id	sid	tid	token	lemma	pos
ap-10666	1	1	acta	acta	PROPN
ap-10666	1	2	polytechnica	polytechnica	PROPN
ap-10666	1	3	https://doi.org/10.14311/ap.2025.65.0562	https://doi.org/10.14311/ap.2025.65.0562	PROPN
ap-10666	1	4	acta	acta	PROPN
ap-10666	1	5	polytechnica	polytechnica	PROPN
ap-10666	1	6	65(5):562–565	65(5):562–565	PROPN
ap-10666	1	7	,	,	PUNCT
ap-10666	1	8	2025	2025	NUM
ap-10666	1	9	©	©	ADP
ap-10666	1	10	2025	2025	NUM
ap-10666	1	11	the	the	DET
ap-10666	1	12	author(s	author(s	NOUN
ap-10666	1	13	)	)	PUNCT
ap-10666	1	14	.	.	PUNCT
ap-10666	2	1	licensed	license	VERB
ap-10666	2	2	under	under	ADP
ap-10666	2	3	a	a	DET
ap-10666	2	4	cc	cc	NOUN
ap-10666	2	5	-	-	PUNCT
ap-10666	2	6	by	by	ADP
ap-10666	2	7	4.0	4.0	NUM
ap-10666	2	8	licence	licence	NOUN
ap-10666	2	9	published	publish	VERB
ap-10666	2	10	by	by	ADP
ap-10666	2	11	the	the	DET
ap-10666	2	12	czech	czech	PROPN
ap-10666	2	13	technical	technical	PROPN
ap-10666	2	14	university	university	PROPN
ap-10666	2	15	in	in	ADP
ap-10666	2	16	prague	prague	NOUN
ap-10666	2	17	gl3	gl3	PROPN
ap-10666	2	18	algebra	algebra	NOUN
ap-10666	2	19	in	in	ADP
ap-10666	2	20	mixed	mixed	ADJ
ap-10666	2	21	matrix	matrix	NOUN
ap-10666	2	22	representations	representation	NOUN
ap-10666	2	23	alexander	alexander	PROPN
ap-10666	2	24	v.	v.	ADP
ap-10666	2	25	turbiner	turbiner	PROPN
ap-10666	2	26	universidad	universidad	PROPN
ap-10666	2	27	nacional	nacional	PROPN
ap-10666	2	28	autónoma	autónoma	PROPN
ap-10666	2	29	de	de	PROPN
ap-10666	2	30	méxico	méxico	PROPN
ap-10666	2	31	,	,	PUNCT
ap-10666	2	32	instituto	instituto	PROPN
ap-10666	2	33	de	de	PROPN
ap-10666	2	34	ciencias	ciencias	PROPN
ap-10666	2	35	nucleares	nucleares	PROPN
ap-10666	2	36	,	,	PUNCT
ap-10666	2	37	apartado	apartado	X
ap-10666	2	38	postal	postal	ADJ
ap-10666	2	39	70	70	NUM
ap-10666	2	40	-	-	SYM
ap-10666	2	41	543	543	NUM
ap-10666	2	42	,	,	PUNCT
ap-10666	2	43	04510	04510	NUM
ap-10666	2	44	méxico	méxico	PROPN
ap-10666	2	45	,	,	PUNCT
ap-10666	2	46	mexico	mexico	PROPN
ap-10666	2	47	correspondence	correspondence	NOUN
ap-10666	2	48	:	:	PUNCT
ap-10666	2	49	turbiner@nucleares.unam.mx	turbiner@nucleares.unam.mx	DET
ap-10666	2	50	abstract	abstract	ADJ
ap-10666	2	51	.	.	PUNCT
ap-10666	3	1	it	it	PRON
ap-10666	3	2	is	be	AUX
ap-10666	3	3	demonstrated	demonstrate	VERB
ap-10666	3	4	that	that	SCONJ
ap-10666	3	5	the	the	DET
ap-10666	3	6	so	so	ADV
ap-10666	3	7	-	-	PUNCT
ap-10666	3	8	called	call	VERB
ap-10666	3	9	mixed	mixed	ADJ
ap-10666	3	10	realization	realization	NOUN
ap-10666	3	11	of	of	ADP
ap-10666	3	12	the	the	DET
ap-10666	3	13	gl3	gl3	PROPN
ap-10666	3	14	algebra	algebra	NOUN
ap-10666	3	15	generators	generator	NOUN
ap-10666	3	16	in	in	ADP
ap-10666	3	17	terms	term	NOUN
ap-10666	3	18	of	of	ADP
ap-10666	3	19	matrix	matrix	NOUN
ap-10666	3	20	differential	differential	NOUN
ap-10666	3	21	operators	operator	NOUN
ap-10666	3	22	in	in	ADP
ap-10666	3	23	two	two	NUM
ap-10666	3	24	variables	variable	NOUN
ap-10666	3	25	,	,	PUNCT
ap-10666	3	26	as	as	SCONJ
ap-10666	3	27	presented	present	VERB
ap-10666	3	28	by	by	ADP
ap-10666	3	29	smirnov	smirnov	NOUN
ap-10666	3	30	-	-	NOUN
ap-10666	3	31	turbiner	turbiner	NOUN
ap-10666	3	32	(	(	PUNCT
ap-10666	3	33	2013	2013	NUM
ap-10666	3	34	)	)	PUNCT
ap-10666	3	35	,	,	PUNCT
ap-10666	3	36	can	can	AUX
ap-10666	3	37	be	be	AUX
ap-10666	3	38	“	"	PUNCT
ap-10666	3	39	lifted	lift	VERB
ap-10666	3	40	”	"	PUNCT
ap-10666	3	41	into	into	ADP
ap-10666	3	42	the	the	DET
ap-10666	3	43	action	action	NOUN
ap-10666	3	44	in	in	ADP
ap-10666	3	45	the	the	DET
ap-10666	3	46	fock	fock	ADJ
ap-10666	3	47	space	space	NOUN
ap-10666	3	48	associated	associate	VERB
ap-10666	3	49	with	with	ADP
ap-10666	3	50	the	the	DET
ap-10666	3	51	five	five	NUM
ap-10666	3	52	-	-	PUNCT
ap-10666	3	53	dimensional	dimensional	ADJ
ap-10666	3	54	heisenberg	heisenberg	PROPN
ap-10666	3	55	algebra	algebra	NOUN
ap-10666	3	56	h5	h5	PROPN
ap-10666	3	57	.	.	PUNCT
ap-10666	4	1	a	a	DET
ap-10666	4	2	realization	realization	NOUN
ap-10666	4	3	of	of	ADP
ap-10666	4	4	the	the	DET
ap-10666	4	5	gl3	gl3	PROPN
ap-10666	4	6	generators	generator	NOUN
ap-10666	4	7	in	in	ADP
ap-10666	4	8	terms	term	NOUN
ap-10666	4	9	of	of	ADP
ap-10666	4	10	matrix	matrix	NOUN
ap-10666	4	11	finite	finite	NOUN
ap-10666	4	12	-	-	PUNCT
ap-10666	4	13	difference	difference	NOUN
ap-10666	4	14	(	(	PUNCT
ap-10666	4	15	translation	translation	NOUN
ap-10666	4	16	-	-	PUNCT
ap-10666	4	17	invariant	invariant	ADJ
ap-10666	4	18	)	)	PUNCT
ap-10666	4	19	operators	operator	NOUN
ap-10666	4	20	,	,	PUNCT
ap-10666	4	21	matrix	matrix	NOUN
ap-10666	4	22	discrete	discrete	NOUN
ap-10666	4	23	(	(	PUNCT
ap-10666	4	24	dilatation	dilatation	NOUN
ap-10666	4	25	-	-	PUNCT
ap-10666	4	26	invariant	invariant	ADJ
ap-10666	4	27	)	)	PUNCT
ap-10666	4	28	operators	operator	NOUN
ap-10666	4	29	,	,	PUNCT
ap-10666	4	30	matrix	matrix	NOUN
ap-10666	4	31	complex	complex	ADJ
ap-10666	4	32	operators	operator	NOUN
ap-10666	4	33	in	in	ADP
ap-10666	4	34	(	(	PUNCT
ap-10666	4	35	z	z	NOUN
ap-10666	4	36	,	,	PUNCT
ap-10666	4	37	z̄	z̄	NOUN
ap-10666	4	38	)	)	PUNCT
ap-10666	4	39	,	,	PUNCT
ap-10666	4	40	and	and	CCONJ
ap-10666	4	41	their	their	PRON
ap-10666	4	42	mixtures	mixture	NOUN
ap-10666	4	43	is	be	AUX
ap-10666	4	44	presented	present	VERB
ap-10666	4	45	.	.	PUNCT
ap-10666	5	1	keywords	keyword	NOUN
ap-10666	5	2	:	:	PUNCT
ap-10666	5	3	mixed	mixed	ADJ
ap-10666	5	4	representations	representation	NOUN
ap-10666	5	5	in	in	ADP
ap-10666	5	6	fock	fock	ADJ
ap-10666	5	7	space	space	NOUN
ap-10666	5	8	,	,	PUNCT
ap-10666	5	9	matrix	matrix	NOUN
ap-10666	5	10	differential	differential	NOUN
ap-10666	5	11	operators	operator	NOUN
ap-10666	5	12	,	,	PUNCT
ap-10666	5	13	matrix	matrix	NOUN
ap-10666	5	14	finite	finite	NOUN
ap-10666	5	15	-	-	PUNCT
ap-10666	5	16	difference	difference	NOUN
ap-10666	5	17	(	(	PUNCT
ap-10666	5	18	discrete	discrete	NOUN
ap-10666	5	19	)	)	PUNCT
ap-10666	5	20	operators	operator	NOUN
ap-10666	5	21	,	,	PUNCT
ap-10666	5	22	matrix	matrix	NOUN
ap-10666	5	23	complex	complex	ADJ
ap-10666	5	24	operators	operator	NOUN
ap-10666	5	25	in	in	ADP
ap-10666	5	26	(	(	PUNCT
ap-10666	5	27	z	z	NOUN
ap-10666	5	28	,	,	PUNCT
ap-10666	5	29	z̄	z̄	NOUN
ap-10666	5	30	)	)	PUNCT
ap-10666	5	31	.	.	PUNCT
ap-10666	6	1	to	to	ADP
ap-10666	6	2	the	the	DET
ap-10666	6	3	memory	memory	NOUN
ap-10666	6	4	of	of	ADP
ap-10666	6	5	miloslav	miloslav	NOUN
ap-10666	6	6	havlíček	havlíček	NOUN
ap-10666	6	7	1	1	NUM
ap-10666	6	8	.	.	PUNCT
ap-10666	6	9	introduction	introduction	NOUN
ap-10666	6	10	as	as	ADP
ap-10666	6	11	a	a	DET
ap-10666	6	12	result	result	NOUN
ap-10666	6	13	of	of	ADP
ap-10666	6	14	numerous	numerous	ADJ
ap-10666	6	15	discussions	discussion	NOUN
ap-10666	6	16	with	with	ADP
ap-10666	6	17	miloslav	miloslav	NOUN
ap-10666	6	18	havlíček	havlíček	NOUN
ap-10666	6	19	(	(	PUNCT
ap-10666	6	20	havlicek)1	havlicek)1	NOUN
ap-10666	6	21	,	,	PUNCT
ap-10666	6	22	which	which	PRON
ap-10666	6	23	ran	run	VERB
ap-10666	6	24	over	over	ADP
ap-10666	6	25	many	many	ADJ
ap-10666	6	26	years	year	NOUN
ap-10666	6	27	about	about	ADP
ap-10666	6	28	mixing	mix	VERB
ap-10666	6	29	the	the	DET
ap-10666	6	30	representations	representation	NOUN
ap-10666	6	31	of	of	ADP
ap-10666	6	32	lie	lie	NOUN
ap-10666	6	33	algebras	algebra	NOUN
ap-10666	6	34	[	[	X
ap-10666	6	35	1	1	NUM
ap-10666	6	36	]	]	PUNCT
ap-10666	6	37	,	,	PUNCT
ap-10666	6	38	as	as	SCONJ
ap-10666	6	39	discussed	discuss	VERB
ap-10666	6	40	between	between	ADP
ap-10666	6	41	yu	yu	PROPN
ap-10666	6	42	.	.	PUNCT
ap-10666	6	43	f.	f.	PROPN
ap-10666	6	44	smirnov	smirnov	PROPN
ap-10666	6	45	(	(	PUNCT
ap-10666	6	46	1935–2008	1935–2008	NOUN
ap-10666	6	47	)	)	PUNCT
ap-10666	6	48	and	and	CCONJ
ap-10666	6	49	the	the	DET
ap-10666	6	50	present	present	ADJ
ap-10666	6	51	author	author	NOUN
ap-10666	6	52	,	,	PUNCT
ap-10666	6	53	in	in	ADP
ap-10666	6	54	the	the	DET
ap-10666	6	55	article	article	NOUN
ap-10666	6	56	[	[	X
ap-10666	6	57	2	2	X
ap-10666	6	58	]	]	PUNCT
ap-10666	6	59	there	there	PRON
ap-10666	6	60	were	be	VERB
ap-10666	6	61	constructed	construct	VERB
ap-10666	6	62	the	the	DET
ap-10666	6	63	so	so	ADV
ap-10666	6	64	-	-	PUNCT
ap-10666	6	65	called	call	VERB
ap-10666	6	66	mixed	mixed	ADJ
ap-10666	6	67	representations	representation	NOUN
ap-10666	6	68	of	of	ADP
ap-10666	6	69	the	the	DET
ap-10666	6	70	gln+1	gln+1	NOUN
ap-10666	6	71	algebra	algebra	NOUN
ap-10666	6	72	realized	realize	VERB
ap-10666	6	73	by	by	ADP
ap-10666	6	74	differential	differential	ADJ
ap-10666	6	75	operators	operator	NOUN
ap-10666	6	76	of	of	ADP
ap-10666	6	77	the	the	DET
ap-10666	6	78	first	first	ADJ
ap-10666	6	79	order	order	NOUN
ap-10666	6	80	in	in	ADP
ap-10666	6	81	n	n	DET
ap-10666	6	82	variables	variable	NOUN
ap-10666	6	83	with	with	ADP
ap-10666	6	84	matrix	matrix	NOUN
ap-10666	6	85	coefficients2	coefficients2	NOUN
ap-10666	6	86	.	.	PUNCT
ap-10666	7	1	in	in	ADP
ap-10666	7	2	the	the	DET
ap-10666	7	3	particular	particular	ADJ
ap-10666	7	4	case	case	NOUN
ap-10666	7	5	of	of	ADP
ap-10666	7	6	the	the	DET
ap-10666	7	7	gl3	gl3	PROPN
ap-10666	7	8	algebra	algebra	NOUN
ap-10666	7	9	,	,	PUNCT
ap-10666	7	10	these	these	DET
ap-10666	7	11	generators	generator	NOUN
ap-10666	7	12	take	take	VERB
ap-10666	7	13	the	the	DET
ap-10666	7	14	form	form	NOUN
ap-10666	7	15	:	:	PUNCT
ap-10666	7	16	e11	e11	X
ap-10666	7	17	=	=	SYM
ap-10666	8	1	x1∂1	x1∂1	PROPN
ap-10666	8	2	+	+	PUNCT
ap-10666	8	3	m11	m11	NOUN
ap-10666	8	4	,	,	PUNCT
ap-10666	8	5	e22	e22	NOUN
ap-10666	8	6	=	=	SYM
ap-10666	9	1	x2∂2	x2∂2	PROPN
ap-10666	10	1	+	+	PROPN
ap-10666	10	2	m22	m22	PROPN
ap-10666	10	3	,	,	PUNCT
ap-10666	10	4	e12	e12	NOUN
ap-10666	10	5	=	=	SYM
ap-10666	10	6	x1∂2	x1∂2	PROPN
ap-10666	10	7	+	+	NUM
ap-10666	10	8	m12	m12	PROPN
ap-10666	10	9	,	,	PUNCT
ap-10666	10	10	e21	e21	PROPN
ap-10666	11	1	=	=	SYM
ap-10666	11	2	x2∂1	x2∂1	PROPN
ap-10666	11	3	+	+	NUM
ap-10666	11	4	m21	m21	PROPN
ap-10666	11	5	,	,	PUNCT
ap-10666	11	6	e0	e0	PROPN
ap-10666	11	7	=	=	PUNCT
ap-10666	12	1	k	k	PROPN
ap-10666	12	2	−	−	PROPN
ap-10666	13	1	x1∂1	x1∂1	PROPN
ap-10666	13	2	−	−	PROPN
ap-10666	14	1	x2∂2	x2∂2	PROPN
ap-10666	14	2	,	,	PUNCT
ap-10666	14	3	t	t	PROPN
ap-10666	14	4	−	−	PROPN
ap-10666	14	5	1	1	NUM
ap-10666	14	6	=	=	SYM
ap-10666	14	7	∂1	∂1	ADJ
ap-10666	14	8	,	,	PUNCT
ap-10666	14	9	t	t	NOUN
ap-10666	14	10	−	−	PROPN
ap-10666	14	11	2	2	NUM
ap-10666	14	12	=	=	SYM
ap-10666	14	13	∂2	∂2	PROPN
ap-10666	14	14	,	,	PUNCT
ap-10666	14	15	t	t	PROPN
ap-10666	14	16	+	+	NOUN
ap-10666	14	17	1	1	NUM
ap-10666	14	18	=	=	SYM
ap-10666	14	19	x1(k	x1(k	PROPN
ap-10666	15	1	−	−	NOUN
ap-10666	15	2	x1∂1	x1∂1	PROPN
ap-10666	15	3	−	−	PROPN
ap-10666	16	1	x2∂2	x2∂2	PROPN
ap-10666	16	2	)	)	PUNCT
ap-10666	16	3	−	−	PROPN
ap-10666	17	1	x1m11	x1m11	PUNCT
ap-10666	17	2	−	−	PROPN
ap-10666	17	3	x2m12	x2m12	PROPN
ap-10666	17	4	,	,	PUNCT
ap-10666	17	5	t	t	PROPN
ap-10666	17	6	+	+	CCONJ
ap-10666	17	7	2	2	NUM
ap-10666	17	8	=	=	SYM
ap-10666	17	9	x2(k	x2(k	PROPN
ap-10666	18	1	−	−	PROPN
ap-10666	18	2	x1∂1	x1∂1	PROPN
ap-10666	19	1	−	−	PROPN
ap-10666	19	2	x2∂2	x2∂2	PROPN
ap-10666	19	3	)	)	PUNCT
ap-10666	19	4	−	−	PROPN
ap-10666	19	5	x1m21	x1m21	X
ap-10666	20	1	−	−	PROPN
ap-10666	20	2	x2m22	x2m22	PROPN
ap-10666	20	3	,	,	PUNCT
ap-10666	20	4	(	(	PUNCT
ap-10666	20	5	1	1	X
ap-10666	20	6	)	)	PUNCT
ap-10666	20	7	see	see	VERB
ap-10666	20	8	[	[	X
ap-10666	20	9	2	2	NUM
ap-10666	20	10	]	]	PUNCT
ap-10666	20	11	,	,	PUNCT
ap-10666	20	12	section	section	NOUN
ap-10666	20	13	3	3	NUM
ap-10666	20	14	,	,	PUNCT
ap-10666	20	15	where	where	SCONJ
ap-10666	20	16	m11	m11	NOUN
ap-10666	20	17	,	,	PUNCT
ap-10666	20	18	m12	m12	PROPN
ap-10666	20	19	,	,	PUNCT
ap-10666	20	20	m21	m21	PROPN
ap-10666	20	21	,	,	PUNCT
ap-10666	20	22	m22	m22	PROPN
ap-10666	20	23	are	be	AUX
ap-10666	20	24	the	the	DET
ap-10666	20	25	generators	generator	NOUN
ap-10666	20	26	of	of	ADP
ap-10666	20	27	the	the	DET
ap-10666	20	28	gl2	gl2	PROPN
ap-10666	20	29	algebra	algebra	PROPN
ap-10666	20	30	realized	realize	VERB
ap-10666	20	31	by	by	ADP
ap-10666	20	32	n×n	n×n	PROPN
ap-10666	20	33	matrices	matrix	NOUN
ap-10666	20	34	,	,	PUNCT
ap-10666	20	35	here	here	ADV
ap-10666	20	36	,	,	PUNCT
ap-10666	20	37	the	the	DET
ap-10666	20	38	notations	notation	NOUN
ap-10666	20	39	∂1	∂1	X
ap-10666	20	40	≡	≡	PROPN
ap-10666	20	41	∂	∂	PRON
ap-10666	21	1	∂x1	∂x1	NOUN
ap-10666	21	2	,	,	PUNCT
ap-10666	21	3	∂2	∂2	PROPN
ap-10666	21	4	≡	≡	PROPN
ap-10666	21	5	∂	∂	PRON
ap-10666	21	6	∂x2	∂x2	NOUN
ap-10666	21	7	are	be	AUX
ap-10666	21	8	used	use	VERB
ap-10666	21	9	.	.	PUNCT
ap-10666	22	1	for	for	ADP
ap-10666	22	2	a	a	DET
ap-10666	22	3	non	non	ADJ
ap-10666	22	4	-	-	ADJ
ap-10666	22	5	negative	negative	ADJ
ap-10666	22	6	integer	integer	NOUN
ap-10666	22	7	k	k	NOUN
ap-10666	22	8	,	,	PUNCT
ap-10666	22	9	this	this	DET
ap-10666	22	10	representation	representation	NOUN
ap-10666	22	11	is	be	AUX
ap-10666	22	12	finitedimensional	finitedimensional	ADJ
ap-10666	22	13	with	with	ADP
ap-10666	22	14	marks	mark	NOUN
ap-10666	22	15	/	/	SYM
ap-10666	22	16	spins	spin	NOUN
ap-10666	23	1	[	[	X
ap-10666	23	2	k	k	X
ap-10666	23	3	,	,	PUNCT
ap-10666	23	4	n	n	CCONJ
ap-10666	23	5	]	]	PUNCT
ap-10666	23	6	,	,	PUNCT
ap-10666	23	7	it	it	PRON
ap-10666	23	8	is	be	AUX
ap-10666	23	9	characterized	characterize	VERB
ap-10666	23	10	by	by	ADP
ap-10666	23	11	the	the	DET
ap-10666	23	12	young	young	ADJ
ap-10666	23	13	tableau	tableau	NOUN
ap-10666	23	14	with	with	ADP
ap-10666	23	15	two	two	NUM
ap-10666	23	16	rows	row	NOUN
ap-10666	23	17	of	of	ADP
ap-10666	23	18	length	length	NOUN
ap-10666	23	19	k	k	PROPN
ap-10666	23	20	and	and	CCONJ
ap-10666	23	21	n	n	CCONJ
ap-10666	23	22	,	,	PUNCT
ap-10666	23	23	correspondingly	correspondingly	ADV
ap-10666	23	24	.	.	PUNCT
ap-10666	24	1	one	one	PRON
ap-10666	24	2	can	can	AUX
ap-10666	24	3	check	check	VERB
ap-10666	24	4	explicitly	explicitly	ADV
ap-10666	24	5	that	that	SCONJ
ap-10666	24	6	t	t	PROPN
ap-10666	24	7	−	−	PROPN
ap-10666	25	1	i	i	PRON
ap-10666	25	2	,	,	PUNCT
ap-10666	25	3	eij	eij	PROPN
ap-10666	25	4	,	,	PUNCT
ap-10666	25	5	e0	e0	PROPN
ap-10666	25	6	,	,	PUNCT
ap-10666	25	7	t	t	PROPN
ap-10666	26	1	+	+	CCONJ
ap-10666	26	2	i	i	PRON
ap-10666	26	3	span	span	VERB
ap-10666	26	4	the	the	DET
ap-10666	26	5	algebra	algebra	NOUN
ap-10666	26	6	gl3	gl3	PRON
ap-10666	26	7	.	.	PUNCT
ap-10666	27	1	in	in	ADP
ap-10666	27	2	particular	particular	ADJ
ap-10666	27	3	:	:	PUNCT
ap-10666	27	4	[	[	X
ap-10666	27	5	e	e	X
ap-10666	27	6	,	,	PUNCT
ap-10666	27	7	t	t	PROPN
ap-10666	28	1	+	+	NOUN
ap-10666	28	2	]	]	X
ap-10666	28	3	=	=	SYM
ap-10666	28	4	t	t	PROPN
ap-10666	28	5	+	+	PROPN
ap-10666	28	6	,	,	PUNCT
ap-10666	28	7	1	1	NUM
ap-10666	28	8	in	in	ADP
ap-10666	28	9	many	many	ADJ
ap-10666	28	10	instances	instance	NOUN
ap-10666	28	11	in	in	ADP
ap-10666	28	12	the	the	DET
ap-10666	28	13	scientific	scientific	ADJ
ap-10666	28	14	literature	literature	NOUN
ap-10666	28	15	the	the	DET
ap-10666	28	16	family	family	NOUN
ap-10666	28	17	name	name	NOUN
ap-10666	28	18	of	of	ADP
ap-10666	28	19	miloslav	miloslav	NOUN
ap-10666	28	20	is	be	AUX
ap-10666	28	21	written	write	VERB
ap-10666	28	22	as	as	ADP
ap-10666	28	23	havlicek	havlicek	NOUN
ap-10666	28	24	,	,	PUNCT
ap-10666	28	25	to	to	PART
ap-10666	28	26	avoid	avoid	VERB
ap-10666	28	27	confusions	confusion	NOUN
ap-10666	28	28	since	since	SCONJ
ap-10666	28	29	now	now	ADV
ap-10666	28	30	on	on	ADV
ap-10666	28	31	we	we	PRON
ap-10666	28	32	will	will	AUX
ap-10666	28	33	use	use	VERB
ap-10666	28	34	this	this	DET
ap-10666	28	35	name	name	NOUN
ap-10666	28	36	.	.	PUNCT
ap-10666	29	1	2for	2for	DET
ap-10666	29	2	convenience	convenience	NOUN
ap-10666	29	3	,	,	PUNCT
ap-10666	29	4	we	we	PRON
ap-10666	29	5	will	will	AUX
ap-10666	29	6	always	always	ADV
ap-10666	29	7	assume	assume	VERB
ap-10666	29	8	the	the	DET
ap-10666	29	9	canonical	canonical	ADJ
ap-10666	29	10	commutation	commutation	NOUN
ap-10666	29	11	relations	relation	NOUN
ap-10666	29	12	:	:	PUNCT
ap-10666	30	1	[	[	X
ap-10666	30	2	ẽij	ẽij	X
ap-10666	30	3	,	,	PUNCT
ap-10666	30	4	ẽkl	ẽkl	PROPN
ap-10666	30	5	]	]	X
ap-10666	30	6	=	=	PUNCT
ap-10666	30	7	δjkẽil	δjkẽil	PROPN
ap-10666	30	8	−	−	PROPN
ap-10666	31	1	δilẽkj	δilẽkj	PROPN
ap-10666	31	2	,	,	PUNCT
ap-10666	31	3	for	for	ADP
ap-10666	31	4	the	the	DET
ap-10666	31	5	gln+1	gln+1	NOUN
ap-10666	31	6	generators	generator	NOUN
ap-10666	31	7	if	if	SCONJ
ap-10666	31	8	they	they	PRON
ap-10666	31	9	are	be	AUX
ap-10666	31	10	not	not	PART
ap-10666	31	11	specified	specify	VERB
ap-10666	31	12	otherwise	otherwise	ADV
ap-10666	31	13	.	.	PUNCT
ap-10666	32	1	symbolically	symbolically	ADV
ap-10666	32	2	,	,	PUNCT
ap-10666	32	3	while	while	SCONJ
ap-10666	32	4	:	:	PUNCT
ap-10666	32	5	[	[	X
ap-10666	32	6	t	t	X
ap-10666	32	7	+	+	CCONJ
ap-10666	32	8	i	i	PROPN
ap-10666	32	9	,	,	PUNCT
ap-10666	32	10	t	t	PROPN
ap-10666	32	11	−	−	PROPN
ap-10666	32	12	j	j	PROPN
ap-10666	32	13	]	]	X
ap-10666	32	14	=	=	SYM
ap-10666	32	15	eii	eii	PROPN
ap-10666	32	16	−	−	PROPN
ap-10666	32	17	δije0	δije0	PROPN
ap-10666	32	18	.	.	PUNCT
ap-10666	33	1	the	the	DET
ap-10666	33	2	generator	generator	NOUN
ap-10666	33	3	e0	e0	PROPN
ap-10666	33	4	is	be	AUX
ap-10666	33	5	called	call	VERB
ap-10666	33	6	the	the	DET
ap-10666	33	7	euler	euler	PROPN
ap-10666	33	8	-	-	PUNCT
ap-10666	33	9	cartan	cartan	PROPN
ap-10666	33	10	generator	generator	NOUN
ap-10666	33	11	or	or	CCONJ
ap-10666	33	12	number	number	NOUN
ap-10666	33	13	operator	operator	NOUN
ap-10666	33	14	.	.	PUNCT
ap-10666	34	1	it	it	PRON
ap-10666	34	2	plays	play	VERB
ap-10666	34	3	the	the	DET
ap-10666	34	4	role	role	NOUN
ap-10666	34	5	of	of	ADP
ap-10666	34	6	a	a	DET
ap-10666	34	7	constant	constant	ADJ
ap-10666	34	8	having	have	VERB
ap-10666	34	9	the	the	DET
ap-10666	34	10	grading	grade	VERB
ap-10666	34	11	zero	zero	NUM
ap-10666	34	12	in	in	ADP
ap-10666	34	13	whatever	whatever	DET
ap-10666	34	14	sense	sense	NOUN
ap-10666	34	15	.	.	PUNCT
ap-10666	35	1	the	the	DET
ap-10666	35	2	representation	representation	NOUN
ap-10666	35	3	(	(	PUNCT
ap-10666	35	4	1	1	X
ap-10666	35	5	)	)	PUNCT
ap-10666	35	6	acts	act	NOUN
ap-10666	35	7	in	in	ADP
ap-10666	35	8	the	the	DET
ap-10666	35	9	space	space	NOUN
ap-10666	35	10	of	of	ADP
ap-10666	35	11	n	n	CCONJ
ap-10666	35	12	-	-	PUNCT
ap-10666	35	13	tuples	tuple	NOUN
ap-10666	35	14	,	,	PUNCT
ap-10666	35	15	with	with	ADP
ap-10666	35	16	columns	column	NOUN
ap-10666	35	17	of	of	ADP
ap-10666	35	18	a	a	DET
ap-10666	35	19	size	size	NOUN
ap-10666	35	20	n.	n.	NOUN
ap-10666	35	21	the	the	DET
ap-10666	35	22	casimir	casimir	PROPN
ap-10666	35	23	operators	operator	NOUN
ap-10666	35	24	of	of	ADP
ap-10666	35	25	gl3	gl3	PROPN
ap-10666	35	26	algebra	algebra	NOUN
ap-10666	35	27	in	in	ADP
ap-10666	35	28	this	this	DET
ap-10666	35	29	realization	realization	NOUN
ap-10666	35	30	are	be	AUX
ap-10666	35	31	given	give	VERB
ap-10666	35	32	by	by	ADP
ap-10666	35	33	:	:	PUNCT
ap-10666	35	34	c1	c1	NOUN
ap-10666	35	35	=	=	PUNCT
ap-10666	35	36	e11	e11	PROPN
ap-10666	35	37	+	+	CCONJ
ap-10666	35	38	e22	e22	X
ap-10666	35	39	+	+	CCONJ
ap-10666	35	40	e0	e0	PROPN
ap-10666	35	41	=	=	PUNCT
ap-10666	36	1	k	k	PROPN
ap-10666	37	1	+	+	PUNCT
ap-10666	37	2	m11	m11	PROPN
ap-10666	37	3	+	+	CCONJ
ap-10666	37	4	m22	m22	PROPN
ap-10666	37	5	≡	≡	PROPN
ap-10666	37	6	k	k	PROPN
ap-10666	37	7	+	+	PROPN
ap-10666	37	8	c1(m	c1(m	PROPN
ap-10666	37	9	)	)	PUNCT
ap-10666	37	10	,	,	PUNCT
ap-10666	37	11	c2	c2	PROPN
ap-10666	37	12	=	=	PUNCT
ap-10666	37	13	e12e21	e12e21	VERB
ap-10666	37	14	+	+	CCONJ
ap-10666	37	15	e21e12	e21e12	NOUN
ap-10666	37	16	+	+	X
ap-10666	37	17	t	t	NOUN
ap-10666	37	18	+	+	CCONJ
ap-10666	37	19	1	1	NUM
ap-10666	37	20	t	t	NOUN
ap-10666	37	21	−	−	NOUN
ap-10666	37	22	1	1	NUM
ap-10666	38	1	+	+	NUM
ap-10666	38	2	t	t	NOUN
ap-10666	38	3	−	−	NUM
ap-10666	38	4	1	1	NUM
ap-10666	38	5	t	t	NOUN
ap-10666	38	6	+	+	CCONJ
ap-10666	38	7	1	1	NUM
ap-10666	38	8	+	+	NUM
ap-10666	38	9	t	t	NOUN
ap-10666	38	10	+	+	CCONJ
ap-10666	38	11	2	2	NUM
ap-10666	38	12	t	t	NOUN
ap-10666	38	13	−	−	NOUN
ap-10666	38	14	2	2	NUM
ap-10666	39	1	+	+	NUM
ap-10666	39	2	t	t	NOUN
ap-10666	39	3	−	−	NUM
ap-10666	39	4	2	2	NUM
ap-10666	39	5	t	t	NOUN
ap-10666	39	6	+	+	CCONJ
ap-10666	39	7	2	2	NUM
ap-10666	39	8	+	+	CCONJ
ap-10666	39	9	e2	e2	PROPN
ap-10666	39	10	11	11	NUM
ap-10666	39	11	+	+	CCONJ
ap-10666	39	12	e2	e2	PROPN
ap-10666	39	13	22	22	NUM
ap-10666	40	1	+	+	CCONJ
ap-10666	40	2	e2	e2	PROPN
ap-10666	40	3	0	0	PUNCT
ap-10666	41	1	=	=	PUNCT
ap-10666	42	1	k(k	k(k	NOUN
ap-10666	42	2	+	+	CCONJ
ap-10666	42	3	2	2	X
ap-10666	42	4	)	)	PUNCT
ap-10666	42	5	+	+	NUM
ap-10666	42	6	m2	m2	PROPN
ap-10666	42	7	11	11	NUM
ap-10666	42	8	+	+	NUM
ap-10666	42	9	m2	m2	PROPN
ap-10666	42	10	22	22	NUM
ap-10666	42	11	+	+	NUM
ap-10666	42	12	m12m21	m12m21	PROPN
ap-10666	42	13	+	+	CCONJ
ap-10666	42	14	m21m12	m21m12	PROPN
ap-10666	42	15	−	−	NOUN
ap-10666	42	16	m11	m11	NOUN
ap-10666	42	17	−	−	PROPN
ap-10666	42	18	m22	m22	PROPN
ap-10666	42	19	≡	≡	PROPN
ap-10666	42	20	k(k	k(k	PROPN
ap-10666	43	1	+	+	PROPN
ap-10666	43	2	2	2	X
ap-10666	43	3	)	)	PUNCT
ap-10666	43	4	+	+	NUM
ap-10666	43	5	c2(m	c2(m	SYM
ap-10666	43	6	)	)	PUNCT
ap-10666	43	7	−	−	PROPN
ap-10666	44	1	c1(m	c1(m	NUM
ap-10666	44	2	)	)	PUNCT
ap-10666	44	3	,	,	PUNCT
ap-10666	44	4	and	and	CCONJ
ap-10666	44	5	,	,	PUNCT
ap-10666	44	6	finally	finally	ADV
ap-10666	44	7	:	:	PUNCT
ap-10666	45	1	c3	c3	PROPN
ap-10666	45	2	=	=	SYM
ap-10666	45	3	−1	−1	NOUN
ap-10666	45	4	2c3	2c3	NUM
ap-10666	45	5	1	1	NUM
ap-10666	45	6	+	+	CCONJ
ap-10666	45	7	3	3	NUM
ap-10666	45	8	2c1c2	2c1c2	NUM
ap-10666	45	9	+	+	CCONJ
ap-10666	45	10	3c2	3c2	NUM
ap-10666	45	11	−	−	NUM
ap-10666	45	12	2c2	2c2	NUM
ap-10666	45	13	1	1	NUM
ap-10666	45	14	−	−	NOUN
ap-10666	45	15	2c1	2c1	NUM
ap-10666	45	16	,	,	PUNCT
ap-10666	45	17	where	where	SCONJ
ap-10666	45	18	c1(m	c1(m	NOUN
ap-10666	45	19	)	)	PUNCT
ap-10666	45	20	,	,	PUNCT
ap-10666	45	21	c2(m	c2(m	NUM
ap-10666	45	22	)	)	PUNCT
ap-10666	45	23	are	be	AUX
ap-10666	45	24	the	the	DET
ap-10666	45	25	casimir	casimir	NOUN
ap-10666	45	26	operators	operator	NOUN
ap-10666	45	27	of	of	ADP
ap-10666	45	28	the	the	DET
ap-10666	45	29	gl2	gl2	PROPN
ap-10666	45	30	algebra	algebra	PROPN
ap-10666	45	31	.	.	PUNCT
ap-10666	46	1	in	in	ADP
ap-10666	46	2	this	this	DET
ap-10666	46	3	realization	realization	NOUN
ap-10666	46	4	(	(	PUNCT
ap-10666	46	5	1	1	NUM
ap-10666	46	6	)	)	PUNCT
ap-10666	46	7	,	,	PUNCT
ap-10666	46	8	the	the	DET
ap-10666	46	9	casimir	casimir	NOUN
ap-10666	46	10	operator	operator	NOUN
ap-10666	46	11	c3	c3	PROPN
ap-10666	46	12	is	be	AUX
ap-10666	46	13	algebraically	algebraically	ADV
ap-10666	46	14	dependent	dependent	ADJ
ap-10666	46	15	on	on	ADP
ap-10666	46	16	c1	c1	PROPN
ap-10666	46	17	and	and	CCONJ
ap-10666	46	18	c2	c2	PROPN
ap-10666	46	19	.	.	PUNCT
ap-10666	47	1	in	in	ADP
ap-10666	47	2	fact	fact	NOUN
ap-10666	47	3	,	,	PUNCT
ap-10666	47	4	c1	c1	PROPN
ap-10666	47	5	and	and	CCONJ
ap-10666	47	6	c2	c2	PROPN
ap-10666	47	7	are	be	AUX
ap-10666	47	8	nothing	nothing	PRON
ap-10666	47	9	but	but	SCONJ
ap-10666	47	10	the	the	DET
ap-10666	47	11	casimir	casimir	PROPN
ap-10666	47	12	operators	operators	PROPN
ap-10666	47	13	c1(m	c1(m	PROPN
ap-10666	47	14	)	)	PUNCT
ap-10666	47	15	,	,	PUNCT
ap-10666	47	16	c2(m	c2(m	NUM
ap-10666	47	17	)	)	PUNCT
ap-10666	47	18	of	of	ADP
ap-10666	47	19	the	the	DET
ap-10666	47	20	gl2	gl2	PROPN
ap-10666	47	21	sub	sub	NOUN
ap-10666	47	22	-	-	NOUN
ap-10666	47	23	algebra	algebra	NOUN
ap-10666	47	24	.	.	PUNCT
ap-10666	48	1	therefore	therefore	ADV
ap-10666	48	2	,	,	PUNCT
ap-10666	48	3	the	the	DET
ap-10666	48	4	center	center	NOUN
ap-10666	48	5	of	of	ADP
ap-10666	48	6	the	the	DET
ap-10666	48	7	gl3	gl3	ADJ
ap-10666	48	8	universal	universal	ADJ
ap-10666	48	9	enveloping	enveloping	NOUN
ap-10666	48	10	algebra	algebra	NOUN
ap-10666	48	11	in	in	ADP
ap-10666	48	12	realization	realization	NOUN
ap-10666	48	13	(	(	PUNCT
ap-10666	48	14	1	1	X
ap-10666	48	15	)	)	PUNCT
ap-10666	48	16	is	be	AUX
ap-10666	48	17	generated	generate	VERB
ap-10666	48	18	by	by	ADP
ap-10666	48	19	the	the	DET
ap-10666	48	20	casimir	casimir	PROPN
ap-10666	48	21	operators	operator	NOUN
ap-10666	48	22	of	of	ADP
ap-10666	48	23	the	the	DET
ap-10666	48	24	gl2	gl2	PROPN
ap-10666	48	25	sub	sub	NOUN
ap-10666	48	26	-	-	NOUN
ap-10666	48	27	algebra	algebra	NOUN
ap-10666	48	28	realized	realize	VERB
ap-10666	48	29	by	by	ADP
ap-10666	48	30	mij	mij	NOUN
ap-10666	48	31	.	.	PUNCT
ap-10666	49	1	thus	thus	ADV
ap-10666	49	2	,	,	PUNCT
ap-10666	49	3	it	it	PRON
ap-10666	49	4	seems	seem	VERB
ap-10666	49	5	natural	natural	ADJ
ap-10666	49	6	that	that	SCONJ
ap-10666	49	7	these	these	DET
ap-10666	49	8	reps	rep	NOUN
ap-10666	49	9	should	should	AUX
ap-10666	49	10	be	be	AUX
ap-10666	49	11	irreducible	irreducible	ADJ
ap-10666	49	12	.	.	PUNCT
ap-10666	50	1	in	in	ADP
ap-10666	50	2	this	this	DET
ap-10666	50	3	short	short	ADJ
ap-10666	50	4	note	note	NOUN
ap-10666	50	5	we	we	PRON
ap-10666	50	6	will	will	AUX
ap-10666	50	7	show	show	VERB
ap-10666	50	8	that	that	SCONJ
ap-10666	50	9	the	the	DET
ap-10666	50	10	mixed	mixed	ADJ
ap-10666	50	11	representation	representation	NOUN
ap-10666	50	12	(	(	PUNCT
ap-10666	50	13	1	1	X
ap-10666	50	14	)	)	PUNCT
ap-10666	50	15	can	can	AUX
ap-10666	50	16	be	be	AUX
ap-10666	50	17	converted	convert	VERB
ap-10666	50	18	into	into	ADP
ap-10666	50	19	a	a	DET
ap-10666	50	20	representation	representation	NOUN
ap-10666	50	21	acting	act	VERB
ap-10666	50	22	on	on	ADP
ap-10666	50	23	a	a	DET
ap-10666	50	24	fock	fock	ADJ
ap-10666	50	25	space	space	NOUN
ap-10666	50	26	associated	associate	VERB
ap-10666	50	27	with	with	ADP
ap-10666	50	28	the	the	DET
ap-10666	50	29	heisenberg	heisenberg	PROPN
ap-10666	50	30	algebra	algebra	PROPN
ap-10666	50	31	h5	h5	PROPN
ap-10666	50	32	.	.	PUNCT
ap-10666	51	1	in	in	ADP
ap-10666	51	2	turn	turn	NOUN
ap-10666	51	3	,	,	PUNCT
ap-10666	51	4	the	the	DET
ap-10666	51	5	fock	fock	ADJ
ap-10666	51	6	space	space	NOUN
ap-10666	51	7	can	can	AUX
ap-10666	51	8	be	be	AUX
ap-10666	51	9	realized	realize	VERB
ap-10666	51	10	by	by	ADP
ap-10666	51	11	finite	finite	NOUN
ap-10666	51	12	-	-	NOUN
ap-10666	51	13	difference	difference	NOUN
ap-10666	51	14	(	(	PUNCT
ap-10666	51	15	on	on	ADP
ap-10666	51	16	the	the	DET
ap-10666	51	17	uniform	uniform	PROPN
ap-10666	51	18	lattice	lattice	PROPN
ap-10666	51	19	)	)	PUNCT
ap-10666	51	20	,	,	PUNCT
ap-10666	51	21	discrete	discrete	ADJ
ap-10666	51	22	(	(	PUNCT
ap-10666	51	23	on	on	ADP
ap-10666	51	24	562	562	NUM
ap-10666	51	25	https://doi.org/10.14311/ap.2025.65.0562	https://doi.org/10.14311/ap.2025.65.0562	PROPN
ap-10666	51	26	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
ap-10666	51	27	https://www.cvut.cz/en	https://www.cvut.cz/en	NUM
ap-10666	51	28	vol	vol	NOUN
ap-10666	51	29	.	.	PROPN
ap-10666	52	1	65	65	NUM
ap-10666	52	2	no	no	NOUN
ap-10666	52	3	.	.	PUNCT
ap-10666	53	1	5/2025	5/2025	NUM
ap-10666	53	2	gl3	gl3	NOUN
ap-10666	53	3	algebra	algebra	NOUN
ap-10666	53	4	in	in	ADP
ap-10666	53	5	mixed	mixed	ADJ
ap-10666	53	6	matrix	matrix	NOUN
ap-10666	53	7	representations	representation	VERB
ap-10666	53	8	the	the	DET
ap-10666	53	9	exponential	exponential	ADJ
ap-10666	53	10	lattice	lattice	NOUN
ap-10666	53	11	)	)	PUNCT
ap-10666	53	12	operators	operator	NOUN
ap-10666	53	13	,	,	PUNCT
ap-10666	53	14	and	and	CCONJ
ap-10666	53	15	by	by	ADP
ap-10666	53	16	complex	complex	ADJ
ap-10666	53	17	operators	operator	NOUN
ap-10666	53	18	in	in	ADP
ap-10666	53	19	(	(	PUNCT
ap-10666	53	20	z	z	NOUN
ap-10666	53	21	,	,	PUNCT
ap-10666	53	22	z̄	z̄	NOUN
ap-10666	53	23	)	)	PUNCT
ap-10666	53	24	.	.	PUNCT
ap-10666	54	1	this	this	PRON
ap-10666	54	2	leads	lead	VERB
ap-10666	54	3	to	to	PART
ap-10666	54	4	matrix	matrix	VERB
ap-10666	54	5	finite	finite	NOUN
ap-10666	54	6	-	-	PUNCT
ap-10666	54	7	difference	difference	NOUN
ap-10666	54	8	(	(	PUNCT
ap-10666	54	9	translation	translation	NOUN
ap-10666	54	10	-	-	PUNCT
ap-10666	54	11	invariant	invariant	ADJ
ap-10666	54	12	)	)	PUNCT
ap-10666	54	13	operators	operator	NOUN
ap-10666	54	14	,	,	PUNCT
ap-10666	54	15	to	to	PART
ap-10666	54	16	matrix	matrix	VERB
ap-10666	54	17	discrete	discrete	ADJ
ap-10666	54	18	(	(	PUNCT
ap-10666	54	19	dilatation	dilatation	NOUN
ap-10666	54	20	-	-	PUNCT
ap-10666	54	21	invariant	invariant	ADJ
ap-10666	54	22	)	)	PUNCT
ap-10666	54	23	operators	operator	NOUN
ap-10666	54	24	,	,	PUNCT
ap-10666	54	25	or	or	CCONJ
ap-10666	54	26	to	to	PART
ap-10666	54	27	matrix	matrix	VERB
ap-10666	54	28	complex	complex	ADJ
ap-10666	54	29	operators	operator	NOUN
ap-10666	54	30	in	in	ADP
ap-10666	54	31	(	(	PUNCT
ap-10666	54	32	z	z	NOUN
ap-10666	54	33	,	,	PUNCT
ap-10666	54	34	z̄	z̄	NUM
ap-10666	54	35	)	)	PUNCT
ap-10666	54	36	and	and	CCONJ
ap-10666	54	37	their	their	PRON
ap-10666	54	38	mixtures	mixture	NOUN
ap-10666	54	39	as	as	ADP
ap-10666	54	40	the	the	DET
ap-10666	54	41	generators	generator	NOUN
ap-10666	54	42	of	of	ADP
ap-10666	54	43	the	the	DET
ap-10666	54	44	gl3	gl3	NOUN
ap-10666	54	45	algebra	algebra	NOUN
ap-10666	54	46	.	.	PUNCT
ap-10666	55	1	2	2	X
ap-10666	55	2	.	.	X
ap-10666	55	3	gl3	gl3	PROPN
ap-10666	55	4	mixed	mix	VERB
ap-10666	55	5	representation	representation	NOUN
ap-10666	55	6	in	in	ADP
ap-10666	55	7	a	a	DET
ap-10666	55	8	fock	fock	ADJ
ap-10666	55	9	space	space	NOUN
ap-10666	55	10	let	let	VERB
ap-10666	55	11	us	we	PRON
ap-10666	55	12	take	take	VERB
ap-10666	55	13	the	the	DET
ap-10666	55	14	5	5	NUM
ap-10666	55	15	-	-	PUNCT
ap-10666	55	16	dimensional	dimensional	ADJ
ap-10666	55	17	heisenberg	heisenberg	PROPN
ap-10666	55	18	algebra	algebra	PROPN
ap-10666	55	19	h5	h5	PROPN
ap-10666	55	20	spanned	span	VERB
ap-10666	55	21	by	by	ADP
ap-10666	55	22	the	the	DET
ap-10666	55	23	generators	generator	NOUN
ap-10666	55	24	p1	p1	PROPN
ap-10666	55	25	,	,	PUNCT
ap-10666	55	26	p2	p2	NOUN
ap-10666	55	27	,	,	PUNCT
ap-10666	55	28	q1	q1	NOUN
ap-10666	55	29	,	,	PUNCT
ap-10666	55	30	q2	q2	PROPN
ap-10666	55	31	,	,	PUNCT
ap-10666	55	32	i	i	PRON
ap-10666	55	33	,	,	PUNCT
ap-10666	55	34	which	which	PRON
ap-10666	55	35	obey	obey	VERB
ap-10666	55	36	the	the	DET
ap-10666	55	37	commutation	commutation	NOUN
ap-10666	55	38	relations	relation	NOUN
ap-10666	55	39	:	:	PUNCT
ap-10666	56	1	[	[	X
ap-10666	56	2	p1	p1	NOUN
ap-10666	56	3	,	,	PUNCT
ap-10666	56	4	q1	q1	NOUN
ap-10666	56	5	]	]	PUNCT
ap-10666	56	6	=	=	SYM
ap-10666	56	7	1	1	NUM
ap-10666	56	8	,	,	PUNCT
ap-10666	56	9	[	[	X
ap-10666	56	10	p2	p2	X
ap-10666	56	11	,	,	PUNCT
ap-10666	56	12	q2	q2	NOUN
ap-10666	56	13	]	]	PUNCT
ap-10666	56	14	=	=	SYM
ap-10666	56	15	1	1	NUM
ap-10666	56	16	,	,	PUNCT
ap-10666	56	17	[	[	X
ap-10666	56	18	p1	p1	NOUN
ap-10666	56	19	,	,	PUNCT
ap-10666	56	20	q2	q2	NOUN
ap-10666	56	21	]	]	PUNCT
ap-10666	56	22	=	=	PUNCT
ap-10666	56	23	0	0	NUM
ap-10666	56	24	,	,	PUNCT
ap-10666	56	25	[	[	X
ap-10666	56	26	p2	p2	X
ap-10666	56	27	,	,	PUNCT
ap-10666	56	28	q1	q1	NOUN
ap-10666	56	29	]	]	PUNCT
ap-10666	56	30	=	=	SYM
ap-10666	56	31	0	0	NUM
ap-10666	56	32	,	,	PUNCT
ap-10666	56	33	[	[	X
ap-10666	56	34	p1	p1	NOUN
ap-10666	56	35	,	,	PUNCT
ap-10666	56	36	p2	p2	X
ap-10666	56	37	]	]	PUNCT
ap-10666	56	38	=	=	SYM
ap-10666	56	39	0	0	NUM
ap-10666	56	40	,	,	PUNCT
ap-10666	56	41	[	[	X
ap-10666	56	42	q1	q1	NOUN
ap-10666	56	43	,	,	PUNCT
ap-10666	56	44	q2	q2	NOUN
ap-10666	56	45	]	]	PUNCT
ap-10666	56	46	=	=	PUNCT
ap-10666	56	47	0	0	NUM
ap-10666	56	48	,	,	PUNCT
ap-10666	56	49	[	[	X
ap-10666	56	50	p1,2	p1,2	X
ap-10666	56	51	,	,	PUNCT
ap-10666	56	52	i	i	PRON
ap-10666	56	53	]	]	X
ap-10666	56	54	=	=	PUNCT
ap-10666	56	55	0	0	NUM
ap-10666	56	56	,	,	PUNCT
ap-10666	56	57	[	[	X
ap-10666	56	58	q1,2	q1,2	ADJ
ap-10666	56	59	,	,	PUNCT
ap-10666	56	60	i	i	PRON
ap-10666	56	61	]	]	X
ap-10666	56	62	=	=	PUNCT
ap-10666	56	63	0	0	X
ap-10666	56	64	.	.	PUNCT
ap-10666	57	1	(	(	PUNCT
ap-10666	57	2	2	2	X
ap-10666	57	3	)	)	PUNCT
ap-10666	57	4	the	the	DET
ap-10666	57	5	universal	universal	ADJ
ap-10666	57	6	enveloping	enveloping	NOUN
ap-10666	57	7	algebra	algebra	NOUN
ap-10666	57	8	of	of	ADP
ap-10666	57	9	the	the	DET
ap-10666	57	10	algebra	algebra	NOUN
ap-10666	57	11	h5	h5	NOUN
ap-10666	57	12	:	:	PUNCT
ap-10666	57	13	uh5	uh5	NOUN
ap-10666	57	14	,	,	PUNCT
ap-10666	57	15	is	be	AUX
ap-10666	57	16	spanned	span	VERB
ap-10666	57	17	by	by	ADP
ap-10666	57	18	all	all	DET
ap-10666	57	19	ordered	order	VERB
ap-10666	57	20	monomials	monomial	NOUN
ap-10666	57	21	in	in	ADP
ap-10666	57	22	p1	p1	NOUN
ap-10666	57	23	,	,	PUNCT
ap-10666	57	24	p2	p2	NOUN
ap-10666	57	25	,	,	PUNCT
ap-10666	57	26	q1	q1	NOUN
ap-10666	57	27	,	,	PUNCT
ap-10666	57	28	q2	q2	NOUN
ap-10666	57	29	.	.	PUNCT
ap-10666	58	1	introducing	introduce	VERB
ap-10666	58	2	the	the	DET
ap-10666	58	3	vacuum	vacuum	NOUN
ap-10666	58	4	|0⟩	|0⟩	NOUN
ap-10666	58	5	as	as	ADP
ap-10666	58	6	an	an	DET
ap-10666	58	7	object	object	NOUN
ap-10666	58	8	annihilated	annihilate	VERB
ap-10666	58	9	by	by	ADP
ap-10666	58	10	p	p	NOUN
ap-10666	58	11	-	-	PUNCT
ap-10666	58	12	operators	operator	NOUN
ap-10666	58	13	:	:	PUNCT
ap-10666	58	14	p1	p1	NOUN
ap-10666	58	15	|0⟩	|0⟩	NOUN
ap-10666	58	16	=	=	SYM
ap-10666	58	17	0	0	NUM
ap-10666	58	18	,	,	PUNCT
ap-10666	58	19	p2	p2	X
ap-10666	58	20	|0⟩	|0⟩	NOUN
ap-10666	58	21	=	=	SYM
ap-10666	58	22	0	0	NUM
ap-10666	58	23	,	,	PUNCT
ap-10666	58	24	in	in	ADP
ap-10666	58	25	addition	addition	NOUN
ap-10666	58	26	to	to	ADP
ap-10666	58	27	the	the	DET
ap-10666	58	28	universal	universal	ADJ
ap-10666	58	29	enveloping	enveloping	NOUN
ap-10666	58	30	algebra	algebra	NOUN
ap-10666	58	31	uh5	uh5	NOUN
ap-10666	58	32	,	,	PUNCT
ap-10666	58	33	leads	lead	VERB
ap-10666	58	34	to	to	ADP
ap-10666	58	35	the	the	DET
ap-10666	58	36	definition	definition	NOUN
ap-10666	58	37	of	of	ADP
ap-10666	58	38	a	a	DET
ap-10666	58	39	fock	fock	ADJ
ap-10666	58	40	space	space	NOUN
ap-10666	58	41	.	.	PUNCT
ap-10666	59	1	it	it	PRON
ap-10666	59	2	can	can	AUX
ap-10666	59	3	be	be	AUX
ap-10666	59	4	easily	easily	ADV
ap-10666	59	5	shown	show	VERB
ap-10666	59	6	by	by	ADP
ap-10666	59	7	direct	direct	ADJ
ap-10666	59	8	calculation	calculation	NOUN
ap-10666	59	9	that	that	SCONJ
ap-10666	59	10	:	:	PUNCT
ap-10666	59	11	e11	e11	X
ap-10666	59	12	=	=	SYM
ap-10666	59	13	q1p1	q1p1	X
ap-10666	60	1	+	+	NUM
ap-10666	60	2	m11	m11	NOUN
ap-10666	60	3	,	,	PUNCT
ap-10666	60	4	e22	e22	X
ap-10666	60	5	=	=	SYM
ap-10666	60	6	q2p2	q2p2	PROPN
ap-10666	60	7	+	+	NUM
ap-10666	60	8	m22	m22	PROPN
ap-10666	60	9	,	,	PUNCT
ap-10666	60	10	e12	e12	NOUN
ap-10666	60	11	=	=	SYM
ap-10666	60	12	q1p2	q1p2	PROPN
ap-10666	60	13	+	+	SYM
ap-10666	60	14	m12	m12	ADJ
ap-10666	60	15	,	,	PUNCT
ap-10666	60	16	e21	e21	NUM
ap-10666	60	17	=	=	SYM
ap-10666	60	18	q2p1	q2p1	PROPN
ap-10666	60	19	+	+	NUM
ap-10666	60	20	m21	m21	NOUN
ap-10666	60	21	,	,	PUNCT
ap-10666	60	22	e0	e0	PROPN
ap-10666	60	23	=	=	PUNCT
ap-10666	61	1	k	k	PROPN
ap-10666	61	2	−	−	X
ap-10666	61	3	q1p1	q1p1	PUNCT
ap-10666	61	4	−	−	NOUN
ap-10666	61	5	q2p2	q2p2	NOUN
ap-10666	61	6	,	,	PUNCT
ap-10666	61	7	t	t	NOUN
ap-10666	61	8	−	−	PROPN
ap-10666	61	9	1	1	NUM
ap-10666	61	10	=	=	SYM
ap-10666	61	11	p1	p1	PROPN
ap-10666	61	12	,	,	PUNCT
ap-10666	61	13	t	t	NOUN
ap-10666	61	14	−	−	PROPN
ap-10666	61	15	2	2	NUM
ap-10666	61	16	=	=	SYM
ap-10666	61	17	p2	p2	NOUN
ap-10666	61	18	,	,	PUNCT
ap-10666	61	19	t	t	NOUN
ap-10666	61	20	+	+	NOUN
ap-10666	61	21	1	1	NUM
ap-10666	61	22	=	=	SYM
ap-10666	62	1	q1(k	q1(k	ADP
ap-10666	62	2	−	−	PROPN
ap-10666	62	3	q1p1	q1p1	PUNCT
ap-10666	62	4	−	−	NOUN
ap-10666	62	5	q2p2	q2p2	NOUN
ap-10666	62	6	)	)	PUNCT
ap-10666	62	7	−	−	NOUN
ap-10666	62	8	q1m11	q1m11	VERB
ap-10666	62	9	−	−	PROPN
ap-10666	62	10	q2m12	q2m12	PROPN
ap-10666	62	11	,	,	PUNCT
ap-10666	62	12	t	t	PROPN
ap-10666	62	13	+	+	CCONJ
ap-10666	62	14	2	2	NUM
ap-10666	62	15	=	=	SYM
ap-10666	62	16	q2(k	q2(k	NOUN
ap-10666	62	17	−	−	NOUN
ap-10666	62	18	q1p1	q1p1	PUNCT
ap-10666	62	19	−	−	NOUN
ap-10666	62	20	q2p2	q2p2	NOUN
ap-10666	62	21	)	)	PUNCT
ap-10666	62	22	−	−	PROPN
ap-10666	62	23	q1m21	q1m21	NOUN
ap-10666	62	24	−	−	PROPN
ap-10666	62	25	q2m22	q2m22	PROPN
ap-10666	62	26	,	,	PUNCT
ap-10666	62	27	(	(	PUNCT
ap-10666	62	28	3	3	X
ap-10666	62	29	)	)	PUNCT
ap-10666	62	30	span	span	NOUN
ap-10666	62	31	the	the	DET
ap-10666	62	32	gl3	gl3	PROPN
ap-10666	62	33	algebra	algebra	NOUN
ap-10666	62	34	for	for	ADP
ap-10666	62	35	any	any	DET
ap-10666	62	36	k	k	PROPN
ap-10666	62	37	∈	∈	PROPN
ap-10666	62	38	r	r	NOUN
ap-10666	62	39	,	,	PUNCT
ap-10666	62	40	here	here	ADV
ap-10666	62	41	m11	m11	NOUN
ap-10666	62	42	,	,	PUNCT
ap-10666	62	43	m12	m12	PROPN
ap-10666	62	44	,	,	PUNCT
ap-10666	62	45	m21	m21	PROPN
ap-10666	62	46	,	,	PUNCT
ap-10666	62	47	m22	m22	PROPN
ap-10666	62	48	are	be	AUX
ap-10666	62	49	again	again	ADV
ap-10666	62	50	generators	generator	NOUN
ap-10666	62	51	of	of	ADP
ap-10666	62	52	the	the	DET
ap-10666	62	53	gl2	gl2	PROPN
ap-10666	62	54	algebra	algebra	PROPN
ap-10666	62	55	obeying	obey	VERB
ap-10666	62	56	canonical	canonical	ADJ
ap-10666	62	57	commutation	commutation	NOUN
ap-10666	62	58	relations	relation	NOUN
ap-10666	62	59	,	,	PUNCT
ap-10666	62	60	see	see	VERB
ap-10666	62	61	footnote	footnote	VERB
ap-10666	62	62	1	1	NUM
ap-10666	62	63	.	.	PUNCT
ap-10666	63	1	the	the	DET
ap-10666	63	2	representation	representation	NOUN
ap-10666	63	3	(	(	PUNCT
ap-10666	63	4	3	3	X
ap-10666	63	5	)	)	PUNCT
ap-10666	63	6	is	be	AUX
ap-10666	63	7	the	the	DET
ap-10666	63	8	main	main	ADJ
ap-10666	63	9	result	result	NOUN
ap-10666	63	10	of	of	ADP
ap-10666	63	11	the	the	DET
ap-10666	63	12	present	present	ADJ
ap-10666	63	13	paper	paper	NOUN
ap-10666	63	14	.	.	PUNCT
ap-10666	64	1	by	by	ADP
ap-10666	64	2	taking	take	VERB
ap-10666	64	3	the	the	DET
ap-10666	64	4	heisenberg	heisenberg	PROPN
ap-10666	64	5	algebra	algebra	PROPN
ap-10666	64	6	(	(	PUNCT
ap-10666	64	7	2	2	NUM
ap-10666	64	8	)	)	PUNCT
ap-10666	64	9	realized	realize	VERB
ap-10666	64	10	in	in	ADP
ap-10666	64	11	the	the	DET
ap-10666	64	12	coordinate	coordinate	NOUN
ap-10666	64	13	-	-	PUNCT
ap-10666	64	14	momentum	momentum	NOUN
ap-10666	64	15	representation	representation	NOUN
ap-10666	64	16	:	:	PUNCT
ap-10666	64	17	q1	q1	PROPN
ap-10666	64	18	=	=	SYM
ap-10666	64	19	x1	x1	PROPN
ap-10666	64	20	,	,	PUNCT
ap-10666	64	21	p1	p1	NOUN
ap-10666	64	22	=	=	SYM
ap-10666	64	23	∂1	∂1	ADJ
ap-10666	64	24	,	,	PUNCT
ap-10666	64	25	q2	q2	NOUN
ap-10666	64	26	=	=	SYM
ap-10666	64	27	x2	x2	PROPN
ap-10666	64	28	,	,	PUNCT
ap-10666	64	29	p2	p2	PROPN
ap-10666	64	30	=	=	SYM
ap-10666	64	31	∂2	∂2	PROPN
ap-10666	64	32	,	,	PUNCT
ap-10666	64	33	with	with	ADP
ap-10666	64	34	m11	m11	NOUN
ap-10666	64	35	,	,	PUNCT
ap-10666	64	36	m12	m12	PROPN
ap-10666	64	37	,	,	PUNCT
ap-10666	64	38	m21	m21	PROPN
ap-10666	64	39	,	,	PUNCT
ap-10666	64	40	m22	m22	PROPN
ap-10666	64	41	given	give	VERB
ap-10666	64	42	by	by	ADP
ap-10666	64	43	n	n	NUM
ap-10666	64	44	×	×	NOUN
ap-10666	64	45	n	n	PRON
ap-10666	64	46	matrices	matrix	NOUN
ap-10666	64	47	which	which	PRON
ap-10666	64	48	spans	span	VERB
ap-10666	64	49	gl2	gl2	PROPN
ap-10666	64	50	-	-	PUNCT
ap-10666	64	51	algebra	algebra	VERB
ap-10666	64	52	the	the	DET
ap-10666	64	53	representation	representation	NOUN
ap-10666	64	54	(	(	PUNCT
ap-10666	64	55	3	3	X
ap-10666	64	56	)	)	PUNCT
ap-10666	64	57	is	be	AUX
ap-10666	64	58	reduced	reduce	VERB
ap-10666	64	59	to	to	ADP
ap-10666	64	60	(	(	PUNCT
ap-10666	64	61	1	1	NUM
ap-10666	64	62	)	)	PUNCT
ap-10666	64	63	.	.	PUNCT
ap-10666	65	1	it	it	PRON
ap-10666	65	2	is	be	AUX
ap-10666	65	3	also	also	ADV
ap-10666	65	4	worth	worth	ADJ
ap-10666	65	5	noting	note	VERB
ap-10666	65	6	that	that	SCONJ
ap-10666	65	7	in	in	ADP
ap-10666	65	8	the	the	DET
ap-10666	65	9	one	one	NUM
ap-10666	65	10	-	-	PUNCT
ap-10666	65	11	dimensional	dimensional	ADJ
ap-10666	65	12	representation	representation	NOUN
ap-10666	65	13	of	of	ADP
ap-10666	65	14	gl2	gl2	PROPN
ap-10666	65	15	,	,	PUNCT
ap-10666	65	16	when	when	SCONJ
ap-10666	65	17	:	:	PUNCT
ap-10666	65	18	m11	m11	NOUN
ap-10666	65	19	=	=	SYM
ap-10666	65	20	m12	m12	NOUN
ap-10666	65	21	=	=	SYM
ap-10666	65	22	m21	m21	PROPN
ap-10666	65	23	=	=	PUNCT
ap-10666	65	24	m22	m22	PROPN
ap-10666	65	25	=	=	SYM
ap-10666	65	26	0	0	PROPN
ap-10666	65	27	,	,	PUNCT
ap-10666	65	28	the	the	DET
ap-10666	65	29	representation	representation	NOUN
ap-10666	65	30	(	(	PUNCT
ap-10666	65	31	3	3	X
ap-10666	65	32	)	)	PUNCT
ap-10666	65	33	realizes	realize	VERB
ap-10666	65	34	the	the	DET
ap-10666	65	35	hidden	hidden	ADJ
ap-10666	65	36	algebra	algebra	NOUN
ap-10666	65	37	of	of	ADP
ap-10666	65	38	the	the	DET
ap-10666	65	39	a2/3	a2/3	ADJ
ap-10666	65	40	-	-	PUNCT
ap-10666	65	41	body	body	NOUN
ap-10666	65	42	calogero	calogero	NOUN
ap-10666	65	43	rational	rational	ADJ
ap-10666	65	44	/	/	SYM
ap-10666	65	45	tremblay	tremblay	NOUN
ap-10666	65	46	-	-	PUNCT
ap-10666	65	47	turbinerwinternitz	turbinerwinternitz	NOUN
ap-10666	65	48	(	(	PUNCT
ap-10666	65	49	at	at	ADP
ap-10666	65	50	index	index	NOUN
ap-10666	65	51	3	3	NUM
ap-10666	65	52	,	,	PUNCT
ap-10666	65	53	degenerate	degenerate	ADJ
ap-10666	65	54	,	,	PUNCT
ap-10666	65	55	see	see	VERB
ap-10666	65	56	[	[	X
ap-10666	65	57	3	3	NUM
ap-10666	65	58	]	]	PUNCT
ap-10666	65	59	)	)	PUNCT
ap-10666	65	60	model	model	NOUN
ap-10666	65	61	in	in	ADP
ap-10666	65	62	the	the	DET
ap-10666	65	63	fock	fock	ADJ
ap-10666	65	64	space	space	NOUN
ap-10666	65	65	[	[	X
ap-10666	65	66	4	4	NUM
ap-10666	65	67	]	]	PUNCT
ap-10666	65	68	.	.	PUNCT
ap-10666	66	1	3	3	X
ap-10666	66	2	.	.	X
ap-10666	66	3	three	three	NUM
ap-10666	66	4	canonical	canonical	ADJ
ap-10666	66	5	pairs	pair	NOUN
ap-10666	66	6	two	two	NUM
ap-10666	66	7	operators	operator	NOUN
ap-10666	66	8	a	a	PRON
ap-10666	66	9	,	,	PUNCT
ap-10666	66	10	b	b	PROPN
ap-10666	66	11	form	form	NOUN
ap-10666	66	12	a	a	DET
ap-10666	66	13	canonical	canonical	ADJ
ap-10666	66	14	pair	pair	NOUN
ap-10666	66	15	if	if	SCONJ
ap-10666	66	16	their	their	PRON
ap-10666	66	17	commutator	commutator	NOUN
ap-10666	66	18	:	:	PUNCT
ap-10666	66	19	[	[	X
ap-10666	66	20	a	a	X
ap-10666	66	21	,	,	PUNCT
ap-10666	66	22	b	b	NOUN
ap-10666	66	23	]	]	X
ap-10666	66	24	=	=	SYM
ap-10666	66	25	1	1	NUM
ap-10666	66	26	,	,	PUNCT
ap-10666	66	27	where	where	SCONJ
ap-10666	66	28	[	[	X
ap-10666	66	29	a	a	X
ap-10666	66	30	,	,	PUNCT
ap-10666	66	31	b	b	NOUN
ap-10666	66	32	]	]	X
ap-10666	66	33	=	=	SYM
ap-10666	66	34	ab	ab	PROPN
ap-10666	67	1	−	−	PROPN
ap-10666	67	2	ba	ba	PROPN
ap-10666	67	3	.	.	PUNCT
ap-10666	68	1	the	the	DET
ap-10666	68	2	simplest	simple	ADJ
ap-10666	68	3	example	example	NOUN
ap-10666	68	4	of	of	ADP
ap-10666	68	5	a	a	DET
ap-10666	68	6	canonical	canonical	ADJ
ap-10666	68	7	pair	pair	NOUN
ap-10666	68	8	is	be	AUX
ap-10666	68	9	given	give	VERB
ap-10666	68	10	by	by	ADP
ap-10666	68	11	the	the	DET
ap-10666	68	12	coordinate	coordinate	NOUN
ap-10666	68	13	-	-	PUNCT
ap-10666	68	14	momentum	momentum	NOUN
ap-10666	68	15	representation	representation	NOUN
ap-10666	68	16	:	:	PUNCT
ap-10666	69	1	[	[	X
ap-10666	69	2	∂x	∂x	X
ap-10666	69	3	,	,	PUNCT
ap-10666	69	4	x	x	X
ap-10666	69	5	]	]	X
ap-10666	69	6	=	=	SYM
ap-10666	69	7	1	1	NUM
ap-10666	69	8	.	.	NOUN
ap-10666	69	9	3.1	3.1	NUM
ap-10666	69	10	.	.	PUNCT
ap-10666	69	11	translation	translation	NOUN
ap-10666	69	12	-	-	PUNCT
ap-10666	69	13	invariant	invariant	ADJ
ap-10666	69	14	canonical	canonical	ADJ
ap-10666	69	15	pair	pair	NOUN
ap-10666	69	16	let	let	VERB
ap-10666	69	17	us	we	PRON
ap-10666	69	18	take	take	VERB
ap-10666	69	19	the	the	DET
ap-10666	69	20	shift	shift	NOUN
ap-10666	69	21	operator	operator	NOUN
ap-10666	69	22	:	:	PUNCT
ap-10666	69	23	tδf(x	tδf(x	PROPN
ap-10666	69	24	)	)	PUNCT
ap-10666	70	1	=	=	SYM
ap-10666	70	2	f(x	f(x	PROPN
ap-10666	70	3	+	+	CCONJ
ap-10666	70	4	δ	δ	PROPN
ap-10666	70	5	)	)	PUNCT
ap-10666	70	6	,	,	PUNCT
ap-10666	70	7	tδ	tδ	PROPN
ap-10666	70	8	=	=	PUNCT
ap-10666	70	9	eδ∂x	eδ∂x	PROPN
ap-10666	70	10	,	,	PUNCT
ap-10666	70	11	where	where	SCONJ
ap-10666	70	12	δ	δ	PROPN
ap-10666	70	13	∈	∈	PROPN
ap-10666	70	14	c	c	PROPN
ap-10666	70	15	is	be	AUX
ap-10666	70	16	a	a	DET
ap-10666	70	17	parameter	parameter	NOUN
ap-10666	70	18	,	,	PUNCT
ap-10666	70	19	which	which	PRON
ap-10666	70	20	is	be	AUX
ap-10666	70	21	called	call	VERB
ap-10666	70	22	the	the	DET
ap-10666	70	23	spacing	spacing	NOUN
ap-10666	70	24	,	,	PUNCT
ap-10666	70	25	and	and	CCONJ
ap-10666	70	26	construct	construct	VERB
ap-10666	70	27	the	the	DET
ap-10666	70	28	pair	pair	NOUN
ap-10666	70	29	of	of	ADP
ap-10666	70	30	shift	shift	NOUN
ap-10666	70	31	operators	operator	NOUN
ap-10666	70	32	(	(	PUNCT
ap-10666	70	33	see	see	VERB
ap-10666	70	34	e.g.	e.g.	ADV
ap-10666	70	35	[	[	X
ap-10666	70	36	5	5	NUM
ap-10666	70	37	]	]	PUNCT
ap-10666	70	38	):	):	PUNCT
ap-10666	70	39	dδ	dδ	ADP
ap-10666	70	40	=	=	PUNCT
ap-10666	70	41	tδ	tδ	PROPN
ap-10666	70	42	−	−	NUM
ap-10666	70	43	1	1	NUM
ap-10666	70	44	δ	δ	PROPN
ap-10666	70	45	,	,	PUNCT
ap-10666	70	46	xδ	xδ	PROPN
ap-10666	70	47	=	=	X
ap-10666	70	48	xt−δ	xt−δ	PROPN
ap-10666	71	1	=	=	PUNCT
ap-10666	71	2	x(1	x(1	PROPN
ap-10666	71	3	−	−	PROPN
ap-10666	71	4	δd−δ	δd−δ	NOUN
ap-10666	71	5	)	)	PUNCT
ap-10666	71	6	,	,	PUNCT
ap-10666	71	7	(	(	PUNCT
ap-10666	71	8	4	4	X
ap-10666	71	9	)	)	PUNCT
ap-10666	71	10	where	where	SCONJ
ap-10666	71	11	the	the	DET
ap-10666	71	12	operator	operator	NOUN
ap-10666	71	13	dδ	dδ	X
ap-10666	71	14	is	be	AUX
ap-10666	71	15	defined	define	VERB
ap-10666	71	16	as	as	ADP
ap-10666	71	17	:	:	PUNCT
ap-10666	71	18	dδf(x	dδf(x	PROPN
ap-10666	71	19	)	)	PUNCT
ap-10666	71	20	=	=	SYM
ap-10666	72	1	f(x	f(x	PROPN
ap-10666	72	2	+	+	CCONJ
ap-10666	72	3	δ	δ	PROPN
ap-10666	72	4	)	)	PUNCT
ap-10666	72	5	−	−	PROPN
ap-10666	72	6	f(x	f(x	PROPN
ap-10666	72	7	)	)	PUNCT
ap-10666	72	8	δ	δ	PROPN
ap-10666	72	9	,	,	PUNCT
ap-10666	72	10	sometimes	sometimes	ADV
ap-10666	72	11	,	,	PUNCT
ap-10666	72	12	it	it	PRON
ap-10666	72	13	is	be	AUX
ap-10666	72	14	called	call	VERB
ap-10666	72	15	the	the	DET
ap-10666	72	16	norlund	norlund	ADJ
ap-10666	72	17	derivative	derivative	NOUN
ap-10666	72	18	.	.	PUNCT
ap-10666	73	1	the	the	DET
ap-10666	73	2	operators	operator	NOUN
ap-10666	73	3	dδ	dδ	ADP
ap-10666	73	4	,	,	PUNCT
ap-10666	73	5	xδ	xδ	PROPN
ap-10666	73	6	are	be	AUX
ap-10666	73	7	translation	translation	NOUN
ap-10666	73	8	-	-	PUNCT
ap-10666	73	9	invariant	invariant	ADJ
ap-10666	73	10	.	.	PUNCT
ap-10666	74	1	the	the	DET
ap-10666	74	2	vacuum	vacuum	NOUN
ap-10666	74	3	is	be	AUX
ap-10666	74	4	chosen	choose	VERB
ap-10666	74	5	to	to	PART
ap-10666	74	6	be	be	AUX
ap-10666	74	7	one	one	NUM
ap-10666	74	8	,	,	PUNCT
ap-10666	74	9	|0⟩	|0⟩	NOUN
ap-10666	74	10	=	=	SYM
ap-10666	74	11	1	1	X
ap-10666	74	12	.	.	PUNCT
ap-10666	75	1	this	this	DET
ap-10666	75	2	canonical	canonical	ADJ
ap-10666	75	3	pair	pair	NOUN
ap-10666	75	4	acts	act	VERB
ap-10666	75	5	naturally	naturally	ADV
ap-10666	75	6	on	on	ADP
ap-10666	75	7	the	the	DET
ap-10666	75	8	space	space	NOUN
ap-10666	75	9	of	of	ADP
ap-10666	75	10	polynomials	polynomial	NOUN
ap-10666	75	11	(	(	PUNCT
ap-10666	75	12	in	in	ADP
ap-10666	75	13	x	x	NOUN
ap-10666	75	14	)	)	PUNCT
ap-10666	75	15	.	.	PUNCT
ap-10666	76	1	in	in	ADP
ap-10666	76	2	the	the	DET
ap-10666	76	3	limit	limit	NOUN
ap-10666	76	4	δ	δ	PROPN
ap-10666	76	5	→	→	SYM
ap-10666	76	6	0	0	PROPN
ap-10666	76	7	,	,	PUNCT
ap-10666	76	8	this	this	DET
ap-10666	76	9	degenerates	degenerate	NOUN
ap-10666	76	10	into	into	ADP
ap-10666	76	11	the	the	DET
ap-10666	76	12	coordinatemomentum	coordinatemomentum	NOUN
ap-10666	76	13	representation	representation	NOUN
ap-10666	76	14	,	,	PUNCT
ap-10666	76	15	dδ	dδ	ADP
ap-10666	76	16	→	→	SYM
ap-10666	76	17	∂x	∂x	PROPN
ap-10666	76	18	and	and	CCONJ
ap-10666	76	19	xδ	xδ	PROPN
ap-10666	76	20	→	→	PUNCT
ap-10666	77	1	x.	x.	NOUN
ap-10666	78	1	it	it	PRON
ap-10666	78	2	is	be	AUX
ap-10666	78	3	easy	easy	ADJ
ap-10666	78	4	to	to	PART
ap-10666	78	5	check	check	VERB
ap-10666	78	6	that	that	SCONJ
ap-10666	78	7	the	the	DET
ap-10666	78	8	commutator	commutator	NOUN
ap-10666	78	9	[	[	X
ap-10666	78	10	dδ	dδ	ADP
ap-10666	78	11	,	,	PUNCT
ap-10666	78	12	xδ	xδ	X
ap-10666	78	13	]	]	X
ap-10666	78	14	=	=	SYM
ap-10666	78	15	1	1	NUM
ap-10666	78	16	,	,	PUNCT
ap-10666	78	17	hence	hence	ADV
ap-10666	78	18	,	,	PUNCT
ap-10666	78	19	dδ	dδ	PROPN
ap-10666	78	20	,	,	PUNCT
ap-10666	78	21	xδ	xδ	PRON
ap-10666	78	22	form	form	VERB
ap-10666	78	23	a	a	DET
ap-10666	78	24	canonical	canonical	ADJ
ap-10666	78	25	pair	pair	NOUN
ap-10666	78	26	.	.	PUNCT
ap-10666	79	1	3.2	3.2	NUM
ap-10666	79	2	.	.	PUNCT
ap-10666	79	3	dilatation	dilatation	NOUN
ap-10666	79	4	-	-	PUNCT
ap-10666	79	5	invariant	invariant	ADJ
ap-10666	79	6	canonical	canonical	ADJ
ap-10666	79	7	pair	pair	NOUN
ap-10666	79	8	let	let	VERB
ap-10666	79	9	us	we	PRON
ap-10666	79	10	introduce	introduce	VERB
ap-10666	79	11	the	the	DET
ap-10666	79	12	dilatation	dilatation	NOUN
ap-10666	79	13	operator	operator	NOUN
ap-10666	79	14	:	:	PUNCT
ap-10666	79	15	tq	tq	ADP
ap-10666	79	16	f(x	f(x	PROPN
ap-10666	79	17	)	)	PUNCT
ap-10666	80	1	=	=	SYM
ap-10666	80	2	f(qx	f(qx	PROPN
ap-10666	80	3	)	)	PUNCT
ap-10666	80	4	,	,	PUNCT
ap-10666	80	5	tq	tq	ADP
ap-10666	80	6	=	=	SYM
ap-10666	80	7	qa	qa	PROPN
ap-10666	80	8	,	,	PUNCT
ap-10666	80	9	a	a	DET
ap-10666	80	10	≡	≡	PROPN
ap-10666	80	11	x	x	SYM
ap-10666	80	12	∂x	∂x	PROPN
ap-10666	80	13	,	,	PUNCT
ap-10666	80	14	where	where	SCONJ
ap-10666	80	15	q	q	PROPN
ap-10666	80	16	∈	∈	PROPN
ap-10666	80	17	c	c	NOUN
ap-10666	80	18	,	,	PUNCT
ap-10666	80	19	and	and	CCONJ
ap-10666	80	20	construct	construct	VERB
ap-10666	80	21	a	a	DET
ap-10666	80	22	canonical	canonical	ADJ
ap-10666	80	23	pair	pair	NOUN
ap-10666	80	24	of	of	ADP
ap-10666	80	25	dilatation	dilatation	NOUN
ap-10666	80	26	-	-	PUNCT
ap-10666	80	27	invariant	invariant	ADJ
ap-10666	80	28	operators	operator	NOUN
ap-10666	80	29	:	:	PUNCT
ap-10666	80	30	dq	dq	PROPN
ap-10666	80	31	=	=	SYM
ap-10666	81	1	x−1	x−1	PROPN
ap-10666	82	1	tq	tq	ADV
ap-10666	82	2	−	−	PROPN
ap-10666	82	3	1	1	NUM
ap-10666	82	4	q	q	NOUN
ap-10666	82	5	−	−	PROPN
ap-10666	82	6	1	1	NUM
ap-10666	82	7	,	,	PUNCT
ap-10666	82	8	xq	xq	X
ap-10666	82	9	=	=	PUNCT
ap-10666	82	10	a(q	a(q	PROPN
ap-10666	82	11	−	−	PROPN
ap-10666	82	12	1	1	NUM
ap-10666	82	13	)	)	PUNCT
ap-10666	82	14	tq	tq	ADV
ap-10666	82	15	−	−	PROPN
ap-10666	82	16	1	1	NUM
ap-10666	82	17	x	x	NOUN
ap-10666	82	18	,	,	PUNCT
ap-10666	82	19	(	(	PUNCT
ap-10666	82	20	5	5	X
ap-10666	82	21	)	)	PUNCT
ap-10666	82	22	see	see	VERB
ap-10666	82	23	[	[	X
ap-10666	82	24	6	6	NUM
ap-10666	82	25	]	]	PUNCT
ap-10666	82	26	.	.	PUNCT
ap-10666	83	1	it	it	PRON
ap-10666	83	2	can	can	AUX
ap-10666	83	3	be	be	AUX
ap-10666	83	4	easily	easily	ADV
ap-10666	83	5	checked	check	VERB
ap-10666	83	6	that	that	SCONJ
ap-10666	83	7	[	[	X
ap-10666	83	8	dq	dq	X
ap-10666	83	9	,	,	PUNCT
ap-10666	83	10	xq	xq	X
ap-10666	83	11	]	]	X
ap-10666	83	12	=	=	SYM
ap-10666	83	13	1	1	NUM
ap-10666	83	14	for	for	ADP
ap-10666	83	15	any	any	DET
ap-10666	83	16	q	q	NOUN
ap-10666	83	17	,	,	PUNCT
ap-10666	83	18	thus	thus	ADV
ap-10666	83	19	,	,	PUNCT
ap-10666	83	20	dq	dq	PROPN
ap-10666	83	21	,	,	PUNCT
ap-10666	83	22	xq	xq	PROPN
ap-10666	83	23	form	form	VERB
ap-10666	83	24	a	a	DET
ap-10666	83	25	canonical	canonical	ADJ
ap-10666	83	26	pair	pair	NOUN
ap-10666	83	27	.	.	PUNCT
ap-10666	84	1	usually	usually	ADV
ap-10666	84	2	,	,	PUNCT
ap-10666	84	3	the	the	DET
ap-10666	84	4	operator	operator	NOUN
ap-10666	84	5	dq	dq	NOUN
ap-10666	84	6	is	be	AUX
ap-10666	84	7	called	call	VERB
ap-10666	84	8	the	the	DET
ap-10666	84	9	jackson	jackson	PROPN
ap-10666	84	10	symbol	symbol	PROPN
ap-10666	84	11	(	(	PUNCT
ap-10666	84	12	or	or	CCONJ
ap-10666	84	13	the	the	DET
ap-10666	84	14	jackson	jackson	PROPN
ap-10666	84	15	derivative	derivative	PROPN
ap-10666	84	16	)	)	PUNCT
ap-10666	84	17	.	.	PUNCT
ap-10666	85	1	the	the	DET
ap-10666	85	2	vacuum	vacuum	NOUN
ap-10666	85	3	is	be	AUX
ap-10666	85	4	equal	equal	ADJ
ap-10666	85	5	to	to	ADP
ap-10666	85	6	one	one	NUM
ap-10666	85	7	,	,	PUNCT
ap-10666	85	8	|0⟩	|0⟩	NOUN
ap-10666	85	9	=	=	SYM
ap-10666	85	10	1	1	X
ap-10666	85	11	.	.	PUNCT
ap-10666	86	1	this	this	DET
ap-10666	86	2	canonical	canonical	ADJ
ap-10666	86	3	pair	pair	NOUN
ap-10666	86	4	acts	act	VERB
ap-10666	86	5	naturally	naturally	ADV
ap-10666	86	6	on	on	ADP
ap-10666	86	7	the	the	DET
ap-10666	86	8	space	space	NOUN
ap-10666	86	9	of	of	ADP
ap-10666	86	10	polynomials	polynomial	NOUN
ap-10666	86	11	(	(	PUNCT
ap-10666	86	12	in	in	ADP
ap-10666	86	13	x	x	NOUN
ap-10666	86	14	)	)	PUNCT
ap-10666	86	15	.	.	PUNCT
ap-10666	87	1	both	both	DET
ap-10666	87	2	operators	operators	PROPN
ap-10666	87	3	xq	xq	PROPN
ap-10666	87	4	,	,	PUNCT
ap-10666	87	5	dq	dq	PROPN
ap-10666	87	6	are	be	AUX
ap-10666	87	7	pseudodifferential	pseudodifferential	ADJ
ap-10666	87	8	operators	operator	NOUN
ap-10666	87	9	which	which	DET
ap-10666	87	10	action	action	NOUN
ap-10666	87	11	on	on	ADP
ap-10666	87	12	monomials	monomial	NOUN
ap-10666	87	13	as	as	SCONJ
ap-10666	87	14	follows	follow	VERB
ap-10666	87	15	:	:	PUNCT
ap-10666	87	16	dqxn	dqxn	ADJ
ap-10666	87	17	=	=	SYM
ap-10666	87	18	{	{	PUNCT
ap-10666	87	19	n}q	n}q	NOUN
ap-10666	87	20	xn−1	xn−1	PROPN
ap-10666	87	21	,	,	PUNCT
ap-10666	87	22	xqxn	xqxn	X
ap-10666	88	1	=	=	PUNCT
ap-10666	88	2	n	n	PROPN
ap-10666	88	3	+	+	NUM
ap-10666	88	4	1	1	NUM
ap-10666	88	5	{	{	PUNCT
ap-10666	88	6	n	n	PROPN
ap-10666	88	7	+	+	CCONJ
ap-10666	88	8	1}q	1}q	NUM
ap-10666	88	9	xn+1	xn+1	NUM
ap-10666	88	10	,	,	PUNCT
ap-10666	88	11	where	where	SCONJ
ap-10666	88	12	{	{	PUNCT
ap-10666	88	13	n}q	n}q	NOUN
ap-10666	88	14	=	=	SYM
ap-10666	88	15	1−qn	1−qn	NUM
ap-10666	88	16	1−q	1−q	NUM
ap-10666	88	17	is	be	AUX
ap-10666	88	18	the	the	DET
ap-10666	88	19	so	so	ADV
ap-10666	88	20	called	call	VERB
ap-10666	88	21	q	q	ADJ
ap-10666	88	22	-	-	PUNCT
ap-10666	88	23	number	number	NOUN
ap-10666	88	24	n.	n.	NOUN
ap-10666	88	25	563	563	NUM
ap-10666	88	26	alexander	alexander	PROPN
ap-10666	88	27	v.	v.	ADP
ap-10666	88	28	turbiner	turbiner	PROPN
ap-10666	88	29	acta	acta	PROPN
ap-10666	88	30	polytechnica	polytechnica	PROPN
ap-10666	88	31	3.3	3.3	NUM
ap-10666	88	32	.	.	PUNCT
ap-10666	89	1	complex	complex	ADJ
ap-10666	89	2	(	(	PUNCT
ap-10666	89	3	z	z	NOUN
ap-10666	89	4	,	,	PUNCT
ap-10666	89	5	z̄	z̄	ADJ
ap-10666	89	6	)	)	PUNCT
ap-10666	89	7	canonical	canonical	ADJ
ap-10666	89	8	pair	pair	NOUN
ap-10666	89	9	take	take	VERB
ap-10666	89	10	the	the	DET
ap-10666	89	11	space	space	NOUN
ap-10666	89	12	l2(c	l2(c	PROPN
ap-10666	89	13	,	,	PUNCT
ap-10666	89	14	dµ	dµ	PROPN
ap-10666	89	15	)	)	PUNCT
ap-10666	89	16	of	of	ADP
ap-10666	89	17	square	square	ADJ
ap-10666	89	18	-	-	PUNCT
ap-10666	89	19	integrable	integrable	ADJ
ap-10666	89	20	functions	function	NOUN
ap-10666	89	21	on	on	ADP
ap-10666	89	22	c	c	PROPN
ap-10666	89	23	with	with	ADP
ap-10666	89	24	the	the	DET
ap-10666	89	25	gaussian	gaussian	ADJ
ap-10666	89	26	measure	measure	NOUN
ap-10666	89	27	:	:	PUNCT
ap-10666	89	28	dµ(z	dµ(z	NOUN
ap-10666	89	29	)	)	PUNCT
ap-10666	89	30	=	=	SYM
ap-10666	89	31	π−1	π−1	PROPN
ap-10666	89	32	e−z·z̄dv(z	e−z·z̄dv(z	NOUN
ap-10666	89	33	)	)	PUNCT
ap-10666	89	34	,	,	PUNCT
ap-10666	89	35	where	where	SCONJ
ap-10666	89	36	dv(z	dv(z	PRON
ap-10666	89	37	)	)	PUNCT
ap-10666	89	38	=	=	SYM
ap-10666	89	39	dxdy	dxdy	PROPN
ap-10666	89	40	is	be	AUX
ap-10666	89	41	the	the	DET
ap-10666	89	42	euclidean	euclidean	ADJ
ap-10666	89	43	volume	volume	NOUN
ap-10666	89	44	element	element	NOUN
ap-10666	89	45	on	on	ADP
ap-10666	89	46	c	c	NOUN
ap-10666	89	47	=	=	SYM
ap-10666	89	48	r2	r2	PROPN
ap-10666	89	49	.	.	PUNCT
ap-10666	90	1	let	let	VERB
ap-10666	90	2	us	we	PRON
ap-10666	90	3	consider	consider	VERB
ap-10666	90	4	the	the	DET
ap-10666	90	5	following	follow	VERB
ap-10666	90	6	lowering	lower	VERB
ap-10666	90	7	and	and	CCONJ
ap-10666	90	8	raising	raise	VERB
ap-10666	90	9	operators	operator	NOUN
ap-10666	90	10	[	[	X
ap-10666	90	11	7	7	NUM
ap-10666	90	12	]	]	PUNCT
ap-10666	90	13	,	,	PUNCT
ap-10666	90	14	for	for	ADP
ap-10666	90	15	discussion	discussion	NOUN
ap-10666	90	16	see	see	VERB
ap-10666	90	17	[	[	X
ap-10666	90	18	8	8	NUM
ap-10666	90	19	]	]	X
ap-10666	90	20	:	:	PUNCT
ap-10666	90	21	a	a	DET
ap-10666	90	22	=	=	SYM
ap-10666	90	23	∂	∂	NOUN
ap-10666	90	24	∂z̄	∂z̄	NOUN
ap-10666	90	25	,	,	PUNCT
ap-10666	90	26	a†	a†	NOUN
ap-10666	90	27	=	=	SYM
ap-10666	90	28	−	−	PROPN
ap-10666	90	29	∂	∂	NOUN
ap-10666	90	30	∂z	∂z	PROPN
ap-10666	90	31	+	+	CCONJ
ap-10666	90	32	z̄.	z̄.	NUM
ap-10666	90	33	(	(	PUNCT
ap-10666	90	34	6	6	NUM
ap-10666	90	35	)	)	PUNCT
ap-10666	90	36	they	they	PRON
ap-10666	90	37	are	be	AUX
ap-10666	90	38	unitary	unitary	ADJ
ap-10666	90	39	-	-	PUNCT
ap-10666	90	40	conjugated	conjugated	ADJ
ap-10666	90	41	(	(	PUNCT
ap-10666	90	42	adjoint	adjoint	NOUN
ap-10666	90	43	)	)	PUNCT
ap-10666	90	44	.	.	PUNCT
ap-10666	91	1	the	the	DET
ap-10666	91	2	vacuum	vacuum	PROPN
ap-10666	91	3	vector	vector	NOUN
ap-10666	91	4	|0⟩	|0⟩	NOUN
ap-10666	91	5	,	,	PUNCT
ap-10666	91	6	defined	define	VERB
ap-10666	91	7	by	by	ADP
ap-10666	91	8	:	:	PUNCT
ap-10666	91	9	a	a	DET
ap-10666	91	10	|0⟩	|0⟩	NOUN
ap-10666	91	11	=	=	SYM
ap-10666	91	12	0	0	NUM
ap-10666	91	13	,	,	PUNCT
ap-10666	91	14	is	be	AUX
ap-10666	91	15	any	any	DET
ap-10666	91	16	analytic	analytic	ADJ
ap-10666	91	17	function	function	NOUN
ap-10666	91	18	.	.	PUNCT
ap-10666	92	1	it	it	PRON
ap-10666	92	2	is	be	AUX
ap-10666	92	3	easy	easy	ADJ
ap-10666	92	4	to	to	PART
ap-10666	92	5	check	check	VERB
ap-10666	92	6	that	that	PRON
ap-10666	92	7	:	:	PUNCT
ap-10666	93	1	[	[	X
ap-10666	93	2	a	a	X
ap-10666	93	3	,	,	PUNCT
ap-10666	93	4	a†	a†	NOUN
ap-10666	93	5	]	]	PUNCT
ap-10666	93	6	=	=	SYM
ap-10666	93	7	i	i	PROPN
ap-10666	93	8	,	,	PUNCT
ap-10666	93	9	where	where	SCONJ
ap-10666	93	10	i	i	PRON
ap-10666	93	11	is	be	AUX
ap-10666	93	12	the	the	DET
ap-10666	93	13	unit	unit	NOUN
ap-10666	93	14	operator	operator	NOUN
ap-10666	93	15	,	,	PUNCT
ap-10666	93	16	thus	thus	ADV
ap-10666	93	17	,	,	PUNCT
ap-10666	93	18	a	a	DET
ap-10666	93	19	canonical	canonical	ADJ
ap-10666	93	20	pair	pair	NOUN
ap-10666	93	21	is	be	AUX
ap-10666	93	22	formed	form	VERB
ap-10666	93	23	.	.	PUNCT
ap-10666	94	1	4	4	X
ap-10666	94	2	.	.	X
ap-10666	94	3	gl3	gl3	VERB
ap-10666	94	4	mixed	mix	VERB
ap-10666	94	5	representations	representation	NOUN
ap-10666	94	6	in	in	ADP
ap-10666	94	7	matrix	matrix	NOUN
ap-10666	94	8	operators	operator	NOUN
ap-10666	94	9	it	it	PRON
ap-10666	94	10	is	be	AUX
ap-10666	94	11	evident	evident	ADJ
ap-10666	94	12	that	that	SCONJ
ap-10666	94	13	the	the	DET
ap-10666	94	14	representation	representation	NOUN
ap-10666	94	15	(	(	PUNCT
ap-10666	94	16	3	3	X
ap-10666	94	17	)	)	PUNCT
ap-10666	94	18	acting	act	VERB
ap-10666	94	19	in	in	ADP
ap-10666	94	20	the	the	DET
ap-10666	94	21	fock	fock	ADJ
ap-10666	94	22	space	space	NOUN
ap-10666	94	23	of	of	ADP
ap-10666	94	24	columns	column	NOUN
ap-10666	94	25	allows	allow	VERB
ap-10666	94	26	us	we	PRON
ap-10666	94	27	to	to	PART
ap-10666	94	28	construct	construct	VERB
ap-10666	94	29	the	the	DET
ap-10666	94	30	gl3	gl3	ADV
ap-10666	94	31	mixed	mix	VERB
ap-10666	94	32	representations	representation	NOUN
ap-10666	94	33	in	in	ADP
ap-10666	94	34	matrix	matrix	NOUN
ap-10666	94	35	operators	operator	NOUN
ap-10666	94	36	.	.	PUNCT
ap-10666	95	1	4.1	4.1	NUM
ap-10666	95	2	.	.	PUNCT
ap-10666	95	3	matrix	matrix	NOUN
ap-10666	95	4	representation	representation	NOUN
ap-10666	95	5	of	of	ADP
ap-10666	95	6	the	the	DET
ap-10666	95	7	gl3	gl3	ADJ
ap-10666	95	8	algebra	algebra	NOUN
ap-10666	95	9	of	of	ADP
ap-10666	95	10	finite	finite	ADJ
ap-10666	95	11	-	-	PUNCT
ap-10666	95	12	difference	difference	ADJ
ap-10666	95	13	operators	operator	NOUN
ap-10666	95	14	let	let	VERB
ap-10666	95	15	us	we	PRON
ap-10666	95	16	take	take	VERB
ap-10666	95	17	the	the	DET
ap-10666	95	18	translation	translation	NOUN
ap-10666	95	19	-	-	PUNCT
ap-10666	95	20	invariant	invariant	ADJ
ap-10666	95	21	canonical	canonical	ADJ
ap-10666	95	22	pair	pair	NOUN
ap-10666	95	23	(	(	PUNCT
ap-10666	95	24	4	4	NUM
ap-10666	95	25	)	)	PUNCT
ap-10666	95	26	and	and	CCONJ
ap-10666	95	27	construct	construct	VERB
ap-10666	95	28	a	a	DET
ap-10666	95	29	realization	realization	NOUN
ap-10666	95	30	of	of	ADP
ap-10666	95	31	the	the	DET
ap-10666	95	32	heisenberg	heisenberg	PROPN
ap-10666	95	33	generators	generator	NOUN
ap-10666	95	34	of	of	ADP
ap-10666	95	35	h5	h5	PROPN
ap-10666	95	36	:	:	PUNCT
ap-10666	95	37	p1	p1	NOUN
ap-10666	95	38	,	,	PUNCT
ap-10666	95	39	p2	p2	NOUN
ap-10666	95	40	,	,	PUNCT
ap-10666	95	41	q1	q1	NOUN
ap-10666	95	42	,	,	PUNCT
ap-10666	95	43	q2	q2	NOUN
ap-10666	95	44	,	,	PUNCT
ap-10666	95	45	i	i	PRON
ap-10666	95	46	in	in	ADP
ap-10666	95	47	the	the	DET
ap-10666	95	48	following	following	ADJ
ap-10666	95	49	way	way	NOUN
ap-10666	95	50	:	:	PUNCT
ap-10666	95	51	p1	p1	PROPN
ap-10666	95	52	=	=	SYM
ap-10666	95	53	dδ1(x	dδ1(x	PROPN
ap-10666	95	54	)	)	PUNCT
ap-10666	95	55	,	,	PUNCT
ap-10666	95	56	p2	p2	PROPN
ap-10666	95	57	=	=	SYM
ap-10666	95	58	dδ2(y	dδ2(y	PROPN
ap-10666	95	59	)	)	PUNCT
ap-10666	95	60	,	,	PUNCT
ap-10666	95	61	q1	q1	PROPN
ap-10666	95	62	=	=	SYM
ap-10666	95	63	xδ1(x	xδ1(x	PROPN
ap-10666	95	64	)	)	PUNCT
ap-10666	95	65	,	,	PUNCT
ap-10666	95	66	q2	q2	NOUN
ap-10666	95	67	=	=	SYM
ap-10666	95	68	xδ2(y	xδ2(y	PROPN
ap-10666	95	69	)	)	PUNCT
ap-10666	95	70	.	.	PUNCT
ap-10666	96	1	substituting	substitute	VERB
ap-10666	96	2	these	these	PRON
ap-10666	96	3	into	into	ADP
ap-10666	96	4	(	(	PUNCT
ap-10666	96	5	3	3	NUM
ap-10666	96	6	)	)	PUNCT
ap-10666	96	7	,	,	PUNCT
ap-10666	96	8	we	we	PRON
ap-10666	96	9	arrive	arrive	VERB
ap-10666	96	10	at	at	ADP
ap-10666	96	11	a	a	DET
ap-10666	96	12	representation	representation	NOUN
ap-10666	96	13	of	of	ADP
ap-10666	96	14	the	the	DET
ap-10666	96	15	gl3	gl3	PROPN
ap-10666	96	16	algebra	algebra	NOUN
ap-10666	96	17	in	in	ADP
ap-10666	96	18	the	the	DET
ap-10666	96	19	form	form	NOUN
ap-10666	96	20	of	of	ADP
ap-10666	96	21	matrix	matrix	NOUN
ap-10666	96	22	finite	finite	ADJ
ap-10666	96	23	-	-	PUNCT
ap-10666	96	24	difference	difference	ADJ
ap-10666	96	25	operators	operator	NOUN
ap-10666	96	26	acting	act	VERB
ap-10666	96	27	in	in	ADP
ap-10666	96	28	the	the	DET
ap-10666	96	29	(	(	PUNCT
ap-10666	96	30	x	x	NOUN
ap-10666	96	31	,	,	PUNCT
ap-10666	96	32	y	y	NOUN
ap-10666	96	33	)	)	PUNCT
ap-10666	96	34	space	space	NOUN
ap-10666	96	35	of	of	ADP
ap-10666	96	36	columns	column	NOUN
ap-10666	96	37	/	/	SYM
ap-10666	96	38	n	n	CCONJ
ap-10666	96	39	-	-	PUNCT
ap-10666	96	40	tuples	tuple	NOUN
ap-10666	96	41	on	on	ADP
ap-10666	96	42	the	the	DET
ap-10666	96	43	rectangular	rectangular	ADJ
ap-10666	96	44	lattice	lattice	NOUN
ap-10666	96	45	with	with	ADP
ap-10666	96	46	spacings	spacing	NOUN
ap-10666	96	47	δ1	δ1	NOUN
ap-10666	96	48	,	,	PUNCT
ap-10666	96	49	δ2	δ2	PROPN
ap-10666	96	50	.	.	PUNCT
ap-10666	97	1	4.2	4.2	NUM
ap-10666	97	2	.	.	PUNCT
ap-10666	97	3	matrix	matrix	NOUN
ap-10666	97	4	representation	representation	NOUN
ap-10666	97	5	of	of	ADP
ap-10666	97	6	the	the	DET
ap-10666	97	7	gl3	gl3	ADJ
ap-10666	97	8	algebra	algebra	NOUN
ap-10666	97	9	of	of	ADP
ap-10666	97	10	discrete	discrete	ADJ
ap-10666	97	11	operators	operator	NOUN
ap-10666	97	12	let	let	VERB
ap-10666	97	13	us	we	PRON
ap-10666	97	14	take	take	VERB
ap-10666	97	15	the	the	DET
ap-10666	97	16	dilatation	dilatation	NOUN
ap-10666	97	17	-	-	PUNCT
ap-10666	97	18	invariant	invariant	ADJ
ap-10666	97	19	canonical	canonical	ADJ
ap-10666	97	20	pair	pair	NOUN
ap-10666	97	21	(	(	PUNCT
ap-10666	97	22	5	5	NUM
ap-10666	97	23	)	)	PUNCT
ap-10666	97	24	and	and	CCONJ
ap-10666	97	25	construct	construct	VERB
ap-10666	97	26	a	a	DET
ap-10666	97	27	realization	realization	NOUN
ap-10666	97	28	of	of	ADP
ap-10666	97	29	the	the	DET
ap-10666	97	30	heisenberg	heisenberg	PROPN
ap-10666	97	31	generators	generator	NOUN
ap-10666	97	32	of	of	ADP
ap-10666	97	33	h5	h5	PROPN
ap-10666	97	34	:	:	PUNCT
ap-10666	97	35	p1	p1	NOUN
ap-10666	97	36	,	,	PUNCT
ap-10666	97	37	p2	p2	NOUN
ap-10666	97	38	,	,	PUNCT
ap-10666	97	39	q1	q1	NOUN
ap-10666	97	40	,	,	PUNCT
ap-10666	97	41	q2	q2	NOUN
ap-10666	97	42	,	,	PUNCT
ap-10666	97	43	i	i	PRON
ap-10666	97	44	in	in	ADP
ap-10666	97	45	the	the	DET
ap-10666	97	46	following	following	ADJ
ap-10666	97	47	way	way	NOUN
ap-10666	97	48	:	:	PUNCT
ap-10666	97	49	p1	p1	PROPN
ap-10666	97	50	=	=	SYM
ap-10666	97	51	dq1(x	dq1(x	PROPN
ap-10666	97	52	)	)	PUNCT
ap-10666	97	53	,	,	PUNCT
ap-10666	97	54	p2	p2	PROPN
ap-10666	97	55	=	=	SYM
ap-10666	97	56	dq2(y	dq2(y	PROPN
ap-10666	97	57	)	)	PUNCT
ap-10666	97	58	,	,	PUNCT
ap-10666	97	59	q1	q1	X
ap-10666	97	60	=	=	SYM
ap-10666	97	61	xq1(x	xq1(x	PROPN
ap-10666	97	62	)	)	PUNCT
ap-10666	97	63	,	,	PUNCT
ap-10666	97	64	q2	q2	NOUN
ap-10666	97	65	=	=	SYM
ap-10666	97	66	xq2(y	xq2(y	PROPN
ap-10666	97	67	)	)	PUNCT
ap-10666	97	68	.	.	PUNCT
ap-10666	98	1	substituting	substitute	VERB
ap-10666	98	2	these	these	PRON
ap-10666	98	3	into	into	ADP
ap-10666	98	4	(	(	PUNCT
ap-10666	98	5	3	3	NUM
ap-10666	98	6	)	)	PUNCT
ap-10666	98	7	,	,	PUNCT
ap-10666	98	8	we	we	PRON
ap-10666	98	9	arrive	arrive	VERB
ap-10666	98	10	at	at	ADP
ap-10666	98	11	a	a	DET
ap-10666	98	12	representation	representation	NOUN
ap-10666	98	13	of	of	ADP
ap-10666	98	14	the	the	DET
ap-10666	98	15	gl3	gl3	PROPN
ap-10666	98	16	algebra	algebra	NOUN
ap-10666	98	17	in	in	ADP
ap-10666	98	18	the	the	DET
ap-10666	98	19	form	form	NOUN
ap-10666	98	20	of	of	ADP
ap-10666	98	21	discrete	discrete	ADJ
ap-10666	98	22	operators	operator	NOUN
ap-10666	98	23	with	with	ADP
ap-10666	98	24	matrix	matrix	NOUN
ap-10666	98	25	coefficients	coefficient	NOUN
ap-10666	98	26	acting	act	VERB
ap-10666	98	27	in	in	ADP
ap-10666	98	28	the	the	DET
ap-10666	98	29	(	(	PUNCT
ap-10666	98	30	x	x	NOUN
ap-10666	98	31	,	,	PUNCT
ap-10666	98	32	y	y	NOUN
ap-10666	98	33	)	)	PUNCT
ap-10666	98	34	space	space	NOUN
ap-10666	98	35	of	of	ADP
ap-10666	98	36	columns	column	NOUN
ap-10666	98	37	/	/	SYM
ap-10666	98	38	n	n	CCONJ
ap-10666	98	39	-	-	PUNCT
ap-10666	98	40	tuples	tuple	NOUN
ap-10666	98	41	on	on	ADP
ap-10666	98	42	rectangular	rectangular	ADJ
ap-10666	98	43	lattice	lattice	NOUN
ap-10666	98	44	with	with	ADP
ap-10666	98	45	dilations	dilation	NOUN
ap-10666	98	46	q1	q1	NOUN
ap-10666	98	47	,	,	PUNCT
ap-10666	98	48	q2	q2	NOUN
ap-10666	98	49	in	in	ADP
ap-10666	98	50	the	the	DET
ap-10666	98	51	x	x	NOUN
ap-10666	98	52	,	,	PUNCT
ap-10666	98	53	y	y	PROPN
ap-10666	98	54	directions	direction	NOUN
ap-10666	98	55	,	,	PUNCT
ap-10666	98	56	respectively	respectively	ADV
ap-10666	98	57	.	.	PUNCT
ap-10666	99	1	4.3	4.3	NUM
ap-10666	99	2	.	.	PUNCT
ap-10666	99	3	matrix	matrix	NOUN
ap-10666	99	4	representation	representation	NOUN
ap-10666	99	5	of	of	ADP
ap-10666	99	6	the	the	DET
ap-10666	99	7	gl3	gl3	ADJ
ap-10666	99	8	algebra	algebra	NOUN
ap-10666	99	9	of	of	ADP
ap-10666	99	10	mixed	mixed	ADJ
ap-10666	99	11	finite	finite	NOUN
ap-10666	99	12	-	-	PUNCT
ap-10666	99	13	difference	difference	NOUN
ap-10666	99	14	/	/	SYM
ap-10666	99	15	discrete	discrete	NOUN
ap-10666	99	16	operators	operator	NOUN
ap-10666	99	17	let	let	VERB
ap-10666	99	18	us	we	PRON
ap-10666	99	19	take	take	VERB
ap-10666	99	20	the	the	DET
ap-10666	99	21	translation	translation	NOUN
ap-10666	99	22	-	-	PUNCT
ap-10666	99	23	invariant	invariant	ADJ
ap-10666	99	24	canonical	canonical	ADJ
ap-10666	99	25	pair	pair	NOUN
ap-10666	99	26	(	(	PUNCT
ap-10666	99	27	4	4	X
ap-10666	99	28	)	)	PUNCT
ap-10666	99	29	acting	act	VERB
ap-10666	99	30	in	in	ADP
ap-10666	99	31	the	the	DET
ap-10666	99	32	x	x	NOUN
ap-10666	99	33	-	-	NOUN
ap-10666	99	34	direction	direction	NOUN
ap-10666	99	35	and	and	CCONJ
ap-10666	99	36	the	the	DET
ap-10666	99	37	dilatation	dilatation	NOUN
ap-10666	99	38	-	-	PUNCT
ap-10666	99	39	invariant	invariant	ADJ
ap-10666	99	40	canonical	canonical	ADJ
ap-10666	99	41	pair	pair	NOUN
ap-10666	99	42	(	(	PUNCT
ap-10666	99	43	5	5	X
ap-10666	99	44	)	)	PUNCT
ap-10666	99	45	acting	act	VERB
ap-10666	99	46	in	in	ADP
ap-10666	99	47	the	the	DET
ap-10666	99	48	y	y	NOUN
ap-10666	99	49	-	-	PUNCT
ap-10666	99	50	direction	direction	NOUN
ap-10666	99	51	and	and	CCONJ
ap-10666	99	52	construct	construct	VERB
ap-10666	99	53	a	a	DET
ap-10666	99	54	realization	realization	NOUN
ap-10666	99	55	of	of	ADP
ap-10666	99	56	the	the	DET
ap-10666	99	57	heisenberg	heisenberg	PROPN
ap-10666	99	58	generators	generator	NOUN
ap-10666	99	59	of	of	ADP
ap-10666	99	60	h5	h5	PROPN
ap-10666	99	61	:	:	PUNCT
ap-10666	99	62	p1	p1	NOUN
ap-10666	99	63	,	,	PUNCT
ap-10666	99	64	p2	p2	NOUN
ap-10666	99	65	,	,	PUNCT
ap-10666	99	66	q1	q1	NOUN
ap-10666	99	67	,	,	PUNCT
ap-10666	99	68	q2	q2	NOUN
ap-10666	99	69	,	,	PUNCT
ap-10666	99	70	i	i	PRON
ap-10666	99	71	in	in	ADP
ap-10666	99	72	the	the	DET
ap-10666	99	73	following	following	ADJ
ap-10666	99	74	way	way	NOUN
ap-10666	99	75	:	:	PUNCT
ap-10666	99	76	p1	p1	NOUN
ap-10666	99	77	=	=	PRON
ap-10666	99	78	dδ(x	dδ(x	X
ap-10666	99	79	)	)	PUNCT
ap-10666	99	80	,	,	PUNCT
ap-10666	99	81	p2	p2	X
ap-10666	99	82	=	=	SYM
ap-10666	99	83	dq(y	dq(y	X
ap-10666	99	84	)	)	PUNCT
ap-10666	99	85	,	,	PUNCT
ap-10666	99	86	q1	q1	PROPN
ap-10666	99	87	=	=	SYM
ap-10666	99	88	xδ(x	xδ(x	X
ap-10666	99	89	)	)	PUNCT
ap-10666	99	90	,	,	PUNCT
ap-10666	99	91	q2	q2	NOUN
ap-10666	99	92	=	=	PUNCT
ap-10666	99	93	xq(y	xq(y	X
ap-10666	99	94	)	)	PUNCT
ap-10666	99	95	.	.	PUNCT
ap-10666	100	1	substituting	substitute	VERB
ap-10666	100	2	this	this	DET
ap-10666	100	3	realization	realization	NOUN
ap-10666	100	4	into	into	ADP
ap-10666	100	5	(	(	PUNCT
ap-10666	100	6	3	3	X
ap-10666	100	7	)	)	PUNCT
ap-10666	100	8	we	we	PRON
ap-10666	100	9	arrive	arrive	VERB
ap-10666	100	10	at	at	ADP
ap-10666	100	11	a	a	DET
ap-10666	100	12	representation	representation	NOUN
ap-10666	100	13	of	of	ADP
ap-10666	100	14	the	the	DET
ap-10666	100	15	gl3	gl3	PROPN
ap-10666	100	16	algebra	algebra	NOUN
ap-10666	100	17	in	in	ADP
ap-10666	100	18	the	the	DET
ap-10666	100	19	form	form	NOUN
ap-10666	100	20	of	of	ADP
ap-10666	100	21	matrix	matrix	NOUN
ap-10666	100	22	finite	finite	NOUN
ap-10666	100	23	-	-	PUNCT
ap-10666	100	24	difference	difference	NOUN
ap-10666	100	25	/	/	SYM
ap-10666	100	26	discrete	discrete	ADJ
ap-10666	100	27	operators	operator	NOUN
ap-10666	100	28	acting	act	VERB
ap-10666	100	29	in	in	ADP
ap-10666	100	30	the	the	DET
ap-10666	100	31	(	(	PUNCT
ap-10666	100	32	x	x	NOUN
ap-10666	100	33	,	,	PUNCT
ap-10666	100	34	y	y	NOUN
ap-10666	100	35	)	)	PUNCT
ap-10666	100	36	space	space	NOUN
ap-10666	100	37	of	of	ADP
ap-10666	100	38	columns	column	NOUN
ap-10666	100	39	/	/	SYM
ap-10666	100	40	n	n	CCONJ
ap-10666	100	41	-	-	PUNCT
ap-10666	100	42	tuples	tuple	NOUN
ap-10666	100	43	on	on	ADP
ap-10666	100	44	a	a	DET
ap-10666	100	45	rectangular	rectangular	ADJ
ap-10666	100	46	uniform	uniform	ADJ
ap-10666	100	47	/	/	SYM
ap-10666	100	48	exponential	exponential	ADJ
ap-10666	100	49	lattice	lattice	NOUN
ap-10666	100	50	with	with	ADP
ap-10666	100	51	spacings	spacing	NOUN
ap-10666	100	52	δ	δ	PROPN
ap-10666	100	53	in	in	ADP
ap-10666	100	54	the	the	DET
ap-10666	100	55	x	x	NOUN
ap-10666	100	56	direction	direction	NOUN
ap-10666	100	57	and	and	CCONJ
ap-10666	100	58	dilation	dilation	NOUN
ap-10666	100	59	q	q	NOUN
ap-10666	100	60	in	in	ADP
ap-10666	100	61	the	the	DET
ap-10666	100	62	y	y	PROPN
ap-10666	100	63	direction	direction	NOUN
ap-10666	100	64	,	,	PUNCT
ap-10666	100	65	respectively	respectively	ADV
ap-10666	100	66	.	.	PUNCT
ap-10666	101	1	4.4	4.4	NUM
ap-10666	101	2	.	.	PUNCT
ap-10666	101	3	matrix	matrix	NOUN
ap-10666	101	4	representation	representation	NOUN
ap-10666	101	5	of	of	ADP
ap-10666	101	6	complex	complex	ADJ
ap-10666	101	7	(	(	PUNCT
ap-10666	101	8	z	z	NOUN
ap-10666	101	9	,	,	PUNCT
ap-10666	101	10	z̄	z̄	NUM
ap-10666	101	11	)	)	PUNCT
ap-10666	101	12	generators	generator	NOUN
ap-10666	101	13	by	by	ADP
ap-10666	101	14	taking	take	VERB
ap-10666	101	15	two	two	NUM
ap-10666	101	16	(	(	PUNCT
ap-10666	101	17	z1,2	z1,2	ADJ
ap-10666	101	18	,	,	PUNCT
ap-10666	101	19	z̄1,2	z̄1,2	ADJ
ap-10666	101	20	)	)	PUNCT
ap-10666	101	21	representations	representation	NOUN
ap-10666	101	22	(	(	PUNCT
ap-10666	101	23	6	6	NUM
ap-10666	101	24	)	)	PUNCT
ap-10666	101	25	acting	act	VERB
ap-10666	101	26	on	on	ADP
ap-10666	101	27	c2(z1	c2(z1	PROPN
ap-10666	101	28	,	,	PUNCT
ap-10666	101	29	z2	z2	ADJ
ap-10666	101	30	)	)	PUNCT
ap-10666	101	31	complex	complex	ADJ
ap-10666	101	32	space	space	NOUN
ap-10666	101	33	in	in	ADP
ap-10666	101	34	the	the	DET
ap-10666	101	35	form	form	NOUN
ap-10666	101	36	:	:	PUNCT
ap-10666	101	37	p1	p1	NOUN
ap-10666	101	38	=	=	SYM
ap-10666	101	39	a1(z1	a1(z1	ADJ
ap-10666	101	40	,	,	PUNCT
ap-10666	101	41	z̄1	z̄1	NUM
ap-10666	101	42	)	)	PUNCT
ap-10666	101	43	,	,	PUNCT
ap-10666	101	44	q1	q1	NOUN
ap-10666	101	45	=	=	SYM
ap-10666	101	46	a†	a†	PROPN
ap-10666	101	47	1(z1	1(z1	NUM
ap-10666	101	48	,	,	PUNCT
ap-10666	101	49	z̄1	z̄1	NUM
ap-10666	101	50	)	)	PUNCT
ap-10666	101	51	,	,	PUNCT
ap-10666	101	52	p2	p2	PROPN
ap-10666	101	53	=	=	SYM
ap-10666	101	54	a2(z2	a2(z2	NOUN
ap-10666	101	55	,	,	PUNCT
ap-10666	101	56	z̄2	z̄2	NUM
ap-10666	101	57	)	)	PUNCT
ap-10666	101	58	,	,	PUNCT
ap-10666	101	59	q2	q2	NOUN
ap-10666	101	60	=	=	SYM
ap-10666	101	61	a†	a†	PROPN
ap-10666	101	62	2(z2	2(z2	NUM
ap-10666	101	63	,	,	PUNCT
ap-10666	101	64	z̄2	z̄2	NUM
ap-10666	101	65	)	)	PUNCT
ap-10666	101	66	,	,	PUNCT
ap-10666	101	67	(	(	PUNCT
ap-10666	101	68	7	7	X
ap-10666	101	69	)	)	PUNCT
ap-10666	101	70	and	and	CCONJ
ap-10666	101	71	the	the	DET
ap-10666	101	72	unit	unit	NOUN
ap-10666	101	73	generator	generator	NOUN
ap-10666	101	74	i	i	PRON
ap-10666	101	75	we	we	PRON
ap-10666	101	76	construct	construct	VERB
ap-10666	101	77	a	a	DET
ap-10666	101	78	realization	realization	NOUN
ap-10666	101	79	of	of	ADP
ap-10666	101	80	the	the	DET
ap-10666	101	81	five	five	NUM
ap-10666	101	82	-	-	PUNCT
ap-10666	101	83	dimensional	dimensional	ADJ
ap-10666	101	84	heisenberg	heisenberg	PROPN
ap-10666	101	85	algebra	algebra	NOUN
ap-10666	101	86	h5	h5	NOUN
ap-10666	101	87	in	in	ADP
ap-10666	101	88	a	a	DET
ap-10666	101	89	2d	2d	NUM
ap-10666	101	90	complex	complex	ADJ
ap-10666	101	91	space	space	NOUN
ap-10666	101	92	.	.	PUNCT
ap-10666	102	1	by	by	ADP
ap-10666	102	2	taking	take	VERB
ap-10666	102	3	(	(	PUNCT
ap-10666	102	4	7	7	NUM
ap-10666	102	5	)	)	PUNCT
ap-10666	102	6	and	and	CCONJ
ap-10666	102	7	substituting	substitute	VERB
ap-10666	102	8	it	it	PRON
ap-10666	102	9	into	into	ADP
ap-10666	102	10	(	(	PUNCT
ap-10666	102	11	3	3	NUM
ap-10666	102	12	)	)	PUNCT
ap-10666	102	13	,	,	PUNCT
ap-10666	102	14	we	we	PRON
ap-10666	102	15	arrive	arrive	VERB
ap-10666	102	16	at	at	ADP
ap-10666	102	17	the	the	DET
ap-10666	102	18	matrix	matrix	NOUN
ap-10666	102	19	representation	representation	NOUN
ap-10666	102	20	of	of	ADP
ap-10666	102	21	the	the	DET
ap-10666	102	22	gl3	gl3	PROPN
ap-10666	102	23	algebra	algebra	NOUN
ap-10666	102	24	in	in	ADP
ap-10666	102	25	the	the	DET
ap-10666	102	26	c2(z1	c2(z1	NOUN
ap-10666	102	27	,	,	PUNCT
ap-10666	102	28	z2	z2	ADJ
ap-10666	102	29	)	)	PUNCT
ap-10666	102	30	complex	complex	ADJ
ap-10666	102	31	space	space	NOUN
ap-10666	102	32	of	of	ADP
ap-10666	102	33	columns	column	NOUN
ap-10666	102	34	/	/	SYM
ap-10666	102	35	n	n	CCONJ
ap-10666	102	36	-	-	PUNCT
ap-10666	102	37	tuples	tuple	NOUN
ap-10666	102	38	.	.	PUNCT
ap-10666	103	1	5	5	X
ap-10666	103	2	.	.	X
ap-10666	103	3	conclusion	conclusion	NOUN
ap-10666	103	4	in	in	ADP
ap-10666	103	5	this	this	DET
ap-10666	103	6	paper	paper	NOUN
ap-10666	103	7	,	,	PUNCT
ap-10666	103	8	we	we	PRON
ap-10666	103	9	were	be	AUX
ap-10666	103	10	able	able	ADJ
ap-10666	103	11	to	to	PART
ap-10666	103	12	construct	construct	VERB
ap-10666	103	13	the	the	DET
ap-10666	103	14	fock	fock	ADJ
ap-10666	103	15	space	space	NOUN
ap-10666	103	16	representation	representation	NOUN
ap-10666	103	17	[	[	X
ap-10666	103	18	n	n	CCONJ
ap-10666	103	19	,	,	PUNCT
ap-10666	103	20	k	k	X
ap-10666	103	21	]	]	X
ap-10666	103	22	of	of	ADP
ap-10666	103	23	the	the	DET
ap-10666	103	24	gl3	gl3	PROPN
ap-10666	103	25	algebra	algebra	NOUN
ap-10666	103	26	(	(	PUNCT
ap-10666	103	27	3	3	X
ap-10666	103	28	)	)	PUNCT
ap-10666	103	29	acting	act	VERB
ap-10666	103	30	in	in	ADP
ap-10666	103	31	the	the	DET
ap-10666	103	32	fock	fock	ADJ
ap-10666	103	33	space	space	NOUN
ap-10666	103	34	of	of	ADP
ap-10666	103	35	columns	column	NOUN
ap-10666	103	36	/	/	SYM
ap-10666	103	37	n	n	CCONJ
ap-10666	103	38	-	-	PUNCT
ap-10666	103	39	tuples	tuple	NOUN
ap-10666	103	40	.	.	PUNCT
ap-10666	104	1	this	this	DET
ap-10666	104	2	representation	representation	NOUN
ap-10666	104	3	becomes	become	VERB
ap-10666	104	4	finite	finite	ADJ
ap-10666	104	5	-	-	ADJ
ap-10666	104	6	dimensional	dimensional	ADJ
ap-10666	104	7	when	when	SCONJ
ap-10666	104	8	k	k	PROPN
ap-10666	104	9	is	be	AUX
ap-10666	104	10	a	a	DET
ap-10666	104	11	non	non	ADJ
ap-10666	104	12	-	-	ADJ
ap-10666	104	13	negative	negative	ADJ
ap-10666	104	14	integer	integer	NOUN
ap-10666	104	15	and	and	CCONJ
ap-10