ADP
ap-9131	168	11	constructing	construct	VERB
ap-9131	168	12	such	such	ADJ
ap-9131	168	13	decompositions	decomposition	NOUN
ap-9131	168	14	and	and	CCONJ
ap-9131	168	15	leads	lead	VERB
ap-9131	168	16	to	to	ADP
ap-9131	168	17	the	the	DET
ap-9131	168	18	decomposition	decomposition	NOUN
ap-9131	168	19	result	result	NOUN
ap-9131	168	20	using	use	VERB
ap-9131	168	21	only	only	ADV
ap-9131	168	22	basic	basic	ADJ
ap-9131	168	23	,	,	PUNCT
ap-9131	168	24	appropriate	appropriate	ADJ
ap-9131	168	25	classical	classical	ADJ
ap-9131	168	26	tools	tool	NOUN
ap-9131	168	27	from	from	ADP
ap-9131	168	28	representation	representation	NOUN
ap-9131	168	29	theory	theory	NOUN
ap-9131	168	30	.	.	PUNCT
ap-9131	169	1	this	this	PRON
ap-9131	169	2	makes	make	VERB
ap-9131	169	3	the	the	DET
ap-9131	169	4	method	method	NOUN
ap-9131	169	5	approachable	approachable	ADJ
ap-9131	169	6	for	for	ADP
ap-9131	169	7	a	a	DET
ap-9131	169	8	broad	broad	ADJ
ap-9131	169	9	audience	audience	NOUN
ap-9131	169	10	within	within	ADP
ap-9131	169	11	mathematics	mathematics	PROPN
ap-9131	169	12	and	and	CCONJ
ap-9131	169	13	physics	physic	NOUN
ap-9131	169	14	and	and	CCONJ
ap-9131	169	15	it	it	PRON
ap-9131	169	16	can	can	AUX
ap-9131	169	17	be	be	AUX
ap-9131	169	18	useful	useful	ADJ
ap-9131	169	19	for	for	ADP
ap-9131	169	20	obtaining	obtain	VERB
ap-9131	169	21	similar	similar	ADJ
ap-9131	169	22	decompositions	decomposition	NOUN
ap-9131	169	23	based	base	VERB
ap-9131	169	24	on	on	ADP
ap-9131	169	25	other	other	ADJ
ap-9131	169	26	subalgebra	subalgebra	NOUN
ap-9131	169	27	–	–	PUNCT
ap-9131	169	28	algebra	algebra	NOUN
ap-9131	169	29	pairs	pair	NOUN
ap-9131	169	30	.	.	PUNCT
ap-9131	170	1	the	the	DET
ap-9131	170	2	generating	generate	VERB
ap-9131	170	3	function	function	NOUN
ap-9131	170	4	provides	provide	VERB
ap-9131	170	5	a	a	DET
ap-9131	170	6	quick	quick	ADJ
ap-9131	170	7	algorithm	algorithm	NOUN
ap-9131	170	8	to	to	PART
ap-9131	170	9	determine	determine	VERB
ap-9131	170	10	the	the	DET
ap-9131	170	11	multiplicities	multiplicity	NOUN
ap-9131	170	12	for	for	ADP
ap-9131	170	13	so(3	so(3	NOUN
ap-9131	170	14	)	)	PUNCT
ap-9131	170	15	irreducible	irreducible	ADJ
ap-9131	170	16	representations	representation	NOUN
ap-9131	170	17	occurring	occur	VERB
ap-9131	170	18	in	in	ADP
ap-9131	170	19	the	the	DET
ap-9131	170	20	decomposition	decomposition	NOUN
ap-9131	170	21	of	of	ADP
ap-9131	170	22	su(3	su(3	NOUN
ap-9131	170	23	)	)	PUNCT
ap-9131	170	24	representations	representation	NOUN
ap-9131	170	25	.	.	PUNCT
ap-9131	171	1	acknowledgements	acknowledgement	NOUN
ap-9131	171	2	this	this	DET
ap-9131	171	3	work	work	NOUN
ap-9131	171	4	was	be	AUX
ap-9131	171	5	supported	support	VERB
ap-9131	171	6	by	by	ADP
ap-9131	171	7	the	the	DET
ap-9131	171	8	project	project	NOUN
