id	sid	tid	token	lemma	pos
ff365428x4m	1	1	totally	totally	ADV
ff365428x4m	1	2	positive	positive	ADJ
ff365428x4m	1	3	matrices	matrix	NOUN
ff365428x4m	1	4	are	be	AUX
ff365428x4m	1	5	matrices	matrix	NOUN
ff365428x4m	1	6	in	in	ADP
ff365428x4m	1	7	which	which	PRON
ff365428x4m	1	8	each	each	DET
ff365428x4m	1	9	minor	minor	ADJ
ff365428x4m	1	10	is	be	AUX
ff365428x4m	1	11	positive	positive	ADJ
ff365428x4m	1	12	.	.	PUNCT
ff365428x4m	2	1	such	such	ADJ
ff365428x4m	2	2	matrices	matrix	NOUN
ff365428x4m	2	3	appear	appear	VERB
ff365428x4m	2	4	in	in	ADP
ff365428x4m	2	5	many	many	ADJ
ff365428x4m	2	6	different	different	ADJ
ff365428x4m	2	7	areas	area	NOUN
ff365428x4m	2	8	of	of	ADP
ff365428x4m	2	9	theoretical	theoretical	ADJ
ff365428x4m	2	10	and	and	CCONJ
ff365428x4m	2	11	applied	apply	VERB
ff365428x4m	2	12	mathematics	mathematic	NOUN
ff365428x4m	2	13	.	.	PUNCT
ff365428x4m	3	1	investigation	investigation	NOUN
ff365428x4m	3	2	of	of	ADP
ff365428x4m	3	3	the	the	DET
ff365428x4m	3	4	structure	structure	NOUN
ff365428x4m	3	5	of	of	ADP
ff365428x4m	3	6	inequalities	inequality	NOUN
ff365428x4m	3	7	between	between	ADP
ff365428x4m	3	8	the	the	DET
ff365428x4m	3	9	minors	minor	NOUN
ff365428x4m	3	10	of	of	ADP
ff365428x4m	3	11	totally	totally	ADV
ff365428x4m	3	12	positive	positive	ADJ
ff365428x4m	3	13	matrices	matrix	NOUN
ff365428x4m	3	14	plays	play	VERB
ff365428x4m	3	15	an	an	DET
ff365428x4m	3	16	important	important	ADJ
ff365428x4m	3	17	role	role	NOUN
ff365428x4m	3	18	in	in	ADP
ff365428x4m	3	19	many	many	ADJ
ff365428x4m	3	20	problems	problem	NOUN
ff365428x4m	3	21	in	in	ADP
ff365428x4m	3	22	these	these	DET
ff365428x4m	3	23	areas	area	NOUN
ff365428x4m	3	24	.	.	PUNCT
ff365428x4m	4	1	in	in	ADP
ff365428x4m	4	2	representation	representation	NOUN
ff365428x4m	4	3	theory	theory	NOUN
ff365428x4m	4	4	of	of	ADP
ff365428x4m	4	5	quantized	quantize	VERB
ff365428x4m	4	6	enveloping	envelop	VERB
ff365428x4m	4	7	algebras	algebra	NOUN
ff365428x4m	4	8	the	the	DET
ff365428x4m	4	9	notion	notion	NOUN
ff365428x4m	4	10	of	of	ADP
ff365428x4m	4	11	canonical	canonical	ADJ
ff365428x4m	4	12	bases	basis	NOUN
ff365428x4m	4	13	plays	play	VERB
ff365428x4m	4	14	important	important	ADJ
ff365428x4m	4	15	role	role	NOUN
ff365428x4m	4	16	.	.	PUNCT
ff365428x4m	5	1	one	one	NUM
ff365428x4m	5	2	of	of	ADP
ff365428x4m	5	3	the	the	DET
ff365428x4m	5	4	approaches	approach	NOUN
ff365428x4m	5	5	to	to	PART
ff365428x4m	5	6	describe	describe	VERB
ff365428x4m	5	7	canonical	canonical	ADJ
ff365428x4m	5	8	bases	basis	NOUN
ff365428x4m	5	9	is	be	AUX
ff365428x4m	5	10	to	to	PART
ff365428x4m	5	11	study	study	VERB
ff365428x4m	5	12	their	their	PRON
ff365428x4m	5	13	dual	dual	ADJ
ff365428x4m	5	14	objects	object	NOUN
