id	sid	tid	token	lemma	pos
ap-1847	1	1	acta	acta	PROPN
ap-1847	1	2	polytechnica	polytechnica	PROPN
ap-1847	1	3	doi:10.14311	doi:10.14311	PROPN
ap-1847	1	4	/	/	SYM
ap-1847	1	5	ap.2013.53.0395	ap.2013.53.0395	PROPN
ap-1847	1	6	acta	acta	PROPN
ap-1847	1	7	polytechnica	polytechnica	PROPN
ap-1847	1	8	53(5):395–398	53(5):395–398	PROPN
ap-1847	1	9	,	,	PUNCT
ap-1847	1	10	2013	2013	NUM
ap-1847	1	11	©	©	PROPN
ap-1847	1	12	czech	czech	PROPN
ap-1847	1	13	technical	technical	PROPN
ap-1847	1	14	university	university	PROPN
ap-1847	1	15	in	in	ADP
ap-1847	1	16	prague	prague	PROPN
ap-1847	1	17	,	,	PUNCT
ap-1847	1	18	2013	2013	NUM
ap-1847	1	19	available	available	ADJ
ap-1847	1	20	online	online	ADV
ap-1847	1	21	at	at	ADP
ap-1847	1	22	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-1847	1	23	the	the	DET
ap-1847	1	24	shmushkevich	shmushkevich	NOUN
ap-1847	1	25	method	method	NOUN
ap-1847	1	26	for	for	ADP
ap-1847	1	27	higher	high	ADJ
ap-1847	1	28	symmetry	symmetry	NOUN
ap-1847	1	29	groups	group	NOUN
ap-1847	1	30	of	of	ADP
ap-1847	1	31	interacting	interact	VERB
ap-1847	1	32	particles	particle	NOUN
ap-1847	1	33	mark	mark	PROPN
ap-1847	1	34	bodnera	bodnera	PROPN
ap-1847	1	35	,	,	PUNCT
ap-1847	1	36	goce	goce	PROPN
ap-1847	1	37	chadzitaskosb	chadzitaskosb	PROPN
ap-1847	1	38	,	,	PUNCT
ap-1847	1	39	jiří	jiří	NOUN
ap-1847	1	40	paterac	paterac	NOUN
ap-1847	1	41	,	,	PUNCT
ap-1847	1	42	a	a	PRON
ap-1847	1	43	,	,	PUNCT
ap-1847	1	44	agnieszka	agnieszka	PROPN
ap-1847	1	45	tereszkiewiczd	tereszkiewiczd	PROPN
ap-1847	1	46	,	,	PUNCT
ap-1847	1	47	c,∗	c,∗	VERB
ap-1847	1	48	a	a	DET
ap-1847	1	49	mind	mind	NOUN
ap-1847	1	50	research	research	PROPN
ap-1847	1	51	institute	institute	PROPN
ap-1847	1	52	,	,	PUNCT
ap-1847	1	53	111	111	NUM
ap-1847	1	54	academy	academy	NOUN
ap-1847	1	55	drive	drive	NOUN
ap-1847	1	56	,	,	PUNCT
ap-1847	1	57	irvine	irvine	PROPN
ap-1847	1	58	,	,	PUNCT
ap-1847	1	59	ca	ca	PROPN
ap-1847	1	60	92617	92617	NUM
ap-1847	1	61	,	,	PUNCT
ap-1847	1	62	usa	usa	PROPN
ap-1847	1	63	b	b	PROPN
ap-1847	1	64	faculty	faculty	NOUN
ap-1847	1	65	of	of	ADP
ap-1847	1	66	nuclear	nuclear	ADJ
ap-1847	1	67	sciences	science	NOUN
ap-1847	1	68	and	and	CCONJ
ap-1847	1	69	physical	physical	ADJ
ap-1847	1	70	engineering	engineering	NOUN
ap-1847	1	71	,	,	PUNCT
ap-1847	1	72	czech	czech	PROPN
ap-1847	1	73	technical	technical	PROPN
ap-1847	1	74	university	university	PROPN
ap-1847	1	75	in	in	ADP
ap-1847	1	76	prague	prague	PROPN
ap-1847	1	77	,	,	PUNCT
ap-1847	1	78	břehová	břehová	VERB
ap-1847	1	79	7	7	NUM
ap-1847	1	80	,	,	PUNCT
ap-1847	1	81	cz-11519	cz-11519	ADJ
ap-1847	1	82	praha	praha	PROPN
ap-1847	1	83	1	1	NUM
ap-1847	1	84	,	,	PUNCT
ap-1847	1	85	czech	czech	PROPN
ap-1847	1	86	republic	republic	NOUN
ap-1847	1	87	c	c	PROPN
ap-1847	1	88	centre	centre	PROPN
ap-1847	1	89	de	de	X
ap-1847	1	90	recherches	recherche	NOUN
ap-1847	1	91	mathématiques	mathématique	NOUN
ap-1847	1	92	,	,	PUNCT
ap-1847	1	93	université	université	PROPN
ap-1847	1	94	de	de	PROPN
ap-1847	1	95	montréal	montréal	PROPN
ap-1847	1	96	,	,	PUNCT
ap-1847	1	97	c.	c.	PROPN
ap-1847	1	98	p.	p.	PROPN
ap-1847	1	99	6128	6128	NUM
ap-1847	1	100	,	,	PUNCT
ap-1847	1	101	succ	succ	PROPN
ap-1847	1	102	.	.	PUNCT
ap-1847	2	1	centre	centre	PROPN
ap-1847	2	2	-	-	PUNCT
ap-1847	2	3	ville	ville	PROPN
ap-1847	2	4	,	,	PUNCT
ap-1847	2	5	montréal	montréal	PROPN
ap-1847	2	6	,	,	PUNCT
ap-1847	2	7	h3c	h3c	PROPN
ap-1847	2	8	3j7	3j7	NUM
ap-1847	2	9	,	,	PUNCT
ap-1847	2	10	québec	québec	PROPN
ap-1847	2	11	,	,	PUNCT
ap-1847	2	12	canada	canada	PROPN
ap-1847	3	1	d	d	PROPN
ap-1847	3	2	institute	institute	PROPN
ap-1847	3	3	of	of	ADP
ap-1847	3	4	mathematics	mathematics	PROPN
ap-1847	3	5	,	,	PUNCT
ap-1847	3	6	university	university	NOUN
ap-1847	3	7	of	of	ADP
ap-1847	3	8	bialystok	bialystok	ADJ
ap-1847	3	9	,	,	PUNCT
ap-1847	3	10	akademicka	akademicka	PROPN
ap-1847	3	11	2	2	NUM
ap-1847	3	12	,	,	PUNCT
ap-1847	3	13	pl-15	pl-15	NOUN
ap-1847	3	14	-	-	PUNCT
ap-1847	3	15	267	267	NUM
ap-1847	3	16	bialystok	bialystok	ADJ
ap-1847	3	17	,	,	PUNCT
ap-1847	3	18	poland	poland	PROPN
ap-1847	3	19	∗	∗	NOUN
ap-1847	3	20	corresponding	correspond	VERB
ap-1847	3	21	author	author	NOUN
ap-1847	3	22	:	:	PUNCT
ap-1847	3	23	a.tereszkiewicz@uwb.edu.pl	a.tereszkiewicz@uwb.edu.pl	VERB
ap-1847	3	24	abstract	abstract	ADJ
ap-1847	3	25	.	.	PUNCT
ap-1847	4	1	about	about	ADV
ap-1847	4	2	60	60	NUM
ap-1847	4	3	years	year	NOUN
ap-1847	4	4	ago	ago	ADV
ap-1847	4	5	,	,	PUNCT
ap-1847	4	6	i.	i.	PROPN
ap-1847	4	7	shmushkevich	shmushkevich	PROPN
ap-1847	4	8	presented	present	VERB
ap-1847	4	9	a	a	DET
ap-1847	4	10	simple	simple	ADJ
ap-1847	4	11	ingenious	ingenious	ADJ
ap-1847	4	12	method	method	NOUN
ap-1847	4	13	for	for	ADP
ap-1847	4	14	computing	compute	VERB
ap-1847	4	15	the	the	DET
ap-1847	4	16	relative	relative	ADJ
ap-1847	4	17	probabilities	probability	NOUN
ap-1847	4	18	of	of	ADP
ap-1847	4	19	channels	channel	NOUN
ap-1847	4	20	involving	involve	VERB
ap-1847	4	21	the	the	DET
ap-1847	4	22	same	same	ADJ
ap-1847	4	23	interacting	interact	VERB
ap-1847	4	24	multiplets	multiplet	NOUN
ap-1847	4	25	of	of	ADP
ap-1847	4	26	particles	particle	NOUN
ap-1847	4	27	,	,	PUNCT
ap-1847	4	28	without	without	ADP
ap-1847	4	29	the	the	DET
ap-1847	4	30	need	need	NOUN
ap-1847	4	31	to	to	PART
ap-1847	4	32	compute	compute	VERB
ap-1847	4	33	the	the	DET
ap-1847	4	34	clebsch	clebsch	PROPN
ap-1847	4	35	-	-	PUNCT
ap-1847	4	36	gordan	gordan	PROPN
ap-1847	4	37	coefficients	coefficients	PROPN
ap-1847	4	38	.	.	PUNCT
ap-1847	5	1	the	the	DET
ap-1847	5	2	basic	basic	ADJ
ap-1847	5	3	idea	idea	NOUN
ap-1847	5	4	of	of	ADP
ap-1847	5	5	shmushkevich	shmushkevich	NOUN
ap-1847	5	6	is	be	AUX
ap-1847	5	7	“	"	PUNCT
ap-1847	5	8	isotopic	isotopic	ADJ
ap-1847	5	9	non	non	NOUN
ap-1847	5	10	-	-	NOUN
ap-1847	5	11	polarization	polarization	NOUN
ap-1847	5	12	”	"	PUNCT
ap-1847	5	13	of	of	ADP
ap-1847	5	14	the	the	DET
ap-1847	5	15	states	state	NOUN
ap-1847	5	16	before	before	ADP
ap-1847	5	17	the	the	DET
ap-1847	5	18	interaction	interaction	NOUN
ap-1847	5	19	and	and	CCONJ
ap-1847	5	20	after	after	ADP
ap-1847	5	21	it	it	PRON
ap-1847	5	22	.	.	PUNCT
ap-1847	6	1	hence	hence	ADV
ap-1847	6	2	his	his	PRON
ap-1847	6	3	underlying	underlying	ADJ
ap-1847	6	4	lie	lie	NOUN
ap-1847	6	5	group	group	NOUN
ap-1847	6	6	was	be	AUX
ap-1847	6	7	su(2	su(2	NOUN
ap-1847	6	8	)	)	PUNCT
ap-1847	6	9	.	.	PUNCT
ap-1847	7	1	we	we	PRON
ap-1847	7	2	extend	extend	VERB
ap-1847	7	3	this	this	DET
ap-1847	7	4	idea	idea	NOUN
ap-1847	7	5	to	to	ADP
ap-1847	7	6	any	any	DET
ap-1847	7	7	simple	simple	ADJ
ap-1847	7	8	lie	lie	NOUN
ap-1847	7	9	group	group	NOUN
ap-1847	7	10	.	.	PUNCT
ap-1847	8	1	this	this	DET
ap-1847	8	2	paper	paper	NOUN
ap-1847	8	3	determines	determine	VERB
ap-1847	8	4	the	the	DET
ap-1847	8	5	relative	relative	ADJ
ap-1847	8	6	probabilities	probability	NOUN
ap-1847	8	7	of	of	ADP
ap-1847	8	8	various	various	ADJ
ap-1847	8	9	channels	channel	NOUN
ap-1847	8	10	of	of	ADP
ap-1847	8	11	scattering	scatter	VERB
ap-1847	8	12	and	and	CCONJ
ap-1847	8	13	decay	decay	NOUN
ap-1847	8	14	processes	process	NOUN
ap-1847	8	15	following	follow	VERB
ap-1847	8	16	from	from	ADP
ap-1847	8	17	the	the	DET
ap-1847	8	18	invariance	invariance	NOUN
ap-1847	8	19	of	of	ADP
ap-1847	8	20	the	the	DET
ap-1847	8	21	interactions	interaction	NOUN
ap-1847	8	22	with	with	ADP
ap-1847	8	23	respect	respect	NOUN
ap-1847	8	24	to	to	ADP
ap-1847	8	25	a	a	DET
ap-1847	8	26	compact	compact	ADJ
ap-1847	8	27	simple	simple	NOUN
ap-1847	8	28	a	a	DET
ap-1847	8	29	lie	lie	NOUN
ap-1847	8	30	group	group	NOUN
ap-1847	8	31	.	.	PUNCT
ap-1847	9	1	aiming	aim	VERB
ap-1847	9	2	at	at	ADP
ap-1847	9	3	the	the	DET
ap-1847	9	4	probabilities	probability	NOUN
ap-1847	9	5	rather	rather	ADV
ap-1847	9	6	than	than	ADP
ap-1847	9	7	at	at	ADP
ap-1847	9	8	the	the	DET
ap-1847	9	9	clebsch	clebsch	PROPN
ap-1847	9	10	-	-	PROPN
ap-1847	9	11	gordan	gordan	PROPN
ap-1847	9	12	coefficients	coefficient	NOUN
ap-1847	9	13	makes	make	VERB
ap-1847	9	14	the	the	DET
ap-1847	9	15	task	task	NOUN
ap-1847	9	16	easier	easy	ADJ
ap-1847	9	17	,	,	PUNCT
ap-1847	9	18	and	and	CCONJ
ap-1847	9	19	simultaneous	simultaneous	ADJ
ap-1847	9	20	consideration	consideration	NOUN
ap-1847	9	21	of	of	ADP
ap-1847	9	22	all	all	DET
ap-1847	9	23	possible	possible	ADJ
ap-1847	9	24	channels	channel	NOUN
ap-1847	9	25	for	for	ADP
ap-1847	9	26	given	give	VERB
ap-1847	9	27	multiplets	multiplet	NOUN
ap-1847	9	28	involved	involve	VERB
ap-1847	9	29	in	in	ADP
ap-1847	9	30	the	the	DET
ap-1847	9	31	process	process	NOUN
ap-1847	9	32	,	,	PUNCT
ap-1847	9	33	makes	make	VERB
ap-1847	9	34	the	the	DET
ap-1847	9	35	task	task	NOUN
ap-1847	9	36	possible	possible	ADJ
ap-1847	9	37	.	.	PUNCT
ap-1847	10	1	the	the	DET
ap-1847	10	2	probability	probability	NOUN
ap-1847	10	3	of	of	ADP
ap-1847	10	4	states	state	NOUN
ap-1847	10	5	with	with	ADP
ap-1847	10	6	multiplicities	multiplicity	NOUN
ap-1847	10	7	greater	great	ADJ
ap-1847	10	8	than	than	ADP
ap-1847	10	9	1	1	NUM
ap-1847	10	10	is	be	AUX
ap-1847	10	11	averaged	average	VERB
ap-1847	10	12	over	over	ADP
ap-1847	10	13	.	.	PUNCT
ap-1847	11	1	examples	example	NOUN
ap-1847	11	2	with	with	ADP
ap-1847	11	3	symmetry	symmetry	NOUN
ap-1847	11	4	groups	group	NOUN
ap-1847	11	5	o(5	o(5	PROPN
ap-1847	11	6	)	)	PUNCT
ap-1847	11	7	,	,	PUNCT
ap-1847	11	8	f	f	PROPN
ap-1847	11	9	(	(	PUNCT
ap-1847	11	10	4	4	NUM
ap-1847	11	11	)	)	PUNCT
ap-1847	11	12	,	,	PUNCT
ap-1847	11	13	and	and	CCONJ
ap-1847	11	14	e(8	e(8	VERB
ap-1847	11	15	)	)	PUNCT
ap-1847	11	16	are	be	AUX
ap-1847	11	17	shown	show	VERB
ap-1847	11	18	.	.	PUNCT
ap-1847	12	1	keywords	keyword	NOUN
ap-1847	12	2	:	:	PUNCT
ap-1847	12	3	isospin	isospin	VERB
ap-1847	12	4	,	,	PUNCT
ap-1847	12	5	particle	particle	NOUN
ap-1847	12	6	collisions	collision	NOUN
ap-1847	12	7	,	,	PUNCT
ap-1847	12	8	lie	lie	NOUN
ap-1847	12	9	group	group	NOUN
ap-1847	12	10	representation	representation	NOUN
ap-1847	12	11	.	.	PUNCT
ap-1847	13	1	submitted	submit	VERB
ap-1847	13	2	:	:	PUNCT
ap-1847	13	3	1	1	NUM
ap-1847	13	4	april	april	PROPN
ap-1847	13	5	2013	2013	NUM
ap-1847	13	6	.	.	PUNCT
ap-1847	14	1	accepted	accept	VERB
ap-1847	14	2	:	:	PUNCT
ap-1847	14	3	7	7	NUM
ap-1847	14	4	may	may	PROPN
ap-1847	14	5	2013	2013	NUM
ap-1847	14	6	.	.	PUNCT
ap-1847	15	1	1	1	X
ap-1847	15	2	.	.	X
ap-1847	15	3	introduction	introduction	NOUN
ap-1847	15	4	the	the	DET
ap-1847	15	5	method	method	NOUN
ap-1847	15	6	of	of	ADP
ap-1847	15	7	shmushkevich	shmushkevich	NOUN
ap-1847	15	8	[	[	X
ap-1847	15	9	1	1	NUM
ap-1847	15	10	,	,	PUNCT
ap-1847	15	11	2	2	NUM
ap-1847	15	12	]	]	PUNCT
ap-1847	15	13	was	be	AUX
ap-1847	15	14	conceived	conceive	VERB
ap-1847	15	15	as	as	ADP
ap-1847	15	16	a	a	DET
ap-1847	15	17	simpler	simple	ADJ
ap-1847	15	18	alternative	alternative	NOUN
ap-1847	15	19	to	to	ADP
ap-1847	15	20	computing	compute	VERB
ap-1847	15	21	the	the	DET
ap-1847	15	22	relative	relative	ADJ
ap-1847	15	23	probabilities	probability	NOUN
ap-1847	15	24	of	of	ADP
ap-1847	15	25	various	various	ADJ
ap-1847	15	26	channels	channel	NOUN
ap-1847	15	27	of	of	ADP
ap-1847	15	28	scattering	scatter	VERB
ap-1847	15	29	and	and	CCONJ
ap-1847	15	30	decay	decay	NOUN
ap-1847	15	31	processes	process	NOUN
ap-1847	15	32	under	under	ADP
ap-1847	15	33	strict	strict	ADJ
ap-1847	15	34	isospin	isospin	ADJ
ap-1847	15	35	invariance	invariance	NOUN
ap-1847	15	36	(	(	PUNCT
ap-1847	15	37	su(2	su(2	NOUN
ap-1847	15	38	)	)	PUNCT
ap-1847	15	39	invariance	invariance	NOUN
ap-1847	15	40	)	)	PUNCT
ap-1847	15	41	.	.	PUNCT
ap-1847	16	1	the	the	DET
ap-1847	16	2	traditional	traditional	ADJ
ap-1847	16	3	alternative	alternative	ADJ
ap-1847	16	4	method	method	NOUN
ap-1847	16	5	for	for	ADP
ap-1847	16	6	calculating	calculate	VERB
ap-1847	16	7	the	the	DET
ap-1847	16	8	probabilities	probability	NOUN
ap-1847	16	9	of	of	ADP
ap-1847	16	10	the	the	DET
ap-1847	16	11	same	same	ADJ
ap-1847	16	12	channels	channel	NOUN
ap-1847	16	13	is	be	AUX
ap-1847	16	14	to	to	PART
ap-1847	16	15	calculate	calculate	VERB
ap-1847	16	16	first	first	ADV
ap-1847	16	17	all	all	DET
ap-1847	16	18	pertinent	pertinent	ADJ
ap-1847	16	19	clebsch	clebsch	PROPN
ap-1847	16	20	-	-	PUNCT
ap-1847	16	21	gordan	gordan	PROPN
ap-1847	16	22	coefficients	coefficients	PROPN
ap-1847	16	23	(	(	PUNCT
ap-1847	16	24	cgc	cgc	PROPN
ap-1847	16	25	)	)	PUNCT
ap-1847	16	26	for	for	ADP
ap-1847	16	27	the	the	DET
ap-1847	16	28	channel	channel	NOUN
ap-1847	16	29	.	.	PUNCT
ap-1847	17	1	the	the	DET
ap-1847	17	2	most	most	ADV
ap-1847	17	3	remarkable	remarkable	ADJ
ap-1847	17	4	feature	feature	NOUN
ap-1847	17	5	of	of	ADP
ap-1847	17	6	the	the	DET
ap-1847	17	7	shmushkevich	shmushkevich	NOUN
ap-1847	17	8	method	method	NOUN
ap-1847	17	9	is	be	AUX
ap-1847	17	10	the	the	DET
ap-1847	17	11	complete	complete	ADJ
ap-1847	17	12	avoidance	avoidance	NOUN
ap-1847	17	13	of	of	ADP
ap-1847	17	14	the	the	DET
ap-1847	17	15	need	need	NOUN
ap-1847	17	16	to	to	PART
ap-1847	17	17	calculate	calculate	VERB
ap-1847	17	18	the	the	DET
ap-1847	17	19	clebsch	clebsch	PROPN
ap-1847	17	20	-	-	PUNCT
ap-1847	17	21	gordan	gordan	PROPN
ap-1847	17	22	coefficients	coefficients	PROPN
ap-1847	17	23	.	.	PUNCT
ap-1847	18	1	the	the	DET
ap-1847	18	2	underlying	underlying	ADJ
ap-1847	18	3	idea	idea	NOUN
ap-1847	18	4	is	be	AUX
ap-1847	18	5	to	to	PART
ap-1847	18	6	consider	consider	VERB
ap-1847	18	7	isotopically	isotopically	ADV
ap-1847	18	8	unpolarized	unpolarized	ADJ
ap-1847	18	9	states	state	NOUN
ap-1847	18	10	before	before	ADP
ap-1847	18	11	and	and	CCONJ
ap-1847	18	12	after	after	ADP
ap-1847	18	13	the	the	DET
ap-1847	18	14	interaction	interaction	NOUN
ap-1847	18	15	,	,	PUNCT
ap-1847	18	16	assuming	assume	VERB
ap-1847	18	17	that	that	SCONJ
ap-1847	18	18	each	each	DET
ap-1847	18	19	possible	possible	ADJ
ap-1847	18	20	state	state	NOUN
ap-1847	18	21	came	come	VERB
ap-1847	18	22	with	with	ADP
ap-1847	18	23	equal	equal	ADJ
ap-1847	18	24	probability	probability	NOUN
ap-1847	18	25	.	.	PUNCT
ap-1847	19	1	the	the	DET
ap-1847	19	2	simplicity	simplicity	NOUN
ap-1847	19	3	of	of	ADP
ap-1847	19	4	the	the	DET
ap-1847	19	5	idea	idea	NOUN
ap-1847	19	6	has	have	AUX
ap-1847	19	7	attracted	attract	VERB
ap-1847	19	8	the	the	DET
ap-1847	19	9	attention	attention	NOUN
ap-1847	19	10	of	of	ADP
ap-1847	19	11	many	many	ADJ
ap-1847	19	12	physicists	physicist	NOUN
ap-1847	20	1	[	[	X
ap-1847	20	2	3–6	3–6	NUM
ap-1847	20	3	]	]	X
ap-1847	20	4	.	.	PUNCT
ap-1847	21	1	technically	technically	ADV
ap-1847	21	2	,	,	PUNCT
ap-1847	21	3	the	the	DET
ap-1847	21	4	two	two	NUM
ap-1847	21	5	methods	method	NOUN
ap-1847	21	6	differ	differ	VERB
ap-1847	21	7	in	in	ADP
ap-1847	21	8	their	their	PRON
ap-1847	21	9	objective	objective	NOUN
ap-1847	21	10	:	:	PUNCT
ap-1847	21	11	shmushkevich	shmushkevich	PROPN
ap-1847	21	12	’s	’s	PART
ap-1847	21	13	method	method	NOUN
ap-1847	21	14	calculates	calculate	VERB
ap-1847	21	15	just	just	ADV
ap-1847	21	16	the	the	DET
ap-1847	21	17	probabilities	probability	NOUN
ap-1847	21	18	.	.	PUNCT
ap-1847	22	1	the	the	DET
ap-1847	22	2	conventional	conventional	ADJ
ap-1847	22	3	alternative	alternative	ADJ
ap-1847	22	4	method	method	NOUN
ap-1847	22	5	calculates	calculate	VERB
ap-1847	22	6	the	the	DET
ap-1847	22	7	cgc	cgc	NOUN
ap-1847	22	8	,	,	PUNCT
ap-1847	22	9	their	their	PRON
ap-1847	22	10	squares	square	NOUN
ap-1847	22	11	,	,	PUNCT
ap-1847	22	12	and	and	CCONJ
ap-1847	22	13	then	then	ADV
ap-1847	22	14	provides	provide	VERB
ap-1847	22	15	the	the	DET
ap-1847	22	16	probabilities	probability	NOUN
ap-1847	22	17	.	.	PUNCT
ap-1847	23	1	neither	neither	PRON
ap-1847	23	2	of	of	ADP
ap-1847	23	3	the	the	DET
ap-1847	23	4	tasks	task	NOUN
ap-1847	23	5	is	be	AUX
ap-1847	23	6	easy	easy	ADJ
ap-1847	23	7	for	for	ADP
ap-1847	23	8	higher	high	ADJ
ap-1847	23	9	ranks	rank	NOUN
ap-1847	23	10	of	of	ADP
ap-1847	23	11	the	the	DET
ap-1847	23	12	representations	representation	NOUN
ap-1847	23	13	.	.	PUNCT
ap-1847	24	1	from	from	ADP
ap-1847	24	2	the	the	DET
ap-1847	24	3	point	point	NOUN
ap-1847	24	4	of	of	ADP
ap-1847	24	5	view	view	NOUN
ap-1847	24	6	of	of	ADP
ap-1847	24	7	symmetries	symmetry	NOUN
ap-1847	24	8	the	the	DET
ap-1847	24	9	two	two	NUM
ap-1847	24	10	methods	method	NOUN
ap-1847	24	11	differ	differ	VERB
ap-1847	24	12	by	by	ADP
ap-1847	24	13	the	the	DET
ap-1847	24	14	symmetry	symmetry	NOUN
ap-1847	24	15	group	group	NOUN
ap-1847	24	16	that	that	PRON
ap-1847	24	17	they	they	PRON
ap-1847	24	18	exploit	exploit	VERB
ap-1847	24	19	:	:	PUNCT
ap-1847	24	20	shmushkevich	shmushkevich	NOUN
ap-1847	24	21	uses	use	VERB
ap-1847	24	22	just	just	ADV
ap-1847	24	23	the	the	DET
ap-1847	24	24	weyl	weyl	VERB
ap-1847	24	25	group	group	NOUN
ap-1847	24	26	of	of	ADP
ap-1847	24	27	the	the	DET
ap-1847	24	28	lie	lie	NOUN
ap-1847	24	29	group	group	NOUN
ap-1847	24	30	,	,	PUNCT
ap-1847	24	31	while	while	SCONJ
ap-1847	24	32	cgcs	cgcs	NOUN
ap-1847	24	33	are	be	AUX
ap-1847	24	34	built	build	VERB
ap-1847	24	35	using	use	VERB
ap-1847	24	36	the	the	DET
ap-1847	24	37	symmetry	symmetry	NOUN
ap-1847	24	38	group	group	NOUN
ap-1847	24	39	of	of	ADP
ap-1847	24	40	demazure	demazure	NOUN
ap-1847	24	41	-	-	PUNCT
ap-1847	24	42	tits	tit	NOUN
ap-1847	24	43	,	,	PUNCT
ap-1847	24	44	see	see	VERB
ap-1847	24	45	[	[	X
ap-1847	24	46	7	7	NUM
ap-1847	24	47	,	,	PUNCT
ap-1847	24	48	8	8	NUM
ap-1847	24	49	]	]	PUNCT
ap-1847	24	50	.	.	PUNCT
ap-1847	25	1	the	the	DET
ap-1847	25	2	difficulty	difficulty	NOUN
ap-1847	25	3	of	of	ADP
ap-1847	25	4	generalizing	generalize	VERB
ap-1847	25	5	of	of	ADP
ap-1847	25	6	shmushkevich	shmushkevich	NOUN
ap-1847	25	7	’s	’s	PART
ap-1847	25	8	method	method	NOUN
ap-1847	25	9	to	to	ADP
ap-1847	25	10	higher	high	ADJ
ap-1847	25	11	rank	rank	NOUN
ap-1847	25	12	groups	group	NOUN
ap-1847	25	13	lies	lie	VERB
ap-1847	25	14	in	in	ADP
ap-1847	25	15	the	the	DET
ap-1847	25	16	frequent	frequent	ADJ
ap-1847	25	17	occurrence	occurrence	NOUN
ap-1847	25	18	of	of	ADP
ap-1847	25	19	multiple	multiple	ADJ
ap-1847	25	20	states	state	NOUN
ap-1847	25	21	with	with	ADP
ap-1847	25	22	the	the	DET
ap-1847	25	23	same	same	ADJ
ap-1847	25	24	quantum	quantum	NOUN
ap-1847	25	25	numbers	number	NOUN
ap-1847	25	26	,	,	PUNCT
ap-1847	25	27	equivalently	equivalently	ADV
ap-1847	25	28	labeled	label	VERB
ap-1847	25	29	by	by	ADP
ap-1847	25	30	the	the	DET
ap-1847	25	31	same	same	ADJ
ap-1847	25	32	weights	weight	NOUN
ap-1847	25	33	of	of	ADP
ap-1847	25	34	irreducible	irreducible	ADJ
ap-1847	25	35	representations	representation	NOUN
ap-1847	25	36	[	[	X
ap-1847	25	37	9	9	NUM
ap-1847	25	38	]	]	PUNCT
ap-1847	25	39	,	,	PUNCT
ap-1847	25	40	as	as	ADV
ap-1847	25	41	well	well	ADV
ap-1847	25	42	as	as	ADP
ap-1847	25	43	the	the	DET
ap-1847	25	44	sheer	sheer	ADJ
ap-1847	25	45	number	number	NOUN
ap-1847	25	46	of	of	ADP
ap-1847	25	47	channels	channel	NOUN
ap-1847	25	48	that	that	PRON
ap-1847	25	49	need	need	VERB
ap-1847	25	50	to	to	PART
ap-1847	25	51	be	be	AUX
ap-1847	25	52	written	write	VERB
ap-1847	25	53	down	down	ADP
ap-1847	25	54	.	.	PUNCT
ap-1847	26	1	it	it	PRON
ap-1847	26	2	is	be	AUX
ap-1847	26	3	likely	likely	ADJ
ap-1847	26	4	that	that	SCONJ
ap-1847	26	5	practical	practical	ADJ
ap-1847	26	6	exploitation	exploitation	NOUN
ap-1847	26	7	of	of	ADP
ap-1847	26	8	shmushkevich	shmushkevich	NOUN
ap-1847	26	9	’s	’s	PART
ap-1847	26	10	idea	idea	NOUN
ap-1847	26	11	for	for	ADP
ap-1847	26	12	higher	high	ADJ
ap-1847	26	13	groups	group	NOUN
ap-1847	26	14	and	and	CCONJ
ap-1847	26	15	possibly	possibly	ADV
ap-1847	26	16	representations	representation	NOUN
ap-1847	26	17	of	of	ADP
ap-1847	26	18	much	much	ADV
ap-1847	26	19	higher	high	ADJ
ap-1847	26	20	dimensions	dimension	NOUN
ap-1847	26	21	,	,	PUNCT
ap-1847	26	22	will	will	AUX
ap-1847	26	23	not	not	PART
ap-1847	26	24	proceed	proceed	VERB
ap-1847	26	25	by	by	ADP
ap-1847	26	26	spelling	spell	VERB
ap-1847	26	27	out	out	ADP
ap-1847	26	28	the	the	DET
ap-1847	26	29	large	large	ADJ
ap-1847	26	30	number	number	NOUN
ap-1847	26	31	of	of	ADP
ap-1847	26	32	channels	channel	NOUN
ap-1847	26	33	for	for	ADP
ap-1847	26	34	each	each	DET
ap-1847	26	35	case	case	NOUN
ap-1847	26	36	and	and	CCONJ
ap-1847	26	37	counting	count	VERB
ap-1847	26	38	the	the	DET
ap-1847	26	39	number	number	NOUN
ap-1847	26	40	of	of	ADP
ap-1847	26	41	occurrences	occurrence	NOUN
ap-1847	26	42	of	of	ADP
ap-1847	26	43	each	each	DET
ap-1847	26	44	state	state	NOUN
ap-1847	26	45	in	in	ADP
ap-1847	26	46	all	all	DET
ap-1847	26	47	the	the	DET
ap-1847	26	48	channels	channel	NOUN
ap-1847	26	49	.	.	PUNCT
ap-1847	27	1	instead	instead	ADV
ap-1847	27	2	,	,	PUNCT
ap-1847	27	3	one	one	PRON
ap-1847	27	4	would	would	AUX
ap-1847	27	5	start	start	VERB
ap-1847	27	6	from	from	ADP
ap-1847	27	7	one	one	NUM
ap-1847	27	8	known	know	VERB
ap-1847	27	9	channel	channel	NOUN
ap-1847	27	10	and	and	CCONJ
ap-1847	27	11	use	use	VERB
ap-1847	27	12	the	the	DET
ap-1847	27	13	symmetry	symmetry	NOUN
ap-1847	27	14	group	group	NOUN
ap-1847	27	15	,	,	PUNCT
ap-1847	27	16	the	the	DET
ap-1847	27	17	weyl	weyl	VERB
ap-1847	27	18	group	group	NOUN
ap-1847	27	19	in	in	ADP
ap-1847	27	20	this	this	DET
ap-1847	27	21	case	case	NOUN
ap-1847	27	22	,	,	PUNCT
ap-1847	27	23	to	to	PART
ap-1847	27	24	produce	produce	VERB
ap-1847	27	25	other	other	ADJ
ap-1847	27	26	channels	channel	NOUN
ap-1847	27	27	with	with	ADP
ap-1847	27	28	the	the	DET
ap-1847	27	29	same	same	ADJ
ap-1847	27	30	probability	probability	NOUN
ap-1847	27	31	.	.	PUNCT
ap-1847	28	1	this	this	PRON
ap-1847	28	2	is	be	AUX
ap-1847	28	3	a	a	DET
ap-1847	28	4	routine	routine	ADJ
ap-1847	28	5	operation	operation	NOUN
ap-1847	28	6	which	which	PRON
ap-1847	28	7	,	,	PUNCT
ap-1847	28	8	however	however	ADV
ap-1847	28	9	does	do	AUX
ap-1847	28	10	not	not	PART
ap-1847	28	11	produce	produce	VERB
ap-1847	28	12	all	all	DET
ap-1847	28	13	possible	possible	ADJ
ap-1847	28	14	channels	channel	NOUN
ap-1847	28	15	.	.	PUNCT
ap-1847	29	1	this	this	PRON
ap-1847	29	2	will	will	AUX
ap-1847	29	3	relate	relate	VERB
ap-1847	29	4	only	only	ADV
ap-1847	29	5	the	the	DET
ap-1847	29	6	states	state	NOUN
ap-1847	29	7	which	which	PRON
ap-1847	29	8	are	be	AUX
ap-1847	29	9	situated	situate	VERB
ap-1847	29	10	on	on	ADP
ap-1847	29	11	the	the	DET
ap-1847	29	12	same	same	ADJ
ap-1847	29	13	weyl	weyl	VERB
ap-1847	29	14	group	group	NOUN
ap-1847	29	15	orbit	orbit	NOUN
ap-1847	29	16	.	.	PUNCT
ap-1847	30	1	this	this	PRON
ap-1847	30	2	may	may	AUX
ap-1847	30	3	be	be	AUX
ap-1847	30	4	all	all	DET
ap-1847	30	5	that	that	PRON
ap-1847	30	6	one	one	NUM
ap-1847	30	7	needs	need	VERB
ap-1847	30	8	as	as	ADV
ap-1847	30	9	long	long	ADV
ap-1847	30	10	as	as	SCONJ
ap-1847	30	11	only	only	ADV
ap-1847	30	12	the	the	DET
ap-1847	30	13	channels	channel	NOUN
ap-1847	30	14	defined	define	VERB
ap-1847	30	15	by	by	ADP
ap-1847	30	16	individual	individual	ADJ
ap-1847	30	17	orbits	orbit	NOUN
ap-1847	30	18	are	be	AUX
ap-1847	30	19	studied	study	VERB
ap-1847	30	20	.	.	PUNCT
ap-1847	31	1	however	however	ADV
ap-1847	31	2	,	,	PUNCT
ap-1847	31	3	if	if	SCONJ
ap-1847	31	4	the	the	DET
ap-1847	31	5	equal	equal	ADJ
ap-1847	31	6	probability	probability	NOUN
ap-1847	31	7	of	of	ADP
ap-1847	31	8	all	all	DET
ap-1847	31	9	the	the	DET
ap-1847	31	10	states	state	NOUN
ap-1847	31	11	of	of	ADP
ap-1847	31	12	the	the	DET
ap-1847	31	13	lie	lie	NOUN
ap-1847	31	14	group	group	NOUN
ap-1847	31	15	is	be	AUX
ap-1847	31	16	to	to	PART
ap-1847	31	17	be	be	AUX
ap-1847	31	18	involved	involve	VERB
ap-1847	31	19	,	,	PUNCT
ap-1847	31	20	the	the	DET
ap-1847	31	21	link	link	NOUN
ap-1847	31	22	between	between	ADP
ap-1847	31	23	different	different	ADJ
ap-1847	31	24	orbits	orbit	NOUN
ap-1847	31	25	present	present	ADJ
ap-1847	31	26	in	in	ADP
ap-1847	31	27	the	the	DET
ap-1847	31	28	same	same	ADJ
ap-1847	31	29	representation	representation	NOUN
ap-1847	31	30	has	have	VERB
ap-1847	31	31	to	to	PART
ap-1847	31	32	be	be	AUX
ap-1847	31	33	imposed	impose	VERB
ap-1847	31	34	independently	independently	ADV
ap-1847	31	35	.	.	PUNCT
ap-1847	32	1	for	for	ADP
ap-1847	32	2	the	the	DET
ap-1847	32	3	probabilities	probability	NOUN
ap-1847	32	4	,	,	PUNCT
ap-1847	32	5	a	a	DET
ap-1847	32	6	natural	natural	ADJ
ap-1847	32	7	link	link	NOUN
ap-1847	32	8	is	be	AUX
ap-1847	32	9	provided	provide	VERB
ap-1847	32	10	by	by	ADP
ap-1847	32	11	the	the	DET
ap-1847	32	12	requirement	requirement	NOUN
ap-1847	32	13	that	that	SCONJ
ap-1847	32	14	the	the	DET
ap-1847	32	15	probabilities	probability	NOUN
ap-1847	32	16	add	add	VERB
ap-1847	32	17	up	up	ADP
ap-1847	32	18	to	to	ADP
ap-1847	32	19	one	one	NUM
ap-1847	32	20	.	.	PUNCT
ap-1847	33	1	if	if	SCONJ
ap-1847	33	2	an	an	DET
ap-1847	33	3	orbit	orbit	NOUN
ap-1847	33	4	is	be	AUX
ap-1847	33	5	present	present	ADJ
ap-1847	33	6	in	in	ADP
ap-1847	33	7	irreducible	irreducible	ADJ
ap-1847	33	8	representation	representation	NOUN
ap-1847	33	9	more	more	ADV
ap-1847	33	10	than	than	ADP
ap-1847	33	11	once	once	ADV
ap-1847	33	12	,	,	PUNCT
ap-1847	33	13	say	say	VERB
ap-1847	33	14	m	m	NOUN
ap-1847	33	15	times	time	NOUN
ap-1847	33	16	,	,	PUNCT
ap-1847	33	17	we	we	PRON
ap-1847	33	18	count	count	VERB
ap-1847	33	19	them	they	PRON
ap-1847	33	20	as	as	ADP
ap-1847	33	21	equally	equally	ADV
ap-1847	33	22	probable	probable	ADJ
ap-1847	33	23	m	m	NOUN
ap-1847	33	24	channels	channel	NOUN
ap-1847	33	25	.	.	PUNCT
ap-1847	34	1	in	in	ADP
ap-1847	34	2	this	this	DET
ap-1847	34	3	paper	paper	NOUN
ap-1847	34	4	395	395	NUM
ap-1847	34	5	http://dx.doi.org/10.14311/ap.2013.53.0395	http://dx.doi.org/10.14311/ap.2013.53.0395	PRON
ap-1847	34	6	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-1847	34	7	m.	m.	NOUN
ap-1847	34	8	bodner	bodner	NOUN
ap-1847	34	9	,	,	PUNCT
ap-1847	34	10	g.	g.	PROPN
ap-1847	34	11	chadzitaskos	chadzitaskos	PROPN
ap-1847	34	12	,	,	PUNCT
ap-1847	34	13	j.	j.	PROPN
ap-1847	34	14	patera	patera	PROPN
ap-1847	34	15	,	,	PUNCT
ap-1847	34	16	a.	a.	PROPN
ap-1847	34	17	tereszkiewicz	tereszkiewicz	PROPN
ap-1847	34	18	acta	acta	PROPN
ap-1847	34	19	polytechnica	polytechnica	PROPN
ap-1847	34	20	c2	c2	PROPN
ap-1847	34	21	decomposition	decomposition	NOUN
ap-1847	34	22	into	into	ADP
ap-1847	34	23	irreducible	irreducible	ADJ
ap-1847	34	24	representations	representation	NOUN
ap-1847	34	25	with	with	ADP
ap-1847	34	26	multiplicities	multiplicity	NOUN
ap-1847	34	27	multiplicity	multiplicity	NOUN
ap-1847	34	28	orbit	orbit	NOUN
ap-1847	34	29	size	size	NOUN
ap-1847	34	30	(	(	PUNCT
ap-1847	34	31	20	20	NUM
ap-1847	34	32	)	)	PUNCT
ap-1847	34	33	×	×	NOUN
ap-1847	34	34	(	(	PUNCT
ap-1847	34	35	10	10	NUM
ap-1847	34	36	)	)	PUNCT
ap-1847	34	37	(	(	PUNCT
ap-1847	34	38	30	30	NUM
ap-1847	34	39	)	)	PUNCT
ap-1847	34	40	(	(	PUNCT
ap-1847	34	41	11	11	NUM
ap-1847	34	42	)	)	PUNCT
ap-1847	34	43	(	(	PUNCT
ap-1847	34	44	10	10	NUM
ap-1847	34	45	)	)	PUNCT
ap-1847	34	46	10	10	NUM
ap-1847	34	47	×	×	NOUN
ap-1847	34	48	4	4	NUM
ap-1847	35	1	[	[	SYM
ap-1847	35	2	30	30	NUM
ap-1847	35	3	]	]	SYM
ap-1847	35	4	1	1	NUM
ap-1847	35	5	4	4	NUM
ap-1847	36	1	[	[	X
ap-1847	36	2	11	11	NUM
ap-1847	36	3	]	]	X
ap-1847	36	4	[	[	X
ap-1847	36	5	11	11	NUM
ap-1847	36	6	]	]	SYM
ap-1847	36	7	2	2	NUM
ap-1847	36	8	8	8	NUM
ap-1847	36	9	2[10	2[10	NUM
ap-1847	36	10	]	]	PUNCT
ap-1847	37	1	2[10	2[10	NUM
ap-1847	37	2	]	]	PUNCT
ap-1847	38	1	[	[	X
ap-1847	38	2	10	10	NUM
ap-1847	38	3	]	]	SYM
ap-1847	38	4	5	5	NUM
ap-1847	38	5	4	4	NUM
ap-1847	38	6	decomposition	decomposition	NOUN
ap-1847	38	7	into	into	ADP
ap-1847	38	8	orbits	orbit	NOUN
ap-1847	38	9	with	with	ADP
ap-1847	38	10	multiplicities	multiplicity	NOUN
ap-1847	38	11	[	[	X
ap-1847	38	12	30	30	NUM
ap-1847	38	13	]	]	PUNCT
ap-1847	38	14	2[11	2[11	NUM
ap-1847	38	15	]	]	X
ap-1847	38	16	5[10	5[10	NUM
ap-1847	38	17	]	]	PUNCT
ap-1847	38	18	40	40	NUM
ap-1847	38	19	table	table	NOUN
ap-1847	38	20	1	1	NUM
ap-1847	38	21	.	.	PUNCT
ap-1847	38	22	decomposition	decomposition	NOUN
ap-1847	38	23	of	of	ADP
ap-1847	38	24	the	the	DET
ap-1847	38	25	product	product	NOUN
ap-1847	38	26	in	in	ADP
ap-1847	38	27	the	the	DET
ap-1847	38	28	c2	c2	PROPN
ap-1847	38	29	example	example	NOUN
ap-1847	38	30	.	.	PUNCT
ap-1847	39	1	decomposition	decomposition	NOUN
ap-1847	39	2	is	be	AUX
ap-1847	39	3	given	give	VERB
ap-1847	39	4	in	in	ADP
ap-1847	39	5	the	the	DET
ap-1847	39	6	weight	weight	NOUN
ap-1847	39	7	system	system	NOUN
ap-1847	39	8	of	of	ADP
ap-1847	39	9	irreducible	irreducible	ADJ
ap-1847	39	10	representations	representation	NOUN
ap-1847	39	11	(	(	PUNCT
ap-1847	39	12	the	the	DET
ap-1847	39	13	first	first	ADJ
ap-1847	39	14	line	line	NOUN
ap-1847	39	15	)	)	PUNCT
ap-1847	39	16	and	and	CCONJ
ap-1847	39	17	in	in	ADP
ap-1847	39	18	terms	term	NOUN
ap-1847	39	19	of	of	ADP
ap-1847	39	20	orbits	orbit	NOUN
ap-1847	39	21	(	(	PUNCT
ap-1847	39	22	bottom	bottom	ADJ
ap-1847	39	23	line	line	NOUN
ap-1847	39	24	)	)	PUNCT
ap-1847	39	25	.	.	PUNCT
ap-1847	40	1	the	the	DET
ap-1847	40	2	dimensions	dimension	NOUN
ap-1847	40	3	of	of	ADP
ap-1847	40	4	the	the	DET
ap-1847	40	5	representations	representation	NOUN
ap-1847	40	6	and	and	CCONJ
ap-1847	40	7	the	the	DET
ap-1847	40	8	sizes	size	NOUN
ap-1847	40	9	of	of	ADP
ap-1847	40	10	the	the	DET
ap-1847	40	11	orbits	orbit	NOUN
ap-1847	40	12	are	be	AUX
ap-1847	40	13	shown	show	VERB
ap-1847	40	14	together	together	ADV
ap-1847	40	15	with	with	ADP
ap-1847	40	16	the	the	DET
ap-1847	40	17	multiplicities	multiplicity	NOUN
ap-1847	40	18	.	.	PUNCT
ap-1847	41	1	we	we	PRON
ap-1847	41	2	provide	provide	VERB
ap-1847	41	3	an	an	DET
ap-1847	41	4	illustration	illustration	NOUN
ap-1847	41	5	of	of	ADP
ap-1847	41	6	this	this	DET
ap-1847	41	7	approach	approach	NOUN
ap-1847	41	8	,	,	PUNCT
ap-1847	41	9	for	for	ADP
ap-1847	41	10	the	the	DET
ap-1847	41	11	symmetry	symmetry	NOUN
ap-1847	41	12	groups	group	NOUN
ap-1847	41	13	o(5	o(5	PROPN
ap-1847	41	14	)	)	PUNCT
ap-1847	41	15	,	,	PUNCT
ap-1847	41	16	f	f	PROPN
ap-1847	41	17	(	(	PUNCT
ap-1847	41	18	4	4	NUM
ap-1847	41	19	)	)	PUNCT
ap-1847	41	20	,	,	PUNCT
ap-1847	41	21	and	and	CCONJ
ap-1847	41	22	e(8	e(8	VERB
ap-1847	41	23	)	)	PUNCT
ap-1847	41	24	.	.	PUNCT
ap-1847	42	1	the	the	DET
ap-1847	42	2	process	process	NOUN
ap-1847	42	3	that	that	PRON
ap-1847	42	4	consider	consider	VERB
ap-1847	42	5	is	be	AUX
ap-1847	42	6	the	the	DET
ap-1847	42	7	simplest	simple	ADJ
ap-1847	42	8	,	,	PUNCT
ap-1847	42	9	where	where	SCONJ
ap-1847	42	10	three	three	NUM
ap-1847	42	11	multiplets	multiplet	NOUN
ap-1847	42	12	are	be	AUX
ap-1847	42	13	interacting	interact	VERB
ap-1847	42	14	,	,	PUNCT
ap-1847	42	15	more	more	ADV
ap-1847	42	16	precisely	precisely	ADV
ap-1847	42	17	the	the	DET
ap-1847	42	18	interaction	interaction	NOUN
ap-1847	42	19	of	of	ADP
ap-1847	42	20	two	two	NUM
ap-1847	42	21	particles	particle	NOUN
ap-1847	42	22	yields	yield	NOUN
ap-1847	42	23	a	a	DET
ap-1847	42	24	third	third	ADJ
ap-1847	42	25	one	one	NUM
ap-1847	42	26	.	.	PUNCT
ap-1847	43	1	our	our	PRON
ap-1847	43	2	aim	aim	NOUN
ap-1847	43	3	is	be	AUX
ap-1847	43	4	to	to	PART
ap-1847	43	5	show	show	VERB
ap-1847	43	6	how	how	SCONJ
ap-1847	43	7	to	to	PART
ap-1847	43	8	average	average	VERB
ap-1847	43	9	over	over	ADP
ap-1847	43	10	different	different	ADJ
ap-1847	43	11	particles	particle	NOUN
ap-1847	43	12	/	/	SYM
ap-1847	43	13	states	state	NOUN
ap-1847	43	14	which	which	PRON
ap-1847	43	15	carry	carry	VERB
ap-1847	43	16	the	the	DET
ap-1847	43	17	same	same	ADJ
ap-1847	43	18	lie	lie	NOUN
ap-1847	43	19	group	group	NOUN
ap-1847	43	20	representation	representation	NOUN
ap-1847	43	21	labels	label	NOUN
ap-1847	43	22	.	.	PUNCT
ap-1847	44	1	we	we	PRON
ap-1847	44	2	write	write	VERB
ap-1847	44	3	the	the	DET
ap-1847	44	4	highest	high	ADJ
ap-1847	44	5	weights	weight	NOUN
ap-1847	44	6	of	of	ADP
ap-1847	44	7	the	the	DET
ap-1847	44	8	representations	representation	NOUN
ap-1847	44	9	in	in	ADP
ap-1847	44	10	round	round	ADJ
ap-1847	44	11	brackets	bracket	NOUN
ap-1847	44	12	,	,	PUNCT
ap-1847	44	13	and	and	CCONJ
ap-1847	44	14	the	the	DET
ap-1847	44	15	dominant	dominant	ADJ
ap-1847	44	16	weights	weight	NOUN
ap-1847	44	17	of	of	ADP
ap-1847	44	18	the	the	DET
ap-1847	44	19	weyl	weyl	PROPN
ap-1847	44	20	group	group	NOUN
ap-1847	44	21	orbits	orbit	NOUN
ap-1847	44	22	in	in	ADP
ap-1847	44	23	square	square	ADJ
ap-1847	44	24	brackets	bracket	NOUN
ap-1847	44	25	.	.	PUNCT
ap-1847	45	1	in	in	ADP
ap-1847	45	2	the	the	DET
ap-1847	45	3	examples	example	NOUN
ap-1847	45	4	,	,	PUNCT
ap-1847	45	5	we	we	PRON
ap-1847	45	6	show	show	VERB
ap-1847	45	7	that	that	SCONJ
ap-1847	45	8	there	there	PRON
ap-1847	45	9	are	be	VERB
ap-1847	45	10	many	many	ADJ
ap-1847	45	11	states	state	NOUN
ap-1847	45	12	which	which	PRON
ap-1847	45	13	have	have	VERB
ap-1847	45	14	the	the	DET
ap-1847	45	15	group	group	NOUN
ap-1847	45	16	labels	label	NOUN
ap-1847	45	17	(	(	PUNCT
ap-1847	45	18	weights	weight	NOUN
ap-1847	45	19	)	)	PUNCT
ap-1847	45	20	identical	identical	ADJ
ap-1847	45	21	although	although	SCONJ
ap-1847	45	22	they	they	PRON
ap-1847	45	23	label	label	VERB
ap-1847	45	24	different	different	ADJ
ap-1847	45	25	particle	particle	NOUN
ap-1847	45	26	states	state	NOUN
ap-1847	45	27	.	.	PUNCT
ap-1847	46	1	in	in	ADP
ap-1847	46	2	order	order	NOUN
ap-1847	46	3	to	to	PART
ap-1847	46	4	avoid	avoid	VERB
ap-1847	46	5	the	the	DET
ap-1847	46	6	almost	almost	ADV
ap-1847	46	7	impossible	impossible	ADJ
ap-1847	46	8	task	task	NOUN
ap-1847	46	9	of	of	ADP
ap-1847	46	10	distinguishing	distinguish	VERB
ap-1847	46	11	these	these	DET
ap-1847	46	12	states	state	NOUN
ap-1847	46	13	,	,	PUNCT
ap-1847	46	14	we	we	PRON
ap-1847	46	15	add	add	VERB
ap-1847	46	16	them	they	PRON
ap-1847	46	17	up	up	ADP
ap-1847	46	18	and	and	CCONJ
ap-1847	46	19	count	count	VERB
ap-1847	46	20	their	their	PRON
ap-1847	46	21	total	total	ADJ
ap-1847	46	22	probability	probability	NOUN
ap-1847	46	23	.	.	PUNCT
ap-1847	47	1	2	2	X
ap-1847	47	2	.	.	X
ap-1847	47	3	symmetry	symmetry	NOUN
ap-1847	47	4	group	group	PROPN
ap-1847	47	5	o(5	o(5	PROPN
ap-1847	47	6	)	)	PUNCT
ap-1847	47	7	consider	consider	VERB
ap-1847	47	8	the	the	DET
ap-1847	47	9	example	example	NOUN
ap-1847	47	10	where	where	SCONJ
ap-1847	47	11	the	the	DET
ap-1847	47	12	underlying	underlie	VERB
ap-1847	47	13	symmetry	symmetry	NOUN
ap-1847	47	14	group	group	NOUN
ap-1847	47	15	is	be	AUX
ap-1847	47	16	the	the	DET
ap-1847	47	17	weyl	weyl	VERB
ap-1847	47	18	reflection	reflection	NOUN
ap-1847	47	19	group	group	NOUN
ap-1847	47	20	of	of	ADP
ap-1847	47	21	the	the	DET
ap-1847	47	22	lie	lie	NOUN
ap-1847	47	23	group	group	NOUN
ap-1847	47	24	o(5	o(5	PROPN
ap-1847	47	25	)	)	PUNCT
ap-1847	47	26	,	,	PUNCT
ap-1847	47	27	or	or	CCONJ
ap-1847	47	28	equivalently	equivalently	ADV
ap-1847	47	29	of	of	ADP
ap-1847	47	30	the	the	DET
ap-1847	47	31	lie	lie	NOUN
ap-1847	47	32	algebra	algebra	PROPN
ap-1847	47	33	c2	c2	PROPN
ap-1847	47	34	.	.	PUNCT
ap-1847	48	1	we	we	PRON
ap-1847	48	2	label	label	VERB
ap-1847	48	3	the	the	DET
ap-1847	48	4	representations	representation	NOUN
ap-1847	48	5	by	by	ADP
ap-1847	48	6	their	their	PRON
ap-1847	48	7	unique	unique	ADJ
ap-1847	48	8	highest	high	ADJ
ap-1847	48	9	weight	weight	NOUN
ap-1847	48	10	(	(	PUNCT
ap-1847	48	11	relative	relative	ADJ
ap-1847	48	12	to	to	ADP
ap-1847	48	13	the	the	DET
ap-1847	48	14	basis	basis	NOUN
ap-1847	48	15	of	of	ADP
ap-1847	48	16	the	the	DET
ap-1847	48	17	fundamental	fundamental	ADJ
ap-1847	48	18	weights	weight	NOUN
ap-1847	48	19	)	)	PUNCT
ap-1847	48	20	.	.	PUNCT
ap-1847	49	1	the	the	DET
ap-1847	49	2	product	product	NOUN
ap-1847	49	3	of	of	ADP
ap-1847	49	4	representations	representation	NOUN
ap-1847	49	5	of	of	ADP
ap-1847	49	6	dimensions	dimension	NOUN
ap-1847	49	7	10	10	NUM
ap-1847	49	8	and	and	CCONJ
ap-1847	49	9	4	4	NUM
ap-1847	49	10	decomposes	decompose	NOUN
ap-1847	49	11	as	as	SCONJ
ap-1847	49	12	follows	follow	VERB
ap-1847	49	13	,	,	PUNCT
ap-1847	49	14	(	(	PUNCT
ap-1847	49	15	20	20	NUM
ap-1847	49	16	)	)	PUNCT
ap-1847	49	17	×	×	NOUN
ap-1847	49	18	(	(	PUNCT
ap-1847	49	19	10	10	NUM
ap-1847	49	20	)	)	PUNCT
ap-1847	49	21	=	=	SYM
ap-1847	49	22	(	(	PUNCT
ap-1847	49	23	30	30	NUM
ap-1847	49	24	)	)	PUNCT
ap-1847	50	1	+	+	CCONJ
ap-1847	50	2	(	(	PUNCT
ap-1847	50	3	11	11	NUM
ap-1847	50	4	)	)	PUNCT
ap-1847	50	5	+	+	CCONJ
ap-1847	50	6	(	(	PUNCT
ap-1847	50	7	10	10	NUM
ap-1847	50	8	)	)	PUNCT
ap-1847	50	9	,	,	PUNCT
ap-1847	50	10	10	10	NUM
ap-1847	50	11	×	×	NOUN
ap-1847	50	12	4	4	NUM
ap-1847	50	13	=	=	SYM
ap-1847	50	14	20	20	NUM
ap-1847	50	15	+	+	NUM
ap-1847	50	16	16	16	NUM
ap-1847	50	17	+	+	CCONJ
ap-1847	50	18	4	4	NUM
ap-1847	50	19	=	=	SYM
ap-1847	50	20	40	40	NUM
ap-1847	50	21	,	,	PUNCT
ap-1847	50	22	where	where	SCONJ
ap-1847	50	23	the	the	DET
ap-1847	50	24	second	second	ADJ
ap-1847	50	25	line	line	NOUN
ap-1847	50	26	shows	show	VERB
ap-1847	50	27	the	the	DET
ap-1847	50	28	dimensions	dimension	NOUN
ap-1847	50	29	of	of	ADP
ap-1847	50	30	representations	representation	NOUN
ap-1847	50	31	,	,	PUNCT
ap-1847	50	32	see	see	VERB
ap-1847	50	33	[	[	X
ap-1847	50	34	10	10	NUM
ap-1847	50	35	]	]	PUNCT
ap-1847	50	36	.	.	PUNCT
ap-1847	51	1	labeling	label	VERB
ap-1847	51	2	the	the	DET
ap-1847	51	3	weyl	weyl	PROPN
ap-1847	51	4	group	group	NOUN
ap-1847	51	5	orbits	orbit	NOUN
ap-1847	51	6	by	by	ADP
ap-1847	51	7	their	their	PRON
ap-1847	51	8	unique	unique	ADJ
ap-1847	51	9	dominant	dominant	ADJ
ap-1847	51	10	weights	weight	NOUN
ap-1847	51	11	,	,	PUNCT
ap-1847	51	12	the	the	DET
ap-1847	51	13	product	product	NOUN
ap-1847	51	14	of	of	ADP
ap-1847	51	15	the	the	DET
ap-1847	51	16	weight	weight	NOUN
ap-1847	51	17	systems	system	NOUN
ap-1847	51	18	decomposes	decompose	VERB
ap-1847	51	19	into	into	ADP
ap-1847	51	20	the	the	DET
ap-1847	51	21	weyl	weyl	PROPN
ap-1847	51	22	group	group	NOUN
ap-1847	51	23	orbits	orbit	NOUN
ap-1847	51	24	as	as	SCONJ
ap-1847	51	25	follows	follow	VERB
ap-1847	51	26	,	,	PUNCT
ap-1847	51	27	(	(	PUNCT
ap-1847	51	28	20	20	NUM
ap-1847	51	29	)	)	PUNCT
ap-1847	51	30	×	×	NOUN
ap-1847	51	31	(	(	PUNCT
ap-1847	51	32	10	10	NUM
ap-1847	51	33	)	)	PUNCT
ap-1847	51	34	=	=	PUNCT
ap-1847	52	1	[	[	X
ap-1847	52	2	30	30	NUM
ap-1847	52	3	]	]	PUNCT
ap-1847	52	4	+	+	CCONJ
ap-1847	52	5	2[11	2[11	NUM
ap-1847	52	6	]	]	X
ap-1847	53	1	+	+	CCONJ
ap-1847	54	1	5[10	5[10	NUM
ap-1847	54	2	]	]	PUNCT
ap-1847	54	3	,	,	PUNCT
ap-1847	54	4	10	10	NUM
ap-1847	54	5	×	×	NOUN
ap-1847	54	6	4	4	NUM
ap-1847	54	7	=	=	SYM
ap-1847	54	8	4	4	NUM
ap-1847	54	9	+	+	SYM
ap-1847	54	10	2	2	NUM
ap-1847	54	11	·	·	SYM
ap-1847	54	12	8	8	NUM
ap-1847	55	1	+	+	CCONJ
ap-1847	55	2	5	5	NUM
ap-1847	55	3	·	·	SYM
ap-1847	55	4	4	4	NUM
ap-1847	55	5	=	=	SYM
ap-1847	55	6	40	40	NUM
ap-1847	55	7	,	,	PUNCT
ap-1847	55	8	where	where	SCONJ
ap-1847	55	9	the	the	DET
ap-1847	55	10	integers	integer	NOUN
ap-1847	55	11	in	in	ADP
ap-1847	55	12	front	front	NOUN
ap-1847	55	13	of	of	ADP
ap-1847	55	14	the	the	DET
ap-1847	55	15	square	square	ADJ
ap-1847	55	16	brackets	bracket	NOUN
ap-1847	55	17	are	be	AUX
ap-1847	55	18	the	the	DET
ap-1847	55	19	multiplicities	multiplicity	NOUN
ap-1847	55	20	of	of	ADP
ap-1847	55	21	the	the	DET
ap-1847	55	22	occurrence	occurrence	NOUN
ap-1847	55	23	of	of	ADP
ap-1847	55	24	the	the	DET
ap-1847	55	25	respective	respective	ADJ
ap-1847	55	26	orbits	orbit	NOUN
ap-1847	55	27	in	in	ADP
ap-1847	55	28	the	the	DET
ap-1847	55	29	decomposition	decomposition	NOUN
ap-1847	55	30	.	.	PUNCT
ap-1847	56	1	if	if	SCONJ
ap-1847	56	2	only	only	ADV
ap-1847	56	3	the	the	DET
ap-1847	56	4	product	product	NOUN
ap-1847	56	5	of	of	ADP
ap-1847	56	6	the	the	DET
ap-1847	56	7	weyl	weyl	PROPN
ap-1847	56	8	group	group	NOUN
ap-1847	56	9	orbits	orbit	NOUN
ap-1847	56	10	were	be	AUX
ap-1847	56	11	to	to	PART
ap-1847	56	12	be	be	AUX
ap-1847	56	13	considered	consider	VERB
ap-1847	56	14	,	,	PUNCT
ap-1847	56	15	the	the	DET
ap-1847	56	16	decomposition	decomposition	NOUN
ap-1847	56	17	would	would	AUX
ap-1847	56	18	be	be	AUX
ap-1847	56	19	simpler	simple	ADJ
ap-1847	56	20	:	:	PUNCT
ap-1847	57	1	[	[	X
ap-1847	57	2	20	20	NUM
ap-1847	57	3	]	]	SYM
ap-1847	57	4	×	×	NOUN
ap-1847	58	1	[	[	X
ap-1847	58	2	10	10	NUM
ap-1847	58	3	]	]	PUNCT
ap-1847	58	4	=	=	PUNCT
ap-1847	59	1	[	[	X
ap-1847	59	2	30	30	NUM
ap-1847	59	3	]	]	PUNCT
ap-1847	59	4	+	+	CCONJ
ap-1847	60	1	[	[	X
ap-1847	60	2	11	11	NUM
ap-1847	60	3	]	]	PUNCT
ap-1847	60	4	+	+	CCONJ
ap-1847	60	5	[	[	X
ap-1847	60	6	10	10	NUM
ap-1847	60	7	]	]	PUNCT
ap-1847	60	8	,	,	PUNCT
ap-1847	60	9	4	4	NUM
ap-1847	60	10	×	×	NOUN
ap-1847	60	11	4	4	NUM
ap-1847	60	12	=	=	SYM
ap-1847	60	13	4	4	NUM
ap-1847	60	14	+	+	NUM
ap-1847	60	15	8	8	NUM
ap-1847	60	16	+	+	SYM
ap-1847	60	17	4	4	NUM
ap-1847	60	18	=	=	SYM
ap-1847	60	19	16	16	NUM
ap-1847	60	20	.	.	PUNCT
ap-1847	61	1	there	there	PRON
ap-1847	61	2	are	be	VERB
ap-1847	61	3	40	40	NUM
ap-1847	61	4	states	state	NOUN
ap-1847	61	5	in	in	ADP
ap-1847	61	6	the	the	DET
ap-1847	61	7	product	product	NOUN
ap-1847	61	8	.	.	PUNCT
ap-1847	62	1	if	if	SCONJ
ap-1847	62	2	equal	equal	ADJ
ap-1847	62	3	probability	probability	NOUN
ap-1847	62	4	is	be	AUX
ap-1847	62	5	assumed	assume	VERB
ap-1847	62	6	,	,	PUNCT
ap-1847	62	7	each	each	PRON
ap-1847	62	8	of	of	ADP
ap-1847	62	9	the	the	DET
ap-1847	62	10	channels	channel	NOUN
ap-1847	62	11	comes	come	VERB
ap-1847	62	12	with	with	ADP
ap-1847	62	13	the	the	DET
ap-1847	62	14	probability	probability	NOUN
ap-1847	62	15	1	1	NUM
ap-1847	62	16	40	40	NUM
ap-1847	62	17	.	.	PUNCT
ap-1847	63	1	consequently	consequently	ADV
ap-1847	63	2	,	,	PUNCT
ap-1847	63	3	we	we	PRON
ap-1847	63	4	have	have	VERB
ap-1847	63	5	the	the	DET
ap-1847	63	6	probabilities	probability	NOUN
ap-1847	63	7	:	:	PUNCT
ap-1847	63	8	•	•	NUM
ap-1847	63	9	4	4	NUM
ap-1847	63	10	states	state	NOUN
ap-1847	63	11	from	from	ADP
ap-1847	63	12	[	[	X
ap-1847	63	13	30	30	NUM
ap-1847	63	14	]	]	PUNCT
ap-1847	63	15	,	,	PUNCT
ap-1847	63	16	each	each	PRON
ap-1847	63	17	present	present	ADJ
ap-1847	63	18	once	once	ADV
ap-1847	63	19	:	:	PUNCT
ap-1847	63	20	1/40	1/40	NUM
ap-1847	63	21	;	;	PUNCT
ap-1847	63	22	•	•	NUM
ap-1847	63	23	8	8	NUM
ap-1847	63	24	states	state	NOUN
ap-1847	63	25	from	from	ADP
ap-1847	63	26	[	[	X
ap-1847	63	27	11	11	NUM
ap-1847	63	28	]	]	PUNCT
ap-1847	63	29	,	,	PUNCT
ap-1847	63	30	each	each	PRON
ap-1847	63	31	present	present	ADJ
ap-1847	63	32	twice	twice	ADV
ap-1847	63	33	:	:	PUNCT
ap-1847	63	34	1/20	1/20	NUM
ap-1847	63	35	;	;	PUNCT
ap-1847	63	36	•	•	NUM
ap-1847	63	37	4	4	NUM
ap-1847	63	38	states	state	NOUN
ap-1847	63	39	from	from	ADP
ap-1847	63	40	[	[	X
ap-1847	63	41	10	10	NUM
ap-1847	63	42	]	]	PUNCT
ap-1847	63	43	,	,	PUNCT
ap-1847	63	44	each	each	DET
ap-1847	63	45	present	present	ADJ
ap-1847	63	46	5×	5×	NOUN
ap-1847	63	47	:	:	PUNCT
ap-1847	63	48	1/8	1/8	NUM
ap-1847	63	49	.	.	PUNCT
ap-1847	64	1	the	the	DET
ap-1847	64	2	results	result	NOUN
ap-1847	64	3	of	of	ADP
ap-1847	64	4	the	the	DET
ap-1847	64	5	example	example	NOUN
ap-1847	64	6	are	be	AUX
ap-1847	64	7	summarized	summarize	VERB
ap-1847	64	8	in	in	ADP
ap-1847	64	9	table	table	NOUN
ap-1847	64	10	1	1	NUM
ap-1847	64	11	.	.	SYM
ap-1847	64	12	3	3	X
ap-1847	64	13	.	.	X
ap-1847	64	14	symmetry	symmetry	NOUN
ap-1847	64	15	group	group	NOUN
ap-1847	64	16	f	f	PROPN
ap-1847	64	17	(	(	PUNCT
ap-1847	64	18	4	4	X
ap-1847	64	19	)	)	PUNCT
ap-1847	64	20	consider	consider	VERB
ap-1847	64	21	decomposition	decomposition	NOUN
ap-1847	64	22	of	of	ADP
ap-1847	64	23	the	the	DET
ap-1847	64	24	product	product	NOUN
ap-1847	64	25	of	of	ADP
ap-1847	64	26	representations	representation	NOUN
ap-1847	64	27	in	in	ADP
ap-1847	64	28	terms	term	NOUN
ap-1847	64	29	of	of	ADP
ap-1847	64	30	their	their	PRON
ap-1847	64	31	weight	weight	NOUN
ap-1847	64	32	systems	system	NOUN
ap-1847	64	33	,	,	PUNCT
ap-1847	64	34	(	(	PUNCT
ap-1847	64	35	0001	0001	NUM
ap-1847	64	36	)	)	PUNCT
ap-1847	64	37	×	×	NOUN
ap-1847	64	38	(	(	PUNCT
ap-1847	64	39	0001	0001	NUM
ap-1847	64	40	)	)	PUNCT
ap-1847	65	1	=	=	SYM
ap-1847	65	2	(	(	PUNCT
ap-1847	65	3	0002	0002	NUM
ap-1847	65	4	)	)	PUNCT
ap-1847	66	1	+	+	CCONJ
ap-1847	66	2	(	(	PUNCT
ap-1847	66	3	0010	0010	NUM
ap-1847	66	4	)	)	PUNCT
ap-1847	67	1	+	+	CCONJ
ap-1847	67	2	(	(	PUNCT
ap-1847	67	3	1000	1000	NUM
ap-1847	67	4	)	)	PUNCT
ap-1847	68	1	+	+	CCONJ
ap-1847	68	2	(	(	PUNCT
ap-1847	68	3	0001	0001	NUM
ap-1847	68	4	)	)	PUNCT
ap-1847	69	1	+	+	CCONJ
ap-1847	69	2	(	(	PUNCT
ap-1847	69	3	0000	0000	NUM
ap-1847	69	4	)	)	PUNCT
ap-1847	69	5	,	,	PUNCT
ap-1847	69	6	26	26	NUM
ap-1847	69	7	×	×	NOUN
ap-1847	69	8	26	26	NUM
ap-1847	69	9	=	=	SYM
ap-1847	69	10	324	324	NUM
ap-1847	69	11	+	+	CCONJ
ap-1847	69	12	273	273	NUM
ap-1847	69	13	+	+	NUM
ap-1847	69	14	52	52	NUM
ap-1847	69	15	+	+	NUM
ap-1847	69	16	26	26	NUM
ap-1847	69	17	+	+	SYM
ap-1847	69	18	1	1	NUM
ap-1847	69	19	=	=	SYM
ap-1847	69	20	676	676	NUM
ap-1847	69	21	.	.	PUNCT
ap-1847	69	22	decomposition	decomposition	NOUN
ap-1847	69	23	of	of	ADP
ap-1847	69	24	the	the	DET
ap-1847	69	25	same	same	ADJ
ap-1847	69	26	product	product	NOUN
ap-1847	69	27	in	in	ADP
ap-1847	69	28	terms	term	NOUN
ap-1847	69	29	of	of	ADP
ap-1847	69	30	weyl	weyl	PROPN
ap-1847	69	31	group	group	NOUN
ap-1847	69	32	orbits	orbit	NOUN
ap-1847	69	33	,	,	PUNCT
ap-1847	69	34	(	(	PUNCT
ap-1847	69	35	0001	0001	NUM
ap-1847	69	36	)	)	PUNCT
ap-1847	69	37	×	×	NOUN
ap-1847	69	38	(	(	PUNCT
ap-1847	69	39	0001	0001	NUM
ap-1847	69	40	)	)	PUNCT
ap-1847	70	1	=	=	NOUN
ap-1847	71	1	[	[	X
ap-1847	71	2	0002	0002	NUM
ap-1847	71	3	]	]	X
ap-1847	71	4	+	+	PUNCT
ap-1847	72	1	2[0010	2[0010	NUM
ap-1847	72	2	]	]	X
ap-1847	73	1	+	+	CCONJ
ap-1847	74	1	6[1000	6[1000	NUM
ap-1847	74	2	]	]	X
ap-1847	74	3	+	+	X
ap-1847	74	4	12[0001	12[0001	NUM
ap-1847	74	5	]	]	X
ap-1847	74	6	+	+	X
ap-1847	74	7	28[0000	28[0000	NUM
ap-1847	74	8	]	]	PUNCT
ap-1847	74	9	and	and	CCONJ
ap-1847	74	10	the	the	DET
ap-1847	74	11	corresponding	corresponding	ADJ
ap-1847	74	12	equality	equality	NOUN
ap-1847	74	13	of	of	ADP
ap-1847	74	14	the	the	DET
ap-1847	74	15	dimensions	dimension	NOUN
ap-1847	74	16	26	26	NUM
ap-1847	74	17	×	×	NOUN
ap-1847	74	18	26	26	NUM
ap-1847	74	19	=	=	SYM
ap-1847	74	20	24	24	NUM
ap-1847	74	21	+	+	CCONJ
ap-1847	74	22	2	2	NUM
ap-1847	74	23	·	·	SYM
ap-1847	74	24	96	96	NUM
ap-1847	75	1	+	+	CCONJ
ap-1847	75	2	6	6	NUM
ap-1847	75	3	·	·	SYM
ap-1847	75	4	24	24	NUM
ap-1847	75	5	+	+	CCONJ
ap-1847	75	6	12	12	NUM
ap-1847	75	7	·	·	SYM
ap-1847	75	8	24	24	NUM
ap-1847	76	1	+	+	CCONJ
ap-1847	76	2	28	28	NUM
ap-1847	76	3	·	·	SYM
ap-1847	76	4	1	1	X
ap-1847	76	5	.	.	PUNCT
ap-1847	76	6	suppose	suppose	VERB
ap-1847	76	7	that	that	SCONJ
ap-1847	76	8	we	we	PRON
ap-1847	76	9	want	want	VERB
ap-1847	76	10	to	to	PART
ap-1847	76	11	decompose	decompose	VERB
ap-1847	76	12	only	only	ADV
ap-1847	76	13	the	the	DET
ap-1847	76	14	product	product	NOUN
ap-1847	76	15	of	of	ADP
ap-1847	76	16	the	the	DET
ap-1847	76	17	orbits	orbit	NOUN
ap-1847	76	18	of	of	ADP
ap-1847	76	19	the	the	DET
ap-1847	76	20	highest	high	ADJ
ap-1847	76	21	weights	weight	NOUN
ap-1847	77	1	[	[	X
ap-1847	77	2	0001	0001	NUM
ap-1847	77	3	]	]	PUNCT
ap-1847	78	1	×	×	NOUN
ap-1847	79	1	[	[	X
ap-1847	79	2	0001	0001	NUM
ap-1847	79	3	]	]	PUNCT
ap-1847	79	4	=	=	PUNCT
ap-1847	80	1	[	[	X
ap-1847	80	2	0002	0002	NUM
ap-1847	80	3	]	]	X
ap-1847	81	1	+	+	PUNCT
ap-1847	81	2	2[0010	2[0010	NUM
ap-1847	81	3	]	]	X
ap-1847	82	1	+	+	CCONJ
ap-1847	83	1	6[1000	6[1000	NUM
ap-1847	83	2	]	]	X
ap-1847	83	3	+	+	CCONJ
ap-1847	83	4	8[0001	8[0001	NUM
ap-1847	83	5	]	]	X
ap-1847	83	6	+	+	NUM
ap-1847	83	7	24[0000	24[0000	NUM
ap-1847	83	8	]	]	X
ap-1847	83	9	,	,	PUNCT
ap-1847	83	10	24	24	NUM
ap-1847	83	11	×	×	NOUN
ap-1847	83	12	24	24	NUM
ap-1847	83	13	=	=	SYM
ap-1847	83	14	24	24	NUM
ap-1847	83	15	+	+	CCONJ
ap-1847	83	16	2	2	NUM
ap-1847	83	17	·	·	SYM
ap-1847	83	18	96	96	NUM
ap-1847	84	1	+	+	CCONJ
ap-1847	84	2	6	6	NUM
ap-1847	84	3	·	·	SYM
ap-1847	84	4	24	24	NUM
ap-1847	84	5	+	+	CCONJ
ap-1847	84	6	8	8	NUM
ap-1847	84	7	·	·	SYM
ap-1847	84	8	24	24	NUM
ap-1847	84	9	+	+	CCONJ
ap-1847	84	10	24	24	NUM
ap-1847	84	11	·	·	SYM
ap-1847	84	12	1	1	NUM
ap-1847	84	13	if	if	SCONJ
ap-1847	84	14	equal	equal	ADJ
ap-1847	84	15	probability	probability	NOUN
ap-1847	84	16	of	of	ADP
ap-1847	84	17	the	the	DET
ap-1847	84	18	676	676	NUM
ap-1847	84	19	states	state	NOUN
ap-1847	84	20	is	be	AUX
ap-1847	84	21	assumed	assume	VERB
ap-1847	84	22	we	we	PRON
ap-1847	84	23	have	have	VERB
ap-1847	84	24	the	the	DET
ap-1847	84	25	following	follow	VERB
ap-1847	84	26	probabilities	probability	NOUN
ap-1847	84	27	of	of	ADP
ap-1847	84	28	the	the	DET
ap-1847	84	29	channels	channel	NOUN
ap-1847	84	30	:	:	PUNCT
ap-1847	84	31	396	396	NUM
ap-1847	84	32	vol	vol	NOUN
ap-1847	84	33	.	.	PUNCT
ap-1847	85	1	53	53	NUM
ap-1847	85	2	no	no	NOUN
ap-1847	85	3	.	.	PUNCT
ap-1847	86	1	5/2013	5/2013	NUM
ap-1847	86	2	the	the	DET
ap-1847	86	3	shmushkevich	shmushkevich	NOUN
ap-1847	86	4	method	method	NOUN
ap-1847	86	5	for	for	ADP
ap-1847	86	6	higher	high	ADJ
ap-1847	86	7	symmetry	symmetry	NOUN
ap-1847	86	8	groups	group	NOUN
ap-1847	86	9	f	f	X
ap-1847	86	10	(	(	PUNCT
ap-1847	86	11	4	4	NUM
ap-1847	86	12	)	)	PUNCT
ap-1847	86	13	decomposition	decomposition	NOUN
ap-1847	86	14	into	into	ADP
ap-1847	86	15	irreducible	irreducible	ADJ
ap-1847	86	16	representations	representation	NOUN
ap-1847	86	17	with	with	ADP
ap-1847	86	18	multiplicities	multiplicity	NOUN
ap-1847	86	19	multiplicity	multiplicity	NOUN
ap-1847	86	20	orbit	orbit	NOUN
ap-1847	86	21	size	size	NOUN
ap-1847	86	22	(	(	PUNCT
ap-1847	86	23	0001	0001	NUM
ap-1847	86	24	)	)	PUNCT
ap-1847	86	25	×	×	NOUN
ap-1847	86	26	(	(	PUNCT
ap-1847	86	27	0001	0001	NUM
ap-1847	86	28	)	)	PUNCT
ap-1847	86	29	=	=	SYM
ap-1847	86	30	(	(	PUNCT
ap-1847	86	31	0002	0002	NUM
ap-1847	86	32	)	)	PUNCT
ap-1847	86	33	(	(	PUNCT
ap-1847	86	34	0010	0010	NUM
ap-1847	86	35	)	)	PUNCT
ap-1847	86	36	(	(	PUNCT
ap-1847	86	37	1000	1000	NUM
ap-1847	86	38	)	)	PUNCT
ap-1847	86	39	(	(	PUNCT
ap-1847	86	40	0001	0001	NUM
ap-1847	86	41	)	)	PUNCT
ap-1847	86	42	(	(	PUNCT
ap-1847	86	43	0000	0000	NUM
ap-1847	86	44	)	)	PUNCT
ap-1847	86	45	26	26	NUM
ap-1847	86	46	×	×	NOUN
ap-1847	86	47	26	26	NUM
ap-1847	87	1	[	[	X
ap-1847	87	2	0002	0002	NUM
ap-1847	87	3	]	]	X
ap-1847	87	4	1	1	NUM
ap-1847	87	5	24	24	NUM
ap-1847	88	1	[	[	X
ap-1847	88	2	0010	0010	NUM
ap-1847	88	3	]	]	X
ap-1847	88	4	[	[	X
ap-1847	88	5	0010	0010	NUM
ap-1847	88	6	]	]	SYM
ap-1847	88	7	2	2	NUM
ap-1847	88	8	96	96	NUM
ap-1847	88	9	3[1000	3[1000	NUM
ap-1847	88	10	]	]	X
ap-1847	88	11	2[1000	2[1000	NUM
ap-1847	88	12	]	]	PUNCT
ap-1847	89	1	[	[	X
ap-1847	89	2	1000	1000	NUM
ap-1847	89	3	]	]	SYM
ap-1847	89	4	6	6	NUM
ap-1847	89	5	24	24	NUM
ap-1847	89	6	5[0001	5[0001	NUM
ap-1847	89	7	]	]	X
ap-1847	90	1	5[0001	5[0001	NUM
ap-1847	90	2	]	]	X
ap-1847	91	1	[	[	X
ap-1847	91	2	0001	0001	NUM
ap-1847	91	3	]	]	PUNCT
ap-1847	92	1	[	[	X
ap-1847	92	2	0001	0001	NUM
ap-1847	92	3	]	]	SYM
ap-1847	92	4	12	12	NUM
ap-1847	92	5	24	24	NUM
ap-1847	92	6	12[0000	12[0000	NUM
ap-1847	92	7	]	]	PUNCT
ap-1847	92	8	9[0000	9[0000	NUM
ap-1847	92	9	]	]	X
ap-1847	92	10	4[0000	4[0000	NUM
ap-1847	92	11	]	]	PUNCT
ap-1847	93	1	2[0000	2[0000	NUM
ap-1847	93	2	]	]	X
ap-1847	93	3	[	[	X
ap-1847	93	4	0000	0000	NUM
ap-1847	93	5	]	]	SYM
ap-1847	93	6	28	28	NUM
ap-1847	93	7	1	1	NUM
ap-1847	93	8	decomposition	decomposition	NOUN
ap-1847	93	9	into	into	ADP
ap-1847	93	10	orbits	orbit	NOUN
ap-1847	93	11	with	with	ADP
ap-1847	93	12	multiplicities	multiplicity	NOUN
ap-1847	93	13	[	[	X
ap-1847	93	14	0002	0002	NUM
ap-1847	93	15	]	]	X
ap-1847	94	1	2[0010	2[0010	NUM
ap-1847	94	2	]	]	PUNCT
ap-1847	94	3	6[1000	6[1000	NUM
ap-1847	94	4	]	]	X
ap-1847	94	5	12[0001	12[0001	NUM
ap-1847	94	6	]	]	X
ap-1847	94	7	28[0000	28[0000	NUM
ap-1847	94	8	]	]	PUNCT
ap-1847	94	9	676	676	NUM
ap-1847	94	10	=	=	SYM
ap-1847	94	11	262	262	NUM
ap-1847	94	12	table	table	NOUN
ap-1847	94	13	2	2	NUM
ap-1847	94	14	.	.	PUNCT
ap-1847	94	15	decomposition	decomposition	NOUN
ap-1847	94	16	of	of	ADP
ap-1847	94	17	the	the	DET
ap-1847	94	18	product	product	NOUN
ap-1847	94	19	in	in	ADP
ap-1847	94	20	the	the	DET
ap-1847	94	21	f	f	PROPN
ap-1847	94	22	(	(	PUNCT
ap-1847	94	23	4	4	NUM
ap-1847	94	24	)	)	PUNCT
ap-1847	94	25	example	example	NOUN
ap-1847	94	26	.	.	PUNCT
ap-1847	95	1	the	the	DET
ap-1847	95	2	decomposition	decomposition	NOUN
ap-1847	95	3	is	be	AUX
ap-1847	95	4	given	give	VERB
ap-1847	95	5	in	in	ADP
ap-1847	95	6	the	the	DET
ap-1847	95	7	weight	weight	NOUN
ap-1847	95	8	system	system	NOUN
ap-1847	95	9	of	of	ADP
ap-1847	95	10	irreducible	irreducible	ADJ
ap-1847	95	11	representations	representation	NOUN
ap-1847	95	12	(	(	PUNCT
ap-1847	95	13	the	the	DET
ap-1847	95	14	first	first	ADJ
ap-1847	95	15	line	line	NOUN
ap-1847	95	16	)	)	PUNCT
ap-1847	95	17	and	and	CCONJ
ap-1847	95	18	in	in	ADP
ap-1847	95	19	terms	term	NOUN
ap-1847	95	20	of	of	ADP
ap-1847	95	21	orbits	orbit	NOUN
ap-1847	95	22	(	(	PUNCT
ap-1847	95	23	bottom	bottom	ADJ
ap-1847	95	24	line	line	NOUN
ap-1847	95	25	)	)	PUNCT
ap-1847	95	26	.	.	PUNCT
ap-1847	96	1	the	the	DET
ap-1847	96	2	dimensions	dimension	NOUN
ap-1847	96	3	of	of	ADP
ap-1847	96	4	the	the	DET
ap-1847	96	5	representations	representation	NOUN
ap-1847	96	6	and	and	CCONJ
ap-1847	96	7	the	the	DET
ap-1847	96	8	sizes	size	NOUN
ap-1847	96	9	of	of	ADP
ap-1847	96	10	the	the	DET
ap-1847	96	11	orbits	orbit	NOUN
ap-1847	96	12	are	be	AUX
ap-1847	96	13	shown	show	VERB
ap-1847	96	14	together	together	ADV
ap-1847	96	15	with	with	ADP
ap-1847	96	16	the	the	DET
ap-1847	96	17	multiplicities	multiplicity	NOUN
ap-1847	96	18	.	.	PUNCT
ap-1847	97	1	•	•	NUM
ap-1847	97	2	24	24	NUM
ap-1847	97	3	states	state	NOUN
ap-1847	97	4	from	from	ADP
ap-1847	97	5	[	[	X
ap-1847	97	6	0002	0002	NUM
ap-1847	97	7	]	]	X
ap-1847	97	8	,	,	PUNCT
ap-1847	97	9	each	each	PRON
ap-1847	97	10	present	present	ADJ
ap-1847	97	11	once	once	ADV
ap-1847	97	12	:	:	PUNCT
ap-1847	97	13	1/676	1/676	NUM
ap-1847	97	14	;	;	PUNCT
ap-1847	97	15	•	•	NUM
ap-1847	97	16	96	96	NUM
ap-1847	97	17	states	state	NOUN
ap-1847	97	18	from	from	ADP
ap-1847	97	19	[	[	X
ap-1847	97	20	0010	0010	NUM
ap-1847	97	21	]	]	PUNCT
ap-1847	97	22	,	,	PUNCT
ap-1847	97	23	each	each	PRON
ap-1847	97	24	present	present	ADJ
ap-1847	97	25	twice	twice	ADV
ap-1847	97	26	:	:	PUNCT
ap-1847	97	27	2/676	2/676	NUM
ap-1847	97	28	;	;	PUNCT
ap-1847	97	29	•	•	NUM
ap-1847	97	30	24	24	NUM
ap-1847	97	31	states	state	NOUN
ap-1847	97	32	from	from	ADP
ap-1847	97	33	[	[	X
ap-1847	97	34	1000	1000	NUM
ap-1847	97	35	]	]	PUNCT
ap-1847	97	36	,	,	PUNCT
ap-1847	97	37	each	each	DET
ap-1847	97	38	present	present	ADJ
ap-1847	97	39	6×	6×	NOUN
ap-1847	97	40	:	:	PUNCT
ap-1847	97	41	6/676	6/676	NUM
ap-1847	97	42	;	;	PUNCT
ap-1847	97	43	•	•	NUM
ap-1847	97	44	24	24	NUM
ap-1847	97	45	states	state	NOUN
ap-1847	97	46	from	from	ADP
ap-1847	97	47	[	[	X
ap-1847	97	48	0001	0001	NUM
ap-1847	97	49	]	]	PUNCT
ap-1847	97	50	,	,	PUNCT
ap-1847	97	51	each	each	DET
ap-1847	97	52	present	present	ADJ
ap-1847	97	53	12×	12×	NUM
ap-1847	97	54	:	:	PUNCT
ap-1847	97	55	12/676	12/676	NUM
ap-1847	97	56	;	;	PUNCT
ap-1847	97	57	•	•	NUM
ap-1847	97	58	1	1	NUM
ap-1847	97	59	state	state	NOUN
ap-1847	97	60	from	from	ADP
ap-1847	97	61	[	[	X
ap-1847	97	62	0000	0000	NUM
ap-1847	97	63	]	]	PUNCT
ap-1847	97	64	,	,	PUNCT
ap-1847	97	65	each	each	DET
ap-1847	97	66	present	present	ADJ
ap-1847	97	67	28×	28×	NUM
ap-1847	97	68	:	:	PUNCT
ap-1847	97	69	28/676	28/676	NUM
ap-1847	97	70	.	.	PUNCT
ap-1847	98	1	the	the	DET
ap-1847	98	2	results	result	NOUN
ap-1847	98	3	of	of	ADP
ap-1847	98	4	the	the	DET
ap-1847	98	5	example	example	NOUN
ap-1847	98	6	are	be	AUX
ap-1847	98	7	summarized	summarize	VERB
ap-1847	98	8	in	in	ADP
ap-1847	98	9	table	table	NOUN
ap-1847	98	10	2	2	NUM
ap-1847	98	11	.	.	SYM
ap-1847	98	12	4	4	NUM
ap-1847	98	13	.	.	NOUN
ap-1847	98	14	symmetry	symmetry	NOUN
ap-1847	98	15	group	group	NOUN
ap-1847	98	16	e(8	e(8	NOUN
ap-1847	98	17	)	)	PUNCT
ap-1847	98	18	consider	consider	VERB
ap-1847	98	19	decomposition	decomposition	NOUN
ap-1847	98	20	of	of	ADP
ap-1847	98	21	the	the	DET
ap-1847	98	22	product	product	NOUN
ap-1847	98	23	of	of	ADP
ap-1847	98	24	the	the	DET
ap-1847	98	25	representations	representation	NOUN
ap-1847	98	26	in	in	ADP
ap-1847	98	27	terms	term	NOUN
ap-1847	98	28	of	of	ADP
ap-1847	98	29	their	their	PRON
ap-1847	98	30	weight	weight	NOUN
ap-1847	98	31	systems	system	NOUN
ap-1847	98	32	(	(	PUNCT
ap-1847	98	33	0	0	NUM
ap-1847	98	34	1000000	1000000	NUM
ap-1847	98	35	)	)	PUNCT
ap-1847	98	36	×	×	NOUN
ap-1847	98	37	(	(	PUNCT
ap-1847	98	38	0	0	NUM
ap-1847	98	39	1000000	1000000	NUM
ap-1847	98	40	)	)	PUNCT
ap-1847	99	1	=	=	PRON
ap-1847	99	2	(	(	PUNCT
ap-1847	99	3	0	0	NUM
ap-1847	99	4	2000000	2000000	NUM
ap-1847	99	5	)	)	PUNCT
ap-1847	100	1	+	+	CCONJ
ap-1847	100	2	(	(	PUNCT
ap-1847	100	3	0	0	NUM
ap-1847	100	4	0100000	0100000	NUM
ap-1847	100	5	)	)	PUNCT
ap-1847	101	1	+	+	CCONJ
ap-1847	101	2	(	(	PUNCT
ap-1847	101	3	0	0	NUM
ap-1847	101	4	0000001	0000001	NUM
ap-1847	101	5	)	)	PUNCT
ap-1847	102	1	+	+	CCONJ
ap-1847	102	2	(	(	PUNCT
ap-1847	102	3	0	0	NUM
ap-1847	102	4	1000000	1000000	NUM
ap-1847	102	5	)	)	PUNCT
ap-1847	103	1	+	+	CCONJ
ap-1847	103	2	(	(	PUNCT
ap-1847	103	3	0	0	NUM
ap-1847	103	4	0000000	0000000	NUM
ap-1847	103	5	)	)	PUNCT
ap-1847	103	6	with	with	ADP
ap-1847	103	7	the	the	DET
ap-1847	103	8	respective	respective	ADJ
ap-1847	103	9	dimensions	dimension	NOUN
ap-1847	103	10	248	248	NUM
ap-1847	103	11	×	×	NOUN
ap-1847	103	12	248	248	NUM
ap-1847	103	13	=	=	SYM
ap-1847	103	14	27000	27000	NUM
ap-1847	103	15	+	+	CCONJ
ap-1847	103	16	30380	30380	NUM
ap-1847	103	17	+	+	CCONJ
ap-1847	103	18	3875	3875	NUM
ap-1847	103	19	+	+	CCONJ
ap-1847	103	20	248	248	NUM
ap-1847	103	21	+	+	SYM
ap-1847	103	22	1	1	NUM
ap-1847	103	23	=	=	SYM
ap-1847	103	24	61504	61504	NUM
ap-1847	103	25	.	.	PUNCT
ap-1847	104	1	we	we	PRON
ap-1847	104	2	write	write	VERB
ap-1847	104	3	the	the	DET
ap-1847	104	4	components	component	NOUN
ap-1847	104	5	of	of	ADP
ap-1847	104	6	e(8	e(8	NOUN
ap-1847	104	7	)	)	PUNCT
ap-1847	104	8	weights	weight	NOUN
ap-1847	104	9	as	as	SCONJ
ap-1847	104	10	they	they	PRON
ap-1847	104	11	would	would	AUX
ap-1847	104	12	be	be	AUX
ap-1847	104	13	attached	attach	VERB
ap-1847	104	14	to	to	ADP
ap-1847	104	15	the	the	DET
ap-1847	104	16	corresponding	corresponding	ADJ
ap-1847	104	17	dynkin	dynkin	ADJ
ap-1847	104	18	diagram	diagram	NOUN
ap-1847	104	19	.	.	PUNCT
ap-1847	105	1	the	the	DET
ap-1847	105	2	same	same	ADJ
ap-1847	105	3	product	product	NOUN
ap-1847	105	4	decomposed	decompose	VERB
ap-1847	105	5	into	into	ADP
ap-1847	105	6	the	the	DET
ap-1847	105	7	sum	sum	NOUN
ap-1847	105	8	of	of	ADP
ap-1847	105	9	the	the	DET
ap-1847	105	10	weyl	weyl	PROPN
ap-1847	105	11	group	group	NOUN
ap-1847	105	12	orbits	orbit	NOUN
ap-1847	105	13	has	have	VERB
ap-1847	105	14	very	very	ADV
ap-1847	105	15	different	different	ADJ
ap-1847	105	16	multiplicities	multiplicity	NOUN
ap-1847	105	17	,	,	PUNCT
ap-1847	105	18	(	(	PUNCT
ap-1847	105	19	0	0	NUM
ap-1847	105	20	1000000	1000000	NUM
ap-1847	105	21	)	)	PUNCT
ap-1847	105	22	×	×	NOUN
ap-1847	105	23	(	(	PUNCT
ap-1847	105	24	0	0	NUM
ap-1847	105	25	1000000	1000000	NUM
ap-1847	105	26	)	)	PUNCT
ap-1847	106	1	=	=	PUNCT
ap-1847	106	2	[	[	PUNCT
ap-1847	106	3	0	0	NUM
ap-1847	106	4	2000000	2000000	NUM
ap-1847	106	5	]	]	PUNCT
ap-1847	107	1	+	+	CCONJ
ap-1847	107	2	2	2	NUM
ap-1847	107	3	[	[	PUNCT
ap-1847	107	4	0	0	NUM
ap-1847	107	5	0100000	0100000	NUM
ap-1847	107	6	]	]	PUNCT
ap-1847	108	1	+	+	CCONJ
ap-1847	108	2	14	14	NUM
ap-1847	108	3	[	[	PUNCT
ap-1847	108	4	0	0	NUM
ap-1847	108	5	0000001	0000001	NUM
ap-1847	108	6	]	]	PUNCT
ap-1847	109	1	+	+	CCONJ
ap-1847	109	2	72	72	NUM
ap-1847	109	3	[	[	PUNCT
ap-1847	109	4	0	0	NUM
ap-1847	109	5	1000000	1000000	NUM
ap-1847	109	6	]	]	PUNCT
ap-1847	110	1	+	+	CCONJ
ap-1847	110	2	304	304	NUM
ap-1847	110	3	[	[	PUNCT
ap-1847	110	4	0	0	NUM
ap-1847	110	5	0000000	0000000	NUM
ap-1847	110	6	]	]	PUNCT
ap-1847	110	7	,	,	PUNCT
ap-1847	110	8	and	and	CCONJ
ap-1847	110	9	the	the	DET
ap-1847	110	10	equality	equality	NOUN
ap-1847	110	11	of	of	ADP
ap-1847	110	12	the	the	DET
ap-1847	110	13	dimensions	dimension	NOUN
ap-1847	110	14	in	in	ADP
ap-1847	110	15	the	the	DET
ap-1847	110	16	decomposed	decompose	VERB
ap-1847	110	17	product	product	NOUN
ap-1847	110	18	,	,	PUNCT
ap-1847	110	19	248	248	NUM
ap-1847	110	20	×	×	NOUN
ap-1847	110	21	248	248	NUM
ap-1847	110	22	=	=	SYM
ap-1847	110	23	240	240	NUM
ap-1847	110	24	+	+	NUM
ap-1847	110	25	2	2	NUM
ap-1847	110	26	·	·	SYM
ap-1847	110	27	6720	6720	NUM
ap-1847	110	28	+	+	CCONJ
ap-1847	110	29	14	14	NUM
ap-1847	110	30	·	·	SYM
ap-1847	110	31	2160	2160	NUM
ap-1847	110	32	+	+	CCONJ
ap-1847	110	33	72	72	NUM
ap-1847	110	34	·	·	SYM
ap-1847	110	35	240	240	NUM
ap-1847	111	1	+	+	NUM
ap-1847	111	2	304	304	NUM
ap-1847	111	3	·	·	SYM
ap-1847	111	4	1	1	NUM
ap-1847	111	5	=	=	SYM
ap-1847	111	6	61504	61504	NUM
ap-1847	111	7	.	.	PUNCT
ap-1847	112	1	if	if	SCONJ
ap-1847	112	2	only	only	ADV
ap-1847	112	3	the	the	DET
ap-1847	112	4	product	product	NOUN
ap-1847	112	5	of	of	ADP
ap-1847	112	6	the	the	DET
ap-1847	112	7	orbits	orbit	NOUN
ap-1847	112	8	is	be	AUX
ap-1847	112	9	to	to	PART
ap-1847	112	10	be	be	AUX
ap-1847	112	11	calculated	calculate	VERB
ap-1847	112	12	,	,	PUNCT
ap-1847	112	13	the	the	DET
ap-1847	112	14	result	result	NOUN
ap-1847	112	15	is	be	AUX
ap-1847	112	16	much	much	ADV
ap-1847	112	17	simpler	simple	ADJ
ap-1847	112	18	,	,	PUNCT
ap-1847	112	19	[	[	PUNCT
ap-1847	112	20	0	0	NUM
ap-1847	112	21	1000000	1000000	NUM
ap-1847	112	22	]	]	PUNCT
ap-1847	112	23	×	×	NOUN
ap-1847	112	24	[	[	PUNCT
ap-1847	112	25	0	0	NUM
ap-1847	112	26	1000000	1000000	NUM
ap-1847	112	27	]	]	PUNCT
ap-1847	113	1	=	=	PUNCT
ap-1847	113	2	[	[	PUNCT
ap-1847	113	3	0	0	NUM
ap-1847	113	4	2000000	2000000	NUM
ap-1847	113	5	]	]	PUNCT
ap-1847	114	1	+	+	CCONJ
ap-1847	114	2	2	2	NUM
ap-1847	114	3	[	[	PUNCT
ap-1847	114	4	0	0	NUM
ap-1847	114	5	0100000	0100000	NUM
ap-1847	114	6	]	]	PUNCT
ap-1847	115	1	+	+	CCONJ
ap-1847	115	2	14	14	NUM
ap-1847	115	3	[	[	PUNCT
ap-1847	115	4	0	0	NUM
ap-1847	115	5	0000001	0000001	NUM
ap-1847	115	6	]	]	PUNCT
ap-1847	116	1	+	+	CCONJ
ap-1847	116	2	56	56	NUM
ap-1847	116	3	[	[	PUNCT
ap-1847	116	4	0	0	NUM
ap-1847	116	5	1000000	1000000	NUM
ap-1847	116	6	]	]	PUNCT
ap-1847	117	1	+	+	CCONJ
ap-1847	117	2	240	240	NUM
ap-1847	117	3	[	[	PUNCT
ap-1847	117	4	0	0	NUM
ap-1847	117	5	0000000	0000000	NUM
ap-1847	117	6	]	]	PUNCT
ap-1847	117	7	,	,	PUNCT
ap-1847	117	8	and	and	CCONJ
ap-1847	117	9	the	the	DET
ap-1847	117	10	corresponding	correspond	VERB
ap-1847	117	11	orbit	orbit	NOUN
ap-1847	117	12	sizes	size	NOUN
ap-1847	117	13	with	with	ADP
ap-1847	117	14	the	the	DET
ap-1847	117	15	appropriate	appropriate	ADJ
ap-1847	117	16	multiplicities	multiplicity	NOUN
ap-1847	117	17	are	be	AUX
ap-1847	117	18	240	240	NUM
ap-1847	117	19	×	×	NOUN
ap-1847	117	20	240	240	NUM
ap-1847	117	21	=	=	SYM
ap-1847	117	22	240	240	NUM
ap-1847	117	23	+	+	NUM
ap-1847	117	24	2	2	NUM
ap-1847	117	25	·	·	SYM
ap-1847	117	26	6720	6720	NUM
ap-1847	117	27	+	+	CCONJ
ap-1847	117	28	14	14	NUM
ap-1847	117	29	·	·	SYM
ap-1847	117	30	2160	2160	NUM
ap-1847	117	31	+	+	CCONJ
ap-1847	118	1	56	56	NUM
ap-1847	118	2	·	·	SYM
ap-1847	118	3	240	240	NUM
ap-1847	118	4	+	+	CCONJ
ap-1847	118	5	240	240	NUM
ap-1847	118	6	·	·	SYM
ap-1847	118	7	1	1	NUM
ap-1847	118	8	=	=	SYM
ap-1847	118	9	57600	57600	NUM
ap-1847	118	10	.	.	PUNCT
ap-1847	119	1	if	if	SCONJ
ap-1847	119	2	equal	equal	ADJ
ap-1847	119	3	probability	probability	NOUN
ap-1847	119	4	of	of	ADP
ap-1847	119	5	the	the	DET
ap-1847	119	6	61504	61504	NUM
ap-1847	119	7	states	state	NOUN
ap-1847	119	8	is	be	AUX
ap-1847	119	9	assumed	assume	VERB
ap-1847	119	10	,	,	PUNCT
ap-1847	119	11	we	we	PRON
ap-1847	119	12	have	have	VERB
ap-1847	119	13	the	the	DET
ap-1847	119	14	following	follow	VERB
ap-1847	119	15	probabilities	probability	NOUN
ap-1847	119	16	of	of	ADP
ap-1847	119	17	the	the	DET
ap-1847	119	18	channels	channel	NOUN
ap-1847	119	19	:	:	PUNCT
ap-1847	119	20	•	•	NUM
ap-1847	119	21	240	240	NUM
ap-1847	119	22	states	state	NOUN
ap-1847	119	23	from	from	ADP
ap-1847	119	24	[	[	PUNCT
ap-1847	119	25	0	0	NUM
ap-1847	119	26	2000000	2000000	NUM
ap-1847	119	27	]	]	PUNCT
ap-1847	119	28	,	,	PUNCT
ap-1847	119	29	each	each	DET
ap-1847	119	30	present	present	ADJ
ap-1847	119	31	once	once	ADV
ap-1847	119	32	:	:	PUNCT
ap-1847	119	33	1/61504	1/61504	NUM
ap-1847	119	34	;	;	PUNCT
ap-1847	119	35	•	•	NUM
ap-1847	119	36	6720	6720	NUM
ap-1847	119	37	states	state	NOUN
ap-1847	119	38	from	from	ADP
ap-1847	119	39	[	[	PUNCT
ap-1847	119	40	0	0	NUM
ap-1847	119	41	0100000	0100000	NUM
ap-1847	119	42	]	]	PUNCT
ap-1847	119	43	,	,	PUNCT
ap-1847	119	44	each	each	PRON
ap-1847	119	45	present	present	ADJ
ap-1847	119	46	twice	twice	ADV
ap-1847	119	47	:	:	PUNCT
ap-1847	119	48	2/61504	2/61504	NUM
ap-1847	119	49	;	;	PUNCT
ap-1847	119	50	•	•	NUM
ap-1847	119	51	2160	2160	NUM
ap-1847	119	52	states	state	NOUN
ap-1847	119	53	from	from	ADP
ap-1847	119	54	[	[	PUNCT
ap-1847	119	55	0	0	NUM
ap-1847	119	56	0000001	0000001	NUM
ap-1847	119	57	]	]	PUNCT
ap-1847	119	58	,	,	PUNCT
ap-1847	119	59	each	each	PRON
ap-1847	119	60	present	present	ADJ
ap-1847	119	61	14	14	NUM
ap-1847	119	62	times	time	NOUN
ap-1847	119	63	:	:	PUNCT
ap-1847	119	64	14/61504	14/61504	NUM
ap-1847	119	65	;	;	PUNCT
ap-1847	119	66	•	•	NUM
ap-1847	119	67	240	240	NUM
ap-1847	119	68	states	state	NOUN
ap-1847	119	69	from	from	ADP
ap-1847	119	70	[	[	PUNCT
ap-1847	119	71	0	0	NUM
ap-1847	119	72	1000000	1000000	NUM
ap-1847	119	73	]	]	PUNCT
ap-1847	119	74	,	,	PUNCT
ap-1847	119	75	each	each	DET
ap-1847	119	76	present	present	ADJ
ap-1847	119	77	72	72	NUM
ap-1847	119	78	times	time	NOUN
ap-1847	119	79	:	:	PUNCT
ap-1847	119	80	72/61504	72/61504	NUM
ap-1847	119	81	;	;	PUNCT
ap-1847	119	82	•	•	NUM
ap-1847	119	83	1	1	NUM
ap-1847	119	84	state	state	NOUN
ap-1847	119	85	from	from	ADP
ap-1847	119	86	[	[	PUNCT
ap-1847	119	87	0	0	NUM
ap-1847	119	88	0000000	0000000	NUM
ap-1847	119	89	]	]	PUNCT
ap-1847	119	90	,	,	PUNCT
ap-1847	119	91	each	each	PRON
ap-1847	119	92	present	present	ADJ
ap-1847	119	93	304	304	NUM
ap-1847	119	94	times	time	NOUN
ap-1847	119	95	:	:	PUNCT
ap-1847	119	96	304/61504	304/61504	NUM
ap-1847	119	97	.	.	PUNCT
ap-1847	120	1	the	the	DET
ap-1847	120	2	results	result	NOUN
ap-1847	120	3	of	of	ADP
ap-1847	120	4	the	the	DET
ap-1847	120	5	example	example	NOUN
ap-1847	120	6	are	be	AUX
ap-1847	120	7	summarized	summarize	VERB
ap-1847	120	8	in	in	ADP
ap-1847	120	9	table	table	NOUN
ap-1847	120	10	3	3	NUM
ap-1847	120	11	.	.	PUNCT
ap-1847	121	1	acknowledgements	acknowledgement	NOUN
ap-1847	121	2	the	the	DET
ap-1847	121	3	authors	author	NOUN
ap-1847	121	4	are	be	AUX
ap-1847	121	5	grateful	grateful	ADJ
ap-1847	121	6	for	for	ADP
ap-1847	121	7	support	support	NOUN
ap-1847	121	8	from	from	ADP
ap-1847	121	9	natural	natural	ADJ
ap-1847	121	10	sciences	science	NOUN
ap-1847	121	11	and	and	CCONJ
ap-1847	121	12	engineering	engineering	NOUN
ap-1847	121	13	research	research	NOUN
ap-1847	121	14	of	of	ADP
ap-1847	121	15	canada	canada	PROPN
ap-1847	121	16	,	,	PUNCT
ap-1847	121	17	to	to	ADP
ap-1847	121	18	the	the	DET
ap-1847	121	19	mind	mind	NOUN
ap-1847	121	20	research	research	PROPN
ap-1847	121	21	institute	institute	PROPN
ap-1847	121	22	of	of	ADP
ap-1847	121	23	irvine	irvine	PROPN
ap-1847	121	24	,	,	PUNCT
ap-1847	121	25	california	california	PROPN
ap-1847	121	26	,	,	PUNCT
ap-1847	121	27	and	and	CCONJ
ap-1847	121	28	to	to	ADP
ap-1847	121	29	mitacs	mitac	NOUN
ap-1847	121	30	.	.	PUNCT
ap-1847	122	1	a.t	a.t	PROPN
ap-1847	122	2	.	.	PROPN
ap-1847	122	3	expresses	express	VERB
ap-1847	122	4	her	her	PRON
ap-1847	122	5	gratitude	gratitude	NOUN
ap-1847	122	6	to	to	ADP
ap-1847	122	7	the	the	DET
ap-1847	122	8	centre	centre	NOUN
ap-1847	122	9	de	de	X
ap-1847	122	10	recherches	recherche	NOUN
ap-1847	122	11	mathématiques	mathématique	NOUN
ap-1847	122	12	,	,	PUNCT
ap-1847	122	13	université	université	PROPN
ap-1847	122	14	de	de	PROPN
ap-1847	122	15	montréal	montréal	PROPN
ap-1847	122	16	for	for	ADP
ap-1847	122	17	the	the	DET
ap-1847	122	18	hospitality	hospitality	NOUN
ap-1847	122	19	during	during	ADP
ap-1847	122	20	her	her	PRON
ap-1847	122	21	postdoctoral	postdoctoral	ADJ
ap-1847	122	22	fellowship	fellowship	NOUN
ap-1847	122	23	.	.	PUNCT
ap-1847	123	1	g.c	g.c	PROPN
ap-1847	123	2	.	.	PROPN
ap-1847	123	3	wishes	wish	VERB
ap-1847	123	4	to	to	PART
ap-1847	123	5	express	express	VERB
ap-1847	123	6	thanks	thank	NOUN
ap-1847	123	7	for	for	ADP
ap-1847	123	8	support	support	NOUN
ap-1847	123	9	from	from	ADP
ap-1847	123	10	the	the	DET
ap-1847	123	11	ministry	ministry	PROPN
ap-1847	123	12	of	of	ADP
ap-1847	123	13	education	education	NOUN
ap-1847	123	14	of	of	ADP
ap-1847	123	15	the	the	DET
ap-1847	123	16	czech	czech	PROPN
ap-1847	123	17	republic	republic	NOUN
ap-1847	123	18	(	(	PUNCT
ap-1847	123	19	project	project	NOUN
ap-1847	123	20	msm6840770039	msm6840770039	NOUN
ap-1847	123	21	)	)	PUNCT
ap-1847	123	22	.	.	PUNCT
ap-1847	124	1	references	reference	NOUN
ap-1847	124	2	[	[	X
ap-1847	124	3	1	1	NUM
ap-1847	124	4	]	]	X
ap-1847	124	5	i.m	i.m	PROPN
ap-1847	124	6	.	.	PROPN
ap-1847	124	7	shmushkevich	shmushkevich	PROPN
ap-1847	124	8	,	,	PUNCT
ap-1847	124	9	on	on	ADP
ap-1847	124	10	deduction	deduction	NOUN
ap-1847	124	11	of	of	ADP
ap-1847	124	12	relations	relation	NOUN
ap-1847	124	13	between	between	ADP
ap-1847	124	14	sections	section	NOUN
ap-1847	124	15	that	that	PRON
ap-1847	124	16	arise	arise	VERB
ap-1847	124	17	from	from	ADP
ap-1847	124	18	the	the	DET
ap-1847	124	19	hypothesis	hypothesis	NOUN
ap-1847	124	20	of	of	ADP
ap-1847	124	21	isotopic	isotopic	ADJ
ap-1847	124	22	invariance	invariance	NOUN
ap-1847	124	23	,	,	PUNCT
ap-1847	124	24	dokl	dokl	NOUN
ap-1847	124	25	.	.	PUNCT
ap-1847	125	1	akad	akad	PROPN
ap-1847	125	2	.	.	PUNCT
ap-1847	126	1	nauk	nauk	PROPN
ap-1847	126	2	sssr	sssr	NOUN
ap-1847	126	3	103	103	NUM
ap-1847	126	4	(	(	PUNCT
ap-1847	126	5	1955	1955	NUM
ap-1847	126	6	)	)	PUNCT
ap-1847	127	1	235–238	235–238	NUM
ap-1847	127	2	(	(	PUNCT
ap-1847	127	3	in	in	ADP
ap-1847	127	4	russian	russian	NOUN
ap-1847	127	5	)	)	PUNCT
ap-1847	128	1	[	[	X
ap-1847	128	2	2	2	X
ap-1847	128	3	]	]	X
ap-1847	128	4	n.	n.	PROPN
ap-1847	128	5	dushin	dushin	PROPN
ap-1847	128	6	,	,	PUNCT
ap-1847	128	7	i.m	i.m	PROPN
ap-1847	128	8	.	.	PROPN
ap-1847	128	9	shmushkevich	shmushkevich	PROPN
ap-1847	128	10	,	,	PUNCT
ap-1847	128	11	on	on	ADP
ap-1847	128	12	the	the	DET
ap-1847	128	13	relations	relation	NOUN
ap-1847	128	14	between	between	ADP
ap-1847	128	15	cross	cross	NOUN
ap-1847	128	16	sections	section	NOUN
ap-1847	128	17	which	which	PRON
ap-1847	128	18	result	result	VERB
ap-1847	128	19	from	from	ADP
ap-1847	128	20	the	the	DET
ap-1847	128	21	hypothesis	hypothesis	NOUN
ap-1847	128	22	of	of	ADP
ap-1847	128	23	isotopic	isotopic	ADJ
ap-1847	128	24	invariance	invariance	NOUN
ap-1847	128	25	,	,	PUNCT
ap-1847	128	26	dokl	dokl	NOUN
ap-1847	128	27	.	.	PUNCT
ap-1847	128	28	akad	akad	PROPN
ap-1847	128	29	.	.	PUNCT
ap-1847	129	1	nauk	nauk	PROPN
ap-1847	129	2	sssr	sssr	NOUN
ap-1847	129	3	106	106	NUM
ap-1847	129	4	(	(	PUNCT
ap-1847	129	5	1956	1956	NUM
ap-1847	129	6	)	)	PUNCT
ap-1847	129	7	801	801	NUM
ap-1847	129	8	-	-	SYM
ap-1847	129	9	805	805	NUM
ap-1847	129	10	;	;	PUNCT
ap-1847	129	11	translated	translate	VERB
ap-1847	129	12	in	in	ADP
ap-1847	129	13	soviet	soviet	ADJ
ap-1847	129	14	phys	phy	NOUN
ap-1847	129	15	.	.	PUNCT
ap-1847	130	1	dokl	dokl	NOUN
ap-1847	130	2	.	.	PUNCT
ap-1847	131	1	1	1	NUM
ap-1847	131	2	(	(	PUNCT
ap-1847	131	3	1956	1956	NUM
ap-1847	131	4	)	)	PUNCT
ap-1847	131	5	94–98	94–98	NUM
ap-1847	131	6	397	397	NUM
ap-1847	131	7	m.	m.	NOUN
ap-1847	131	8	bodner	bodner	NOUN
ap-1847	131	9	,	,	PUNCT
ap-1847	131	10	g.	g.	PROPN
ap-1847	131	11	chadzitaskos	chadzitaskos	PROPN
ap-1847	131	12	,	,	PUNCT
ap-1847	131	13	j.	j.	PROPN
ap-1847	131	14	patera	patera	PROPN
ap-1847	131	15	,	,	PUNCT
ap-1847	131	16	a.	a.	PROPN
ap-1847	131	17	tereszkiewicz	tereszkiewicz	PROPN
ap-1847	131	18	acta	acta	PROPN
ap-1847	131	19	polytechnica	polytechnica	PROPN
ap-1847	131	20	e(8	e(8	NOUN
ap-1847	131	21	)	)	PUNCT
ap-1847	131	22	decomposition	decomposition	NOUN
ap-1847	131	23	into	into	ADP
ap-1847	131	24	irreducible	irreducible	ADJ
ap-1847	131	25	representations	representation	NOUN
ap-1847	131	26	with	with	ADP
ap-1847	131	27	multiplicities	multiplicity	NOUN
ap-1847	131	28	multiplicity	multiplicity	NOUN
ap-1847	131	29	orbit	orbit	NOUN
ap-1847	131	30	size	size	NOUN
ap-1847	131	31	(	(	PUNCT
ap-1847	131	32	0	0	NUM
ap-1847	131	33	1000000	1000000	NUM
ap-1847	131	34	)	)	PUNCT
ap-1847	131	35	×	×	NOUN
ap-1847	131	36	(	(	PUNCT
ap-1847	131	37	0	0	NUM
ap-1847	131	38	1000000	1000000	NUM
ap-1847	131	39	)	)	PUNCT
ap-1847	131	40	(	(	PUNCT
ap-1847	131	41	0	0	NUM
ap-1847	131	42	2000000	2000000	NUM
ap-1847	131	43	)	)	PUNCT
ap-1847	131	44	(	(	PUNCT
ap-1847	131	45	0	0	NUM
ap-1847	131	46	0100000	0100000	NUM
ap-1847	131	47	)	)	PUNCT
ap-1847	131	48	(	(	PUNCT
ap-1847	131	49	0	0	NUM
ap-1847	131	50	0000001	0000001	NUM
ap-1847	131	51	)	)	PUNCT
ap-1847	131	52	(	(	PUNCT
ap-1847	131	53	0	0	NUM
ap-1847	131	54	1000000	1000000	NUM
ap-1847	131	55	)	)	PUNCT
ap-1847	131	56	(	(	PUNCT
ap-1847	131	57	0	0	NUM
ap-1847	131	58	0000000	0000000	NUM
ap-1847	131	59	)	)	PUNCT
ap-1847	131	60	248	248	NUM
ap-1847	131	61	×	×	NOUN
ap-1847	131	62	248	248	NUM
ap-1847	131	63	[	[	PUNCT
ap-1847	131	64	0	0	NUM
ap-1847	131	65	2000000	2000000	NUM
ap-1847	131	66	]	]	PUNCT
ap-1847	131	67	1	1	NUM
ap-1847	131	68	240	240	NUM
ap-1847	131	69	[	[	PUNCT
ap-1847	131	70	0	0	NUM
ap-1847	131	71	0100000	0100000	NUM
ap-1847	131	72	]	]	PUNCT
ap-1847	132	1	[	[	PUNCT
ap-1847	132	2	0	0	NUM
ap-1847	132	3	0100000	0100000	NUM
ap-1847	132	4	]	]	PUNCT
ap-1847	132	5	2	2	NUM
ap-1847	132	6	6720	6720	NUM
ap-1847	132	7	6	6	NUM
ap-1847	132	8	[	[	PUNCT
ap-1847	132	9	0	0	NUM
ap-1847	132	10	0000001	0000001	NUM
ap-1847	132	11	]	]	PUNCT
ap-1847	132	12	7	7	NUM
ap-1847	132	13	[	[	PUNCT
ap-1847	132	14	0	0	NUM
ap-1847	132	15	0000001	0000001	NUM
ap-1847	132	16	]	]	PUNCT
ap-1847	132	17	[	[	PUNCT
ap-1847	132	18	0	0	NUM
ap-1847	132	19	0000001	0000001	NUM
ap-1847	132	20	]	]	PUNCT
ap-1847	132	21	14	14	NUM
ap-1847	132	22	2160	2160	NUM
ap-1847	132	23	29	29	NUM
ap-1847	132	24	[	[	PUNCT
ap-1847	132	25	0	0	NUM
ap-1847	132	26	1000000	1000000	NUM
ap-1847	132	27	]	]	PUNCT
ap-1847	132	28	35	35	NUM
ap-1847	132	29	[	[	PUNCT
ap-1847	132	30	0	0	NUM
ap-1847	132	31	1000000	1000000	NUM
ap-1847	132	32	]	]	PUNCT
ap-1847	132	33	7	7	NUM
ap-1847	132	34	[	[	PUNCT
ap-1847	132	35	0	0	NUM
ap-1847	132	36	1000000	1000000	NUM
ap-1847	132	37	]	]	PUNCT
ap-1847	132	38	[	[	PUNCT
ap-1847	132	39	0	0	NUM
ap-1847	132	40	1000000	1000000	NUM
ap-1847	132	41	]	]	PUNCT
ap-1847	132	42	72	72	NUM
ap-1847	132	43	240	240	NUM
ap-1847	132	44	120	120	NUM
ap-1847	132	45	[	[	PUNCT
ap-1847	132	46	0	0	NUM
ap-1847	132	47	0000000	0000000	NUM
ap-1847	132	48	]	]	PUNCT
ap-1847	132	49	140	140	NUM
ap-1847	132	50	[	[	PUNCT
ap-1847	132	51	0	0	NUM
ap-1847	132	52	0000000	0000000	NUM
ap-1847	132	53	]	]	PUNCT
ap-1847	132	54	35	35	NUM
ap-1847	132	55	[	[	PUNCT
ap-1847	132	56	0	0	NUM
ap-1847	132	57	0000000	0000000	NUM
ap-1847	132	58	]	]	SYM
ap-1847	132	59	8	8	NUM
ap-1847	132	60	[	[	PUNCT
ap-1847	132	61	0	0	NUM
ap-1847	132	62	1000000	1000000	NUM
ap-1847	132	63	]	]	PUNCT
ap-1847	132	64	[	[	PUNCT
ap-1847	132	65	0	0	NUM
ap-1847	132	66	0000000	0000000	NUM
ap-1847	132	67	]	]	PUNCT
ap-1847	132	68	304	304	NUM
ap-1847	132	69	1	1	NUM
ap-1847	132	70	decomposition	decomposition	NOUN
ap-1847	132	71	into	into	ADP
ap-1847	132	72	orbits	orbit	NOUN
ap-1847	132	73	with	with	ADP
ap-1847	132	74	multiplicities	multiplicity	NOUN
ap-1847	132	75	[	[	PUNCT
ap-1847	132	76	0	0	NUM
ap-1847	132	77	2000000	2000000	NUM
ap-1847	132	78	]	]	PUNCT
ap-1847	132	79	2	2	NUM
ap-1847	132	80	[	[	PUNCT
ap-1847	132	81	0	0	NUM
ap-1847	132	82	0100000	0100000	NUM
ap-1847	132	83	]	]	PUNCT
ap-1847	132	84	14	14	NUM
ap-1847	132	85	[	[	PUNCT
ap-1847	132	86	0	0	NUM
ap-1847	132	87	0000001	0000001	NUM
ap-1847	132	88	]	]	PUNCT
ap-1847	132	89	72	72	NUM
ap-1847	132	90	[	[	PUNCT
ap-1847	132	91	0	0	NUM
ap-1847	132	92	1000000	1000000	NUM
ap-1847	132	93	]	]	PUNCT
ap-1847	133	1	304	304	NUM
ap-1847	133	2	[	[	PUNCT
ap-1847	133	3	0	0	NUM
ap-1847	133	4	0000000	0000000	NUM
ap-1847	133	5	]	]	PUNCT
ap-1847	133	6	61504	61504	NUM
ap-1847	133	7	=	=	SYM
ap-1847	133	8	2482	2482	NUM
ap-1847	133	9	table	table	NOUN
ap-1847	133	10	3	3	NUM
ap-1847	133	11	.	.	PUNCT
ap-1847	133	12	decomposition	decomposition	NOUN
ap-1847	133	13	of	of	ADP
ap-1847	133	14	the	the	DET
ap-1847	133	15	product	product	NOUN
ap-1847	133	16	in	in	ADP
ap-1847	133	17	the	the	DET
ap-1847	133	18	e(8	e(8	NOUN
ap-1847	133	19	)	)	PUNCT
ap-1847	133	20	example	example	NOUN
ap-1847	133	21	.	.	PUNCT
ap-1847	134	1	the	the	DET
ap-1847	134	2	decomposition	decomposition	NOUN
ap-1847	134	3	is	be	AUX
ap-1847	134	4	given	give	VERB
ap-1847	134	5	in	in	ADP
ap-1847	134	6	the	the	DET
ap-1847	134	7	weight	weight	NOUN
ap-1847	134	8	system	system	NOUN
ap-1847	134	9	of	of	ADP
ap-1847	134	10	irreducible	irreducible	ADJ
ap-1847	134	11	representations	representation	NOUN
ap-1847	134	12	(	(	PUNCT
ap-1847	134	13	the	the	DET
ap-1847	134	14	first	first	ADJ
ap-1847	134	15	line	line	NOUN
ap-1847	134	16	)	)	PUNCT
ap-1847	134	17	and	and	CCONJ
ap-1847	134	18	in	in	ADP
ap-1847	134	19	terms	term	NOUN
ap-1847	134	20	of	of	ADP
ap-1847	134	21	orbits	orbit	NOUN
ap-1847	134	22	(	(	PUNCT
ap-1847	134	23	bottom	bottom	ADJ
ap-1847	134	24	line	line	NOUN
ap-1847	134	25	)	)	PUNCT
ap-1847	134	26	.	.	PUNCT
ap-1847	135	1	the	the	DET
ap-1847	135	2	dimensions	dimension	NOUN
ap-1847	135	3	of	of	ADP
ap-1847	135	4	the	the	DET
ap-1847	135	5	representations	representation	NOUN
ap-1847	135	6	and	and	CCONJ
ap-1847	135	7	the	the	DET
ap-1847	135	8	sizes	size	NOUN
ap-1847	135	9	of	of	ADP
ap-1847	135	10	the	the	DET
ap-1847	135	11	orbits	orbit	NOUN
ap-1847	135	12	are	be	AUX
ap-1847	135	13	shown	show	VERB
ap-1847	135	14	together	together	ADV
ap-1847	135	15	with	with	ADP
ap-1847	135	16	the	the	DET
ap-1847	135	17	multiplicities	multiplicity	NOUN
ap-1847	135	18	.	.	PUNCT
ap-1847	136	1	[	[	X
ap-1847	136	2	3	3	X
ap-1847	136	3	]	]	X
ap-1847	136	4	g.	g.	PROPN
ap-1847	136	5	pinsky	pinsky	PROPN
ap-1847	136	6	,	,	PUNCT
ap-1847	136	7	a.j	a.j	PROPN
ap-1847	136	8	.	.	PROPN
ap-1847	136	9	macfarlane	macfarlane	PROPN
ap-1847	136	10	,	,	PUNCT
ap-1847	136	11	e.c.g	e.c.g	PROPN
ap-1847	136	12	.	.	PUNCT
ap-1847	137	1	sudarshan	sudarshan	PROPN
ap-1847	137	2	,	,	PUNCT
ap-1847	137	3	shmushkevich	shmushkevich	PROPN
ap-1847	137	4	’s	’s	PART
ap-1847	137	5	method	method	NOUN
ap-1847	137	6	for	for	ADP
ap-1847	137	7	a	a	DET
ap-1847	137	8	charge	charge	NOUN
ap-1847	137	9	-	-	PUNCT
ap-1847	137	10	independent	independent	ADJ
ap-1847	137	11	theory	theory	NOUN
ap-1847	137	12	,	,	PUNCT
ap-1847	137	13	phys	phy	NOUN
ap-1847	137	14	.	.	PUNCT
ap-1847	137	15	rev	rev	PROPN
ap-1847	137	16	.	.	PROPN
ap-1847	137	17	140	140	NUM
ap-1847	137	18	,	,	PUNCT
ap-1847	137	19	(	(	PUNCT
ap-1847	137	20	1965	1965	NUM
ap-1847	137	21	)	)	PUNCT
ap-1847	137	22	,	,	PUNCT
ap-1847	137	23	b1045	b1045	NOUN
ap-1847	137	24	–	–	PUNCT
ap-1847	137	25	b1053	b1053	ADJ
ap-1847	137	26	[	[	X
ap-1847	137	27	4	4	NUM
ap-1847	137	28	]	]	X
ap-1847	137	29	c.g	c.g	PROPN
ap-1847	137	30	.	.	PROPN
ap-1847	137	31	wohl	wohl	PROPN
ap-1847	137	32	,	,	PUNCT
ap-1847	137	33	isospin	isospin	VERB
ap-1847	137	34	relations	relation	NOUN
ap-1847	137	35	by	by	ADP
ap-1847	137	36	counting	count	VERB
ap-1847	137	37	,	,	PUNCT
ap-1847	137	38	amer	amer	PROPN
ap-1847	137	39	.	.	PUNCT
ap-1847	138	1	j.	j.	PROPN
ap-1847	138	2	phys	phys	PROPN
ap-1847	138	3	.	.	PUNCT
ap-1847	139	1	50	50	NUM
ap-1847	139	2	,	,	PUNCT
ap-1847	139	3	(	(	PUNCT
ap-1847	139	4	1982	1982	NUM
ap-1847	139	5	)	)	PUNCT
ap-1847	139	6	,	,	PUNCT
ap-1847	139	7	748	748	NUM
ap-1847	139	8	-	-	SYM
ap-1847	139	9	753	753	NUM
ap-1847	139	10	[	[	X
ap-1847	139	11	5	5	NUM
ap-1847	139	12	]	]	PUNCT
ap-1847	139	13	p.	p.	NOUN
ap-1847	139	14	roman	roman	NOUN
ap-1847	139	15	,	,	PUNCT
ap-1847	139	16	the	the	DET
ap-1847	139	17	theory	theory	NOUN
ap-1847	139	18	of	of	ADP
ap-1847	139	19	elementary	elementary	ADJ
ap-1847	139	20	particles	particle	NOUN
ap-1847	139	21	,	,	PUNCT
ap-1847	139	22	north	north	NOUN
ap-1847	139	23	-	-	PUNCT
ap-1847	139	24	holland	holland	NOUN
ap-1847	139	25	pub	pub	NOUN
ap-1847	139	26	.	.	PUNCT
ap-1847	140	1	co.	co.	PROPN
ap-1847	140	2	(	(	PUNCT
ap-1847	140	3	1960	1960	NUM
ap-1847	140	4	)	)	PUNCT
ap-1847	141	1	[	[	X
ap-1847	141	2	6	6	NUM
ap-1847	141	3	]	]	PUNCT
ap-1847	141	4	r.	r.	PROPN
ap-1847	141	5	marshak	marshak	PROPN
ap-1847	141	6	,	,	PUNCT
ap-1847	141	7	e.	e.	PROPN
ap-1847	141	8	sudarshan	sudarshan	PROPN
ap-1847	141	9	,	,	PUNCT
ap-1847	141	10	introduction	introduction	NOUN
ap-1847	141	11	to	to	ADP
ap-1847	141	12	elementary	elementary	ADJ
ap-1847	141	13	particles	particle	NOUN
ap-1847	141	14	physics	physics	PROPN
ap-1847	141	15	,	,	PUNCT
ap-1847	141	16	new	new	PROPN
ap-1847	141	17	york	york	PROPN
ap-1847	141	18	,	,	PUNCT
ap-1847	141	19	interscience	interscience	NOUN
ap-1847	141	20	publishers	publisher	NOUN
ap-1847	141	21	,	,	PUNCT
ap-1847	141	22	1961	1961	NUM
ap-1847	141	23	[	[	X
ap-1847	141	24	7	7	NUM
ap-1847	141	25	]	]	X
ap-1847	141	26	r.	r.	PROPN
ap-1847	141	27	v.	v.	PROPN
ap-1847	141	28	moody	moody	PROPN
ap-1847	141	29	,	,	PUNCT
ap-1847	141	30	j.	j.	PROPN
ap-1847	141	31	patera	patera	PROPN
ap-1847	141	32	,	,	PUNCT
ap-1847	141	33	general	general	ADJ
ap-1847	141	34	charge	charge	NOUN
ap-1847	141	35	conjugation	conjugation	NOUN
ap-1847	141	36	operators	operator	NOUN
ap-1847	141	37	in	in	ADP
ap-1847	141	38	simple	simple	ADJ
ap-1847	141	39	lie	lie	NOUN
ap-1847	141	40	groups	group	NOUN
ap-1847	141	41	,	,	PUNCT
ap-1847	141	42	j.	j.	PROPN
ap-1847	141	43	math	math	PROPN
ap-1847	141	44	.	.	PUNCT
ap-1847	142	1	phys	phy	NOUN
ap-1847	142	2	.	.	PUNCT
ap-1847	142	3	,	,	PUNCT
ap-1847	142	4	25	25	NUM
ap-1847	142	5	(	(	PUNCT
ap-1847	142	6	1984	1984	NUM
ap-1847	142	7	)	)	PUNCT
ap-1847	142	8	2838–2847	2838–2847	NUM
ap-1847	142	9	[	[	X
ap-1847	142	10	8	8	NUM
ap-1847	142	11	]	]	X
ap-1847	142	12	l.	l.	PROPN
ap-1847	142	13	michel	michel	PROPN
ap-1847	142	14	,	,	PUNCT
ap-1847	142	15	j.	j.	PROPN
ap-1847	142	16	patera	patera	PROPN
ap-1847	142	17	,	,	PUNCT
ap-1847	142	18	r.	r.	PROPN
ap-1847	142	19	t.	t.	PROPN
ap-1847	142	20	sharp	sharp	ADJ
ap-1847	142	21	,	,	PUNCT
ap-1847	142	22	demazure	demazure	NOUN
ap-1847	142	23	-	-	PUNCT
ap-1847	142	24	tits	tit	NOUN
ap-1847	142	25	subgroup	subgroup	NOUN
ap-1847	142	26	of	of	ADP
ap-1847	142	27	a	a	DET
ap-1847	142	28	simple	simple	ADJ
ap-1847	142	29	lie	lie	NOUN
ap-1847	142	30	group	group	NOUN
ap-1847	142	31	,	,	PUNCT
ap-1847	142	32	j.	j.	PROPN
ap-1847	142	33	math	math	PROPN
ap-1847	142	34	.	.	PUNCT
ap-1847	143	1	phys	phy	NOUN
ap-1847	143	2	.	.	PUNCT
ap-1847	143	3	,	,	PUNCT
ap-1847	143	4	29	29	NUM
ap-1847	143	5	(	(	PUNCT
ap-1847	143	6	1988	1988	NUM
ap-1847	143	7	)	)	PUNCT
ap-1847	144	1	777–796	777–796	NOUN
ap-1847	144	2	[	[	X
ap-1847	144	3	9	9	NUM
ap-1847	144	4	]	]	PUNCT
ap-1847	144	5	p.	p.	NOUN
ap-1847	144	6	ramond	ramond	PROPN
ap-1847	144	7	,	,	PUNCT
ap-1847	144	8	group	group	NOUN
ap-1847	144	9	theory	theory	NOUN
ap-1847	144	10	.	.	PUNCT
ap-1847	145	1	a	a	DET
ap-1847	145	2	physicist	physicist	NOUN
ap-1847	145	3	’s	’s	PART
ap-1847	145	4	survey	survey	NOUN
ap-1847	145	5	,	,	PUNCT
ap-1847	145	6	cambridge	cambridge	PROPN
ap-1847	145	7	univ	univ	PROPN
ap-1847	145	8	.	.	PUNCT
ap-1847	146	1	press	press	PROPN
ap-1847	146	2	,	,	PUNCT
ap-1847	146	3	2010	2010	NUM
ap-1847	147	1	[	[	X
ap-1847	147	2	10	10	NUM
ap-1847	147	3	]	]	X
ap-1847	147	4	w.	w.	PROPN
ap-1847	147	5	g.	g.	PROPN
ap-1847	147	6	mckay	mckay	PROPN
ap-1847	147	7	,	,	PUNCT
ap-1847	147	8	j.	j.	PROPN
ap-1847	147	9	patera	patera	PROPN
ap-1847	147	10	,	,	PUNCT
ap-1847	147	11	d.	d.	PROPN
ap-1847	147	12	w.	w.	PROPN
ap-1847	147	13	rand	rand	PROPN
ap-1847	147	14	,	,	PUNCT
ap-1847	147	15	tables	table	NOUN
ap-1847	147	16	of	of	ADP
ap-1847	147	17	representations	representation	NOUN
ap-1847	147	18	of	of	ADP
ap-1847	147	19	simple	simple	ADJ
ap-1847	147	20	lie	lie	NOUN
ap-1847	147	21	algebras	algebra	NOUN
ap-1847	147	22	(	(	PUNCT
ap-1847	147	23	exceptional	exceptional	ADJ
ap-1847	147	24	simple	simple	ADJ
ap-1847	147	25	lie	lie	NOUN
ap-1847	147	26	algebras	algebra	NOUN
ap-1847	147	27	:	:	PUNCT
ap-1847	147	28	vol	vol	NOUN
ap-1847	147	29	.	.	NOUN
ap-1847	147	30	1	1	NUM
ap-1847	147	31	)	)	PUNCT
ap-1847	147	32	,	,	PUNCT
ap-1847	147	33	université	université	PROPN
ap-1847	147	34	de	de	PROPN
ap-1847	147	35	montréal	montréal	PROPN
ap-1847	147	36	,	,	PUNCT
ap-1847	147	37	centre	centre	NOUN
ap-1847	147	38	de	de	X
ap-1847	147	39	recherches	recherche	NOUN
ap-1847	147	40	mathématiques	mathématique	NOUN
ap-1847	147	41	,	,	PUNCT
ap-1847	147	42	1990	1990	NUM
ap-1847	147	43	[	[	X
ap-1847	147	44	11	11	NUM
ap-1847	147	45	]	]	PUNCT
ap-1847	147	46	r.	r.	PROPN
ap-1847	147	47	v.	v.	PROPN
ap-1847	147	48	moody	moody	PROPN
ap-1847	147	49	,	,	PUNCT
ap-1847	147	50	j.	j.	PROPN
ap-1847	147	51	patera	patera	PROPN
ap-1847	147	52	,	,	PUNCT
ap-1847	147	53	fast	fast	ADJ
ap-1847	147	54	recursion	recursion	NOUN
ap-1847	147	55	formula	formula	NOUN
ap-1847	147	56	for	for	ADP
ap-1847	147	57	weight	weight	NOUN
ap-1847	147	58	multiplicities	multiplicity	NOUN
ap-1847	147	59	,	,	PUNCT
ap-1847	147	60	bull	bull	NOUN
ap-1847	147	61	.	.	PUNCT
ap-1847	148	1	amer	amer	PROPN
ap-1847	148	2	.	.	PUNCT
ap-1847	148	3	math	math	PROPN
ap-1847	148	4	.	.	PUNCT
ap-1847	149	1	soc	soc	PROPN
ap-1847	149	2	.	.	PUNCT
ap-1847	150	1	,	,	PUNCT
ap-1847	150	2	7	7	NUM
ap-1847	150	3	(	(	PUNCT
ap-1847	150	4	1982	1982	NUM
ap-1847	150	5	)	)	PUNCT
ap-1847	150	6	237–242	237–242	NUM
ap-1847	150	7	[	[	X
ap-1847	150	8	12	12	NUM
ap-1847	150	9	]	]	PUNCT
ap-1847	150	10	m.	m.	PROPN
ap-1847	150	11	r.	r.	PROPN
ap-1847	150	12	bremner	bremner	PROPN
ap-1847	150	13	,	,	PUNCT
ap-1847	150	14	r.	r.	PROPN
ap-1847	150	15	v.	v.	PROPN
ap-1847	150	16	moody	moody	PROPN
ap-1847	150	17	,	,	PUNCT
ap-1847	150	18	j.	j.	PROPN
ap-1847	150	19	patera	patera	PROPN
ap-1847	150	20	,	,	PUNCT
ap-1847	150	21	tables	table	NOUN
ap-1847	150	22	of	of	ADP
ap-1847	150	23	dominant	dominant	ADJ
ap-1847	150	24	weight	weight	NOUN
ap-1847	150	25	multiplicities	multiplicity	NOUN
ap-1847	150	26	for	for	ADP
ap-1847	150	27	representations	representation	NOUN
ap-1847	150	28	of	of	ADP
ap-1847	150	29	simple	simple	ADJ
ap-1847	150	30	lie	lie	NOUN
ap-1847	150	31	algebras	algebra	NOUN
ap-1847	150	32	,	,	PUNCT
ap-1847	150	33	marcel	marcel	PROPN
ap-1847	150	34	dekker	dekker	PROPN
ap-1847	150	35	,	,	PUNCT
ap-1847	150	36	new	new	PROPN
ap-1847	150	37	york	york	PROPN
ap-1847	150	38	1985	1985	NUM
ap-1847	150	39	,	,	PUNCT
ap-1847	150	40	340	340	NUM
ap-1847	150	41	pages	page	NOUN
ap-1847	150	42	,	,	PUNCT
ap-1847	150	43	isbn	isbn	ADJ
ap-1847	150	44	:	:	PUNCT
ap-1847	150	45	0	0	NUM
ap-1847	150	46	-	-	SYM
ap-1847	150	47	8247	8247	NUM
ap-1847	150	48	-	-	SYM
ap-1847	150	49	7270	7270	NUM
ap-1847	150	50	-	-	SYM
ap-1847	150	51	9	9	NUM
ap-1847	150	52	398	398	NUM
ap-1847	150	53	acta	acta	PROPN
ap-1847	150	54	polytechnica	polytechnica	PROPN
ap-1847	150	55	53(5):395–398	53(5):395–398	PROPN
ap-1847	150	56	,	,	PUNCT
ap-1847	150	57	2013	2013	NUM
ap-1847	150	58	1	1	NUM
ap-1847	150	59	introduction	introduction	NOUN
ap-1847	150	60	2	2	NUM
ap-1847	150	61	symmetry	symmetry	NOUN
ap-1847	150	62	group	group	NOUN
ap-1847	150	63	o(5	o(5	PROPN
ap-1847	150	64	)	)	PUNCT
ap-1847	150	65	3	3	NUM
ap-1847	150	66	symmetry	symmetry	NOUN
ap-1847	150	67	group	group	NOUN
ap-1847	150	68	f(4	f(4	PROPN
ap-1847	150	69	)	)	PUNCT
ap-1847	150	70	4	4	NUM
ap-1847	150	71	symmetry	symmetry	NOUN
ap-1847	150	72	group	group	NOUN
ap-1847	150	73	e(8	e(8	NOUN
ap-1847	150	74	)	)	PUNCT
ap-1847	150	75	acknowledgements	acknowledgement	NOUN
ap-1847	150	76	references	reference	NOUN