ap-9131	171	9	cz.02.1.01/0.0/0.0/16_019/0000778	cz.02.1.01/0.0/0.0/16_019/0000778	NUM
ap-9131	171	10	from	from	ADP
ap-9131	171	11	european	european	PROPN
ap-9131	171	12	regional	regional	PROPN
ap-9131	171	13	development	development	PROPN
ap-9131	171	14	fund	fund	PROPN
ap-9131	171	15	.	.	PUNCT
ap-9131	172	1	339	339	NUM
ap-9131	172	2	č	č	NUM
ap-9131	172	3	.	.	PUNCT
ap-9131	172	4	burdík	burdík	PROPN
ap-9131	172	5	,	,	PUNCT
ap-9131	172	6	s.	s.	PROPN
ap-9131	172	7	pošta	pošta	PROPN
ap-9131	172	8	,	,	PUNCT
ap-9131	173	1	e.	e.	PROPN
ap-9131	173	2	rapp	rapp	PROPN
ap-9131	173	3	acta	acta	PROPN
ap-9131	173	4	polytechnica	polytechnica	PROPN
ap-9131	173	5	references	reference	NOUN
ap-9131	173	6	[	[	X
ap-9131	173	7	1	1	NUM
ap-9131	173	8	]	]	PUNCT
ap-9131	173	9	j.	j.	PROPN
ap-9131	173	10	p.	p.	PROPN
ap-9131	173	11	elliott	elliott	PROPN
ap-9131	173	12	.	.	PUNCT
ap-9131	174	1	collective	collective	ADJ
ap-9131	174	2	motion	motion	NOUN
ap-9131	174	3	in	in	ADP
ap-9131	174	4	the	the	DET
ap-9131	174	5	nuclear	nuclear	ADJ
ap-9131	174	6	shell	shell	NOUN
ap-9131	174	7	model	model	NOUN
ap-9131	174	8	.	.	PUNCT
ap-9131	175	1	i.	i.	PROPN
ap-9131	175	2	classification	classification	NOUN
ap-9131	175	3	schemes	scheme	NOUN
ap-9131	175	4	for	for	ADP
ap-9131	175	5	states	state	NOUN
ap-9131	175	6	of	of	ADP
ap-9131	175	7	mixed	mixed	ADJ
ap-9131	175	8	configurations	configuration	NOUN
ap-9131	175	9	.	.	PUNCT
ap-9131	176	1	in	in	ADP
ap-9131	176	2	proceedings	proceeding	NOUN
ap-9131	176	3	of	of	ADP
ap-9131	176	4	the	the	DET
ap-9131	176	5	royal	royal	ADJ
ap-9131	176	6	society	society	NOUN
ap-9131	176	7	a	a	DET
ap-9131	176	8	,	,	PUNCT
ap-9131	176	9	vol	vol	NOUN
ap-9131	176	10	.	.	PROPN
ap-9131	176	11	245	245	NUM
ap-9131	176	12	,	,	PUNCT
ap-9131	176	13	pp	pp	ADJ
ap-9131	176	14	.	.	PUNCT
ap-9131	177	1	128–145	128–145	NUM
ap-9131	177	2	.	.	PUNCT
ap-9131	178	1	1958	1958	NUM
ap-9131	178	2	.	.	PUNCT
ap-9131	179	1	https://doi.org/10.1098/rspa.1958.0072	https://doi.org/10.1098/rspa.1958.0072	NOUN
ap-9131	180	1	[	[	X
ap-9131	180	2	2	2	X
ap-9131	180	3	]	]	PUNCT
ap-9131	180	4	v.	v.	ADP
ap-9131	180	5	n.	n.	PROPN
ap-9131	180	6	tolstoy	tolstoy	PROPN
ap-9131	180	7	.	.	PUNCT
ap-9131	181	1	su(3	su(3	NOUN
ap-9131	181	2	)	)	PUNCT
ap-9131	181	3	symmetry	symmetry	NOUN
ap-9131	181	4	for	for	ADP
ap-9131	181	5	orbital	orbital	ADJ
ap-9131	181	6	angular	angular	ADJ
ap-9131	181	7	momentum	momentum	NOUN
ap-9131	181	8	and	and	CCONJ
ap-9131	181	9	method	method	NOUN
ap-9131	181	10	of	of	ADP
ap-9131	181	11	extremal	extremal	ADJ
ap-9131	181	12	projection	projection	NOUN
ap-9131	181	13	operators	operator	NOUN
ap-9131	181	14	.	.	PUNCT
ap-9131	182	1	physics	physics	PROPN
ap-9131	182	2	of	of	ADP
ap-9131	182	3	atomic	atomic	ADJ
ap-9131	182	4	nuclei	nucleus	NOUN