ff365428x4m	5	15	,	,	PUNCT
ff365428x4m	5	16	so	so	ADV
ff365428x4m	5	17	called	call	VERB
ff365428x4m	5	18	dual	dual	ADJ
ff365428x4m	5	19	canonical	canonical	ADJ
ff365428x4m	5	20	bases	basis	NOUN
ff365428x4m	5	21	.	.	PUNCT
ff365428x4m	6	1	lusztig	lusztig	PROPN
ff365428x4m	6	2	has	have	AUX
ff365428x4m	6	3	shown	show	VERB
ff365428x4m	6	4	that	that	SCONJ
ff365428x4m	6	5	specializations	specialization	NOUN
ff365428x4m	6	6	of	of	ADP
ff365428x4m	6	7	elements	element	NOUN
ff365428x4m	6	8	of	of	ADP
ff365428x4m	6	9	the	the	DET
ff365428x4m	6	10	dual	dual	ADJ
ff365428x4m	6	11	canonical	canonical	ADJ
ff365428x4m	6	12	bases	basis	NOUN
ff365428x4m	6	13	at	at	ADP
ff365428x4m	6	14	q=1	q=1	NOUN
ff365428x4m	6	15	are	be	AUX
ff365428x4m	6	16	totally	totally	ADV
ff365428x4m	6	17	non	non	ADJ
ff365428x4m	6	18	-	-	ADJ
ff365428x4m	6	19	negative	negative	ADJ
ff365428x4m	6	20	polynomials	polynomial	NOUN
ff365428x4m	6	21	.	.	PUNCT
ff365428x4m	7	1	to	to	ADP
ff365428x4m	7	2	this	this	DET
ff365428x4m	7	3	end	end	NOUN
ff365428x4m	7	4	there	there	PRON
ff365428x4m	7	5	is	be	VERB
ff365428x4m	7	6	an	an	DET
ff365428x4m	7	7	interest	interest	NOUN
ff365428x4m	7	8	in	in	ADP
ff365428x4m	7	9	functions	function	NOUN
ff365428x4m	7	10	that	that	PRON
ff365428x4m	7	11	are	be	AUX
ff365428x4m	7	12	positive	positive	ADJ
ff365428x4m	7	13	on	on	ADP
ff365428x4m	7	14	the	the	DET
ff365428x4m	7	15	locus	locus	NOUN
ff365428x4m	7	16	of	of	ADP
ff365428x4m	7	17	totally	totally	ADV
ff365428x4m	7	18	positive	positive	ADJ
ff365428x4m	7	19	matrices	matrix	NOUN
ff365428x4m	7	20	.	.	PUNCT
ff365428x4m	8	1	we	we	PRON
ff365428x4m	8	2	present	present	VERB
ff365428x4m	8	3	results	result	NOUN
ff365428x4m	8	4	on	on	ADP
ff365428x4m	8	5	multiplicative	multiplicative	ADJ
ff365428x4m	8	6	determinantal	determinantal	ADJ
ff365428x4m	8	7	inequalities	inequality	NOUN
ff365428x4m	8	8	(	(	PUNCT
ff365428x4m	8	9	joint	joint	ADJ
ff365428x4m	8	10	work	work	NOUN
ff365428x4m	8	11	with	with	ADP
ff365428x4m	8	12	m.	m.	NOUN
ff365428x4m	8	13	gekhtman	gekhtman	PROPN
ff365428x4m	8	14	)	)	PUNCT
ff365428x4m	8	15	as	as	ADV
ff365428x4m	8	16	well	well	ADV
ff365428x4m	8	17	as	as	ADP
ff365428x4m	8	18	possible	possible	ADJ
ff365428x4m	8	19	further	further	ADJ
ff365428x4m	8	20	directions	direction	NOUN
ff365428x4m	8	21	including	include	VERB
ff365428x4m	8	22	ratios	ratio	NOUN
ff365428x4m	8	23	containing	contain	VERB
ff365428x4m	8	24	exotic	exotic	ADJ
ff365428x4m	8	25	cluster	cluster	NOUN
ff365428x4m	8	26	variables	variable	NOUN
ff365428x4m	8	27	.	.	PUNCT
ff365428x4m	9	1	furthermore	furthermore	ADV
ff365428x4m	9	2	,	,	PUNCT
ff365428x4m	9	3	we	we	PRON
ff365428x4m	9	4	present	present	VERB
ff365428x4m	9	5	a	a	DET
ff365428x4m	9	6	majorizing	majorize	VERB
ff365428x4m	9	7	monotonicity	monotonicity	NOUN
ff365428x4m	9	8	of	of	ADP
ff365428x4m	9	9	symmetrized	symmetrized	ADJ
ff365428x4m	9	10	fischer	fischer	NOUN
ff365428x4m	9	11	's	's	PART
ff365428x4m	9	12	products	product	NOUN
ff365428x4m	9	13	which	which	PRON
ff365428x4m	9	14	are	be	AUX
ff365428x4m	9	15	a	a	DET
ff365428x4m	9	16	natural	natural	ADJ
ff365428x4m	9	17	generalization	generalization	NOUN
ff365428x4m	9	18	of	of	ADP
ff365428x4m	9	19	hadamard	hadamard	ADJ
ff365428x4m	9	20	-	-	PUNCT
ff365428x4m	9	21	fischer	fischer	NOUN
ff365428x4m	9	22	inequalities	inequality	NOUN
ff365428x4m	9	23	.	.	PUNCT
ff365428x4m	10	1	majorizing	majorize	VERB
ff365428x4m	10	2	monotonicity	monotonicity	NOUN
ff365428x4m	10	3	of	of	ADP
ff365428x4m	10	4	symmetrized	symmetrized	ADJ
ff365428x4m	10	5	fischer	fischer	NOUN
ff365428x4m	10	6	's	's	PART
ff365428x4m	10	7	products	product	NOUN
ff365428x4m	10	8	were	be	AUX
ff365428x4m	10	9	already	already	ADV
ff365428x4m	10	10	known	know	VERB
ff365428x4m	10	11	for	for	ADP
ff365428x4m	10	12	hermitian	hermitian	ADJ
ff365428x4m	10	13	positive	positive	ADJ
ff365428x4m	10	14	semi	semi	ADJ
ff365428x4m	10	15	-	-	ADJ
ff365428x4m	10	16	definite	definite	ADJ
ff365428x4m	10	17	matrices	matrix	NOUN
ff365428x4m	10	18	which	which	PRON
ff365428x4m	10	19	brings	bring	VERB
ff365428x4m	10	20	additional	additional	ADJ
ff365428x4m	10	21	motivation	motivation	NOUN
ff365428x4m	10	22	to	to	PART
ff365428x4m	10	23	verify	verify	VERB
ff365428x4m	10	24	if	if	SCONJ
ff365428x4m	10	25	they	they	PRON
ff365428x4m	10	26	hold	hold	VERB
ff365428x4m	10	27	for	for	ADP
ff365428x4m	10	28	totally	totally	ADV
ff365428x4m	10	29	positive	positive	ADJ
ff365428x4m	10	30	matrices	matrix	NOUN
ff365428x4m	10	31	as	as	ADV
ff365428x4m	10	32	well	well	ADV
ff365428x4m	10	33	(	(	PUNCT
ff365428x4m	10	34	joint	joint	ADJ
ff365428x4m	10	35	work	work	NOUN
ff365428x4m	10	36	with	with	ADP
ff365428x4m	10	37	m.	m.	PROPN
ff365428x4m	10	38	skandera	skandera	PROPN
ff365428x4m	10	39	)	)	PUNCT
ff365428x4m	10	40	.	.	PUNCT
ff365428x4m	11	1	the	the	DET
ff365428x4m	11	2	main	main	ADJ
ff365428x4m	11	3	tools	tool	NOUN
ff365428x4m	11	4	we	we	PRON
ff365428x4m	11	5	employed	employ	VERB
ff365428x4m	11	6	are	be	AUX
ff365428x4m	11	7	network	network	NOUN
ff365428x4m	11	8	parametrization	parametrization	NOUN
ff365428x4m	11	9	and	and	CCONJ
ff365428x4m	11	10	temperley	temperley	PROPN
ff365428x4m	11	11	-	-	PUNCT
ff365428x4m	11	12	lieb	lieb	PROPN
ff365428x4m	11	13	and	and	CCONJ
ff365428x4m	11	14	monomial	monomial	ADJ
ff365428x4m	11	15	trace	trace	NOUN
ff365428x4m	11	16	immanants	immanant	NOUN
ff365428x4m	11	17	.	.	PUNCT