ap-9131	182	5	69(6):1058–1084	69(6):1058–1084	ADP
ap-9131	182	6	,	,	PUNCT
ap-9131	182	7	2006	2006	NUM
ap-9131	182	8	.	.	PUNCT
ap-9131	183	1	https://doi.org/10.1134/s1063778806060160	https://doi.org/10.1134/s1063778806060160	NUM
ap-9131	183	2	[	[	X
ap-9131	183	3	3	3	NUM
ap-9131	183	4	]	]	PUNCT
ap-9131	183	5	m.	m.	NOUN
ap-9131	183	6	moshinsky	moshinsky	PROPN
ap-9131	183	7	,	,	PUNCT
ap-9131	183	8	j.	j.	PROPN
ap-9131	183	9	patera	patera	PROPN
ap-9131	183	10	,	,	PUNCT
ap-9131	183	11	r.	r.	PROPN
ap-9131	183	12	t.	t.	PROPN
ap-9131	183	13	sharp	sharp	PROPN
ap-9131	183	14	,	,	PUNCT
ap-9131	183	15	p.	p.	PROPN
ap-9131	183	16	winternitz	winternitz	PROPN
ap-9131	183	17	.	.	PUNCT
ap-9131	184	1	everything	everything	PRON
ap-9131	184	2	you	you	PRON
ap-9131	184	3	always	always	ADV
ap-9131	184	4	wanted	want	VERB
ap-9131	184	5	to	to	PART
ap-9131	184	6	know	know	VERB
ap-9131	184	7	about	about	ADP
ap-9131	184	8	su(3	su(3	PROPN
ap-9131	184	9	)	)	PUNCT
ap-9131	184	10	⊃	⊃	PROPN
ap-9131	184	11	o(3	o(3	PROPN
ap-9131	184	12	)	)	PUNCT
ap-9131	184	13	.	.	PUNCT
ap-9131	185	1	annals	annal	NOUN
ap-9131	185	2	of	of	ADP
ap-9131	185	3	physics	physics	NOUN
ap-9131	185	4	95(1):139–169	95(1):139–169	PROPN
ap-9131	185	5	,	,	PUNCT
ap-9131	185	6	1975	1975	NUM
ap-9131	185	7	.	.	PUNCT
ap-9131	186	1	https://doi.org/10.1016/0003-4916(75)90048-2	https://doi.org/10.1016/0003-4916(75)90048-2	ADV
ap-9131	186	2	[	[	X
ap-9131	186	3	4	4	NUM
ap-9131	186	4	]	]	X
ap-9131	186	5	r.	r.	PROPN
ap-9131	186	6	m.	m.	PROPN
ap-9131	186	7	asherova	asherova	PROPN
ap-9131	186	8	,	,	PUNCT
ap-9131	186	9	y.	y.	PROPN
ap-9131	186	10	f.	f.	PROPN
ap-9131	186	11	smirnov	smirnov	PROPN
ap-9131	186	12	,	,	PUNCT
ap-9131	186	13	b.	b.	PROPN
ap-9131	186	14	n.	n.	PROPN
ap-9131	186	15	tolstoi	tolstoi	PROPN
ap-9131	186	16	.	.	PUNCT
ap-9131	187	1	projection	projection	NOUN
ap-9131	187	2	operators	operator	NOUN
ap-9131	187	3	for	for	ADP
ap-9131	187	4	simple	simple	ADJ
ap-9131	187	5	lie	lie	NOUN
ap-9131	187	6	groups	group	NOUN
ap-9131	187	7	.	.	PUNCT
ap-9131	188	1	ii	ii	PROPN
ap-9131	188	2	.	.	PUNCT
ap-9131	188	3	general	general	ADJ
ap-9131	188	4	scheme	scheme	NOUN
ap-9131	188	5	for	for	ADP
ap-9131	188	6	constructing	construct	VERB
ap-9131	188	7	lowering	lower	VERB
ap-9131	188	8	operators	operator	NOUN
ap-9131	188	9	.	.	PUNCT
ap-9131	189	1	the	the	DET
ap-9131	189	2	groups	group	NOUN
ap-9131	189	3	su(n	su(n	NOUN
ap-9131	189	4	)	)	PUNCT
ap-9131	189	5	.	.	PUNCT
ap-9131	190	1	theoretical	theoretical	ADJ
ap-9131	190	2	and	and	CCONJ
ap-9131	190	3	mathematical	mathematical	ADJ
ap-9131	190	4	physics	physics	NOUN
ap-9131	190	5	15(1):392	15(1):392	NUM
ap-9131	190	6	–	–	PUNCT
ap-9131	190	7	401	401	NUM
ap-9131	190	8	,	,	PUNCT
ap-9131	190	9	1973	1973	NUM
ap-9131	190	10	.	.	PUNCT
ap-9131	191	1	https://doi.org/10.1007/bf01028268	https://doi.org/10.1007/bf01028268	NOUN
ap-9131	192	1	[	[	X
ap-9131	192	2	5	5	NUM
ap-9131	192	3	]	]	X
ap-9131	192	4	r.	r.	PROPN
ap-9131	192	5	m.	m.	PROPN
ap-9131	192	6	asherova	asherova	PROPN
ap-9131	192	7	,	,	PUNCT
ap-9131	192	8	y.	y.	PROPN
ap-9131	192	9	f.	f.	PROPN
ap-9131	192	10	smirnov	smirnov	PROPN
ap-9131	192	11	.	.	PUNCT
ap-9131	193	1	on	on	ADP
ap-9131	193	2	asymptotic	asymptotic	ADJ
ap-9131	193	3	properties	property	NOUN
ap-9131	193	4	of	of	ADP
ap-9131	193	5	a	a	DET
ap-9131	193	6	quantum	quantum	ADJ
ap-9131	193	7	number	number	NOUN
ap-9131	193	8	ω	ω	PROPN
ap-9131	193	9	in	in	ADP
ap-9131	193	10	a	a	DET
ap-9131	193	11	system	system	NOUN
ap-9131	193	12	with	with	ADP
ap-9131	193	13	su(3	su(3	NOUN
ap-9131	193	14	)	)	PUNCT
ap-9131	193	15	symmetry	symmetry	NOUN
ap-9131	193	16	.	.	PUNCT
ap-9131	194	1	reports	report	NOUN
ap-9131	194	2	on	on	ADP
ap-9131	194	3	mathematical	mathematical	ADJ
ap-9131	194	4	physics	physic	NOUN
ap-9131	194	5	4(2):83–95	4(2):83–95	NUM
ap-9131	194	6	,	,	PUNCT
ap-9131	194	7	1973	1973	NUM
ap-9131	194	8	.	.	PUNCT
ap-9131	195	1	https://doi.org/10.1016/0034-4877(73)90015-3	https://doi.org/10.1016/0034-4877(73)90015-3	PROPN
ap-9131	195	2	[	[	X
ap-9131	195	3	6	6	NUM
ap-9131	195	4	]	]	PUNCT
ap-9131	195	5	t.	t.	PROPN
ap-9131	195	6	cerquetelli	cerquetelli	PROPN
ap-9131	195	7	,	,	PUNCT
ap-9131	195	8	n.	n.	PROPN
ap-9131	195	9	ciccoli	ciccoli	PROPN
ap-9131	195	10	,	,	PUNCT
ap-9131	195	11	m.	m.	NOUN
ap-9131	195	12	c.	c.	PROPN
ap-9131	195	13	nucci	nucci	PROPN
ap-9131	195	14	.	.	PUNCT
ap-9131	196	1	four	four	NUM
ap-9131	196	2	dimensional	dimensional	ADJ
ap-9131	196	3	lie	lie	NOUN
ap-9131	196	4	symmetry	symmetry	NOUN
ap-9131	196	5	algebras	algebra	NOUN
ap-9131	196	6	and	and	CCONJ
ap-9131	196	7	fourth	fourth	ADJ
ap-9131	196	8	order	order	NOUN
ap-9131	196	9	ordinary	ordinary	ADJ
ap-9131	196	10	differential	differential	ADJ
ap-9131	196	11	equations	equation	NOUN
ap-9131	196	12	.	.	PUNCT
ap-9131	197	1	journal	journal	PROPN
ap-9131	197	2	of	of	ADP
ap-9131	197	3	nonlinear	nonlinear	PROPN
ap-9131	197	4	mathematical	mathematical	ADJ
ap-9131	197	5	physics	physics	PROPN
ap-9131	197	6	9:24–35	9:24–35	NUM
ap-9131	197	7	,	,	PUNCT
ap-9131	197	8	2002	2002	NUM
ap-9131	197	9	.	.	PUNCT
ap-9131	198	1	https://doi.org/10.2991/jnmp.2002.9.s2.3	https://doi.org/10.2991/jnmp.2002.9.s2.3	NOUN
ap-9131	199	1	[	[	X
ap-9131	199	2	7	7	X
ap-9131	199	3	]	]	X
ap-9131	199	4	r.	r.	PROPN
ap-9131	199	5	m.	m.	PROPN
ap-9131	199	6	edelstein	edelstein	PROPN
ap-9131	199	7	,	,	PUNCT
ap-9131	199	8	k.	k.	PROPN
ap-9131	199	9	s.	s.	PROPN
ap-9131	199	10	govinder	govinder	PROPN
ap-9131	199	11	,	,	PUNCT
ap-9131	199	12	f.	f.	PROPN
ap-9131	199	13	m.	m.	PROPN
ap-9131	199	14	mahomed	mahome	VERB
ap-9131	199	15	.	.	PUNCT
ap-9131	200	1	solution	solution	NOUN
ap-9131	200	2	of	of	ADP
ap-9131	200	3	ordinary	ordinary	ADJ
ap-9131	200	4	differential	differential	ADJ
ap-9131	200	5	equations	equation	NOUN
ap-9131	200	6	via	via	ADP
ap-9131	200	7	nonlocal	nonlocal	ADJ
ap-9131	200	8	transformations	transformation	NOUN
ap-9131	200	9	.	.	PUNCT
ap-9131	201	1	journal	journal	PROPN
ap-9131	201	2	of	of	ADP
ap-9131	201	3	physics	physics	PROPN
ap-9131	201	4	a	a	PRON
ap-9131	201	5	:	:	PUNCT
ap-9131	201	6	mathematical	mathematical	ADJ
ap-9131	201	7	and	and	CCONJ
ap-9131	201	8	general	general	ADJ
ap-9131	201	9	34(6):1141–1152	34(6):1141–1152	NUM
ap-9131	201	10	,	,	PUNCT
ap-9131	201	11	2001	2001	NUM
ap-9131	201	12	.	.	PUNCT
ap-9131	202	1	https://doi.org/10.1088/0305-4470/34/6/306	https://doi.org/10.1088/0305-4470/34/6/306	NOUN
ap-9131	203	1	[	[	X
ap-9131	203	2	8	8	NUM
ap-9131	203	3	]	]	X
ap-9131	203	4	m.	m.	NOUN
ap-9131	203	5	molati	molati	PROPN
ap-9131	203	6	,	,	PUNCT
ap-9131	203	7	f.	f.	PROPN
ap-9131	203	8	m.	m.	PROPN
ap-9131	203	9	mahomed	mahome	VERB
ap-9131	203	10	,	,	PUNCT
ap-9131	203	11	c.	c.	PROPN
ap-9131	203	12	wafo	wafo	PROPN
ap-9131	203	13	soh	soh	PROPN
ap-9131	203	14	.	.	PUNCT
ap-9131	204	1	a	a	DET
ap-9131	204	2	group	group	NOUN
ap-9131	204	3	classification	classification	NOUN
ap-9131	204	4	of	of	ADP
ap-9131	204	5	a	a	DET
ap-9131	204	6	system	system	NOUN
ap-9131	204	7	of	of	ADP
ap-9131	204	8	partial	partial	ADJ
ap-9131	204	9	differential	differential	ADJ
ap-9131	204	10	equations	equation	NOUN
ap-9131	204	11	modeling	model	VERB
ap-9131	204	12	flow	flow	NOUN
ap-9131	204	13	in	in	ADP
ap-9131	204	14	collapsible	collapsible	ADJ
ap-9131	204	15	tubes	tube	NOUN
ap-9131	204	16	.	.	PUNCT
ap-9131	205	1	journal	journal	PROPN
ap-9131	205	2	of	of	ADP
ap-9131	205	3	nonlinear	nonlinear	PROPN
ap-9131	205	4	mathematical	mathematical	ADJ
ap-9131	205	5	physics	physics	PROPN
ap-9131	205	6	16:179–208	16:179–208	PROPN
ap-9131	205	7	,	,	PUNCT
ap-9131	205	8	2009	2009	NUM
ap-9131	205	9	.	.	PUNCT
ap-9131	206	1	https://doi.org/10.1142/s1402925109000406	https://doi.org/10.1142/s1402925109000406	NUM
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ap-9131	207	2	9	9	NUM
ap-9131	207	3	]	]	X
ap-9131	207	4	o.	o.	PROPN
ap-9131	207	5	o.	o.	PROPN
ap-9131	207	6	vaneeva	vaneeva	PROPN
ap-9131	207	7	,	,	PUNCT
ap-9131	207	8	r.	r.	PROPN
ap-9131	207	9	o.	o.	PROPN
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ap-9131	207	11	,	,	PUNCT
ap-9131	207	12	c.	c.	PROPN
ap-9131	207	13	sophocleous	sophocleous	PROPN
ap-9131	207	14	.	.	PUNCT
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ap-9131	208	2	symmetry	symmetry	NOUN
ap-9131	208	3	analysis	analysis	NOUN
ap-9131	208	4	of	of	ADP
ap-9131	208	5	two	two	NUM
ap-9131	208	6	-	-	PUNCT
ap-9131	208	7	dimensional	dimensional	ADJ
ap-9131	208	8	degenerate	degenerate	ADJ
ap-9131	208	9	burgers	burger	NOUN
ap-9131	208	10	equation	equation	NOUN
ap-9131	208	11	.	.	PUNCT
ap-9131	209	1	journal	journal	NOUN
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ap-9131	209	5	physics	physics	NOUN
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ap-9131	209	7	,	,	PUNCT
ap-9131	209	8	2021	2021	NUM
ap-9131	209	9	.	.	PUNCT
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ap-9131	210	3	10	10	NUM
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ap-9131	210	8	.	.	PUNCT
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ap-9131	211	2	po	po	PROPN
ap-9131	212	1	gruppam	gruppam	PROPN
ap-9131	212	2	dvizhenii	dvizhenii	PROPN
ap-9131	212	3	.	.	PUNCT
ap-9131	213	1	vyp	vyp	VERB
ap-9131	213	2	.	.	PUNCT
ap-9131	214	1	1	1	X
ap-9131	214	2	.	.	PUNCT
ap-9131	215	1	[	[	X
ap-9131	215	2	in	in	ADP
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ap-9131	215	6	on	on	ADP
ap-9131	215	7	groups	group	NOUN
ap-9131	215	8	of	of	ADP
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ap-9131	215	10	.	.	PUNCT
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ap-9131	216	3	1	1	NUM
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ap-9131	216	5	.	.	PUNCT
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ap-9131	217	5	,	,	PUNCT
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ap-9131	217	7	.	.	PUNCT
ap-9131	218	1	[	[	X
ap-9131	218	2	11	11	NUM
ap-9131	218	3	]	]	PUNCT
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ap-9131	218	5	m.	m.	PROPN
ap-9131	218	6	boothby	boothby	PROPN
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ap-9131	219	1	a	a	DET
ap-9131	219	2	transitivity	transitivity	NOUN
ap-9131	219	3	problem	problem	NOUN
ap-9131	219	4	from	from	ADP
ap-9131	219	5	control	control	NOUN
ap-9131	219	6	theory	theory	PROPN
ap-9131	219	7	.	.	PUNCT
ap-9131	220	1	journal	journal	PROPN
ap-9131	220	2	of	of	ADP
ap-9131	220	3	differential	differential	ADJ
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ap-9131	220	5	17(2):296–307	17(2):296–307	NUM
ap-9131	220	6	,	,	PUNCT
ap-9131	220	7	1975	1975	NUM
ap-9131	220	8	.	.	PUNCT
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ap-9131	222	2	12	12	NUM
ap-9131	222	3	]	]	PUNCT
ap-9131	222	4	a.	a.	NOUN
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ap-9131	222	11	,	,	PUNCT
ap-9131	222	12	p.	p.	PROPN
ap-9131	222	13	winternitz	winternitz	PROPN
ap-9131	222	14	.	.	PUNCT
ap-9131	223	1	difference	difference	NOUN
ap-9131	223	2	schemes	scheme	NOUN
ap-9131	223	3	with	with	ADP
ap-9131	223	4	point	point	NOUN
ap-9131	223	5	symmetries	symmetry	NOUN
ap-9131	223	6	and	and	CCONJ
ap-9131	223	7	their	their	PRON
ap-9131	223	8	numerical	numerical	ADJ
ap-9131	223	9	tests	test	NOUN
ap-9131	223	10	.	.	PUNCT
ap-9131	224	1	journal	journal	PROPN
ap-9131	224	2	of	of	ADP
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ap-9131	224	5	:	:	PUNCT
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ap-9131	224	7	and	and	CCONJ
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ap-9131	224	10	,	,	PUNCT
ap-9131	224	11	2006	2006	NUM
ap-9131	224	12	.	.	PUNCT
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ap-9131	226	1	[	[	X
ap-9131	226	2	13	13	NUM
ap-9131	226	3	]	]	PUNCT
ap-9131	226	4	r.	r.	PROPN
ap-9131	226	5	o.	o.	PROPN
ap-9131	226	6	popovych	popovych	PROPN
ap-9131	226	7	,	,	PUNCT
ap-9131	226	8	v.	v.	ADP
ap-9131	226	9	m.	m.	NOUN
ap-9131	226	10	boyko	boyko	PROPN
ap-9131	226	11	,	,	PUNCT
ap-9131	226	12	m.	m.	NOUN
ap-9131	226	13	o.	o.	PROPN
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ap-9131	226	17	w.	w.	PROPN
ap-9131	226	18	lutfullin	lutfullin	PROPN
ap-9131	226	19	.	.	PUNCT
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ap-9131	227	2	of	of	ADP
ap-9131	227	3	real	real	ADJ
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ap-9131	227	5	-	-	PUNCT
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ap-9131	227	9	.	.	PUNCT
ap-9131	228	1	journal	journal	PROPN
ap-9131	228	2	of	of	ADP
ap-9131	228	3	physics	physics	PROPN
ap-9131	228	4	a	a	PRON
ap-9131	228	5	:	:	PUNCT
ap-9131	228	6	mathematical	mathematical	ADJ
ap-9131	228	7	and	and	CCONJ
ap-9131	228	8	general	general	ADJ
ap-9131	228	9	36(26):7337–7360	36(26):7337–7360	NUM
ap-9131	228	10	,	,	PUNCT
ap-9131	228	11	2003	2003	NUM
ap-9131	228	12	.	.	PUNCT
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ap-9131	229	2	[	[	X
ap-9131	229	3	14	14	NUM
ap-9131	229	4	]	]	PUNCT
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ap-9131	229	7	,	,	PUNCT
ap-9131	229	8	m.	m.	PROPN
ap-9131	229	9	reva	reva	PROPN
ap-9131	229	10	,	,	PUNCT
ap-9131	229	11	n.	n.	PROPN
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ap-9131	229	13	,	,	PUNCT
ap-9131	229	14	y.	y.	PROPN
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ap-9131	229	16	.	.	PUNCT
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ap-9131	230	2	representations	representation	NOUN
ap-9131	230	3	of	of	ADP
ap-9131	230	4	classical	classical	ADJ
ap-9131	230	5	lie	lie	NOUN
ap-9131	230	6	algebras	algebra	NOUN
ap-9131	230	7	and	and	CCONJ
ap-9131	230	8	flag	flag	NOUN
ap-9131	230	9	varieties	variety	NOUN
ap-9131	230	10	.	.	PUNCT
ap-9131	231	1	physics	physics	NOUN
ap-9131	231	2	letters	letter	NOUN
ap-9131	231	3	b	b	PROPN
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ap-9131	231	5	,	,	PUNCT
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ap-9131	231	7	.	.	PUNCT
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ap-9131	233	2	15	15	NUM
ap-9131	233	3	]	]	PUNCT
ap-9131	233	4	m.	m.	NOUN
ap-9131	233	5	havlíček	havlíček	PROPN
ap-9131	233	6	,	,	PUNCT
ap-9131	233	7	w.	w.	PROPN
ap-9131	233	8	lassner	lassner	NOUN
ap-9131	233	9	.	.	PUNCT
ap-9131	234	1	canonical	canonical	ADJ
ap-9131	234	2	realizations	realization	NOUN
ap-9131	234	3	of	of	ADP
ap-9131	234	4	the	the	DET
ap-9131	234	5	lie	lie	NOUN
ap-9131	234	6	algebras	algebra	NOUN
ap-9131	234	7	gl(n	gl(n	X
ap-9131	234	8	,	,	PUNCT
ap-9131	234	9	r	r	NOUN
ap-9131	234	10	)	)	PUNCT
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ap-9131	234	13	,	,	PUNCT
ap-9131	234	14	r	r	NOUN
ap-9131	234	15	)	)	PUNCT
ap-9131	234	16	.	.	PUNCT
ap-9131	235	1	i.	i.	PROPN
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ap-9131	235	3	and	and	CCONJ
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ap-9131	235	5	.	.	PUNCT
ap-9131	236	1	reports	report	NOUN
ap-9131	236	2	on	on	ADP
ap-9131	236	3	mathematical	mathematical	ADJ
ap-9131	236	4	physics	physics	NOUN
ap-9131	236	5	8(3):391–399	8(3):391–399	NOUN
ap-9131	236	6	,	,	PUNCT
ap-9131	236	7	1975	1975	NUM
ap-9131	236	8	.	.	PUNCT
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ap-9131	238	3	]	]	PUNCT
ap-9131	238	4	j.	j.	PROPN
ap-9131	238	5	e.	e.	PROPN
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ap-9131	238	7	.	.	PUNCT
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ap-9131	239	2	to	to	PART
ap-9131	239	3	lie	lie	VERB
ap-9131	239	4	algebras	algebra	NOUN
ap-9131	239	5	and	and	CCONJ
ap-9131	239	6	representation	representation	NOUN
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ap-9131	239	8	,	,	PUNCT
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ap-9131	239	10	.	.	PROPN
ap-9131	239	11	9	9	NUM
ap-9131	239	12	of	of	ADP
ap-9131	239	13	graduate	graduate	ADJ
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ap-9131	239	15	in	in	ADP
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ap-9131	239	17	.	.	PUNCT
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ap-9131	240	2	-	-	PUNCT
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ap-9131	240	5	york	york	PROPN
ap-9131	240	6	,	,	PUNCT
ap-9131	240	7	usa	usa	PROPN
ap-9131	240	8	,	,	PUNCT
ap-9131	240	9	1972	1972	NUM
ap-9131	240	10	.	.	PUNCT
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ap-9131	241	2	340	340	NUM
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ap-9131	242	14	1	1	NUM
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ap-9131	242	16	2	2	NUM
ap-9131	242	17	realisation	realisation	NOUN
ap-9131	242	18	of	of	ADP
ap-9131	242	19	su(3	su(3	NOUN
ap-9131	242	20	)	)	PUNCT
ap-9131	242	21	3	3	NUM
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ap-9131	242	23	acknowledgements	acknowledgement	NOUN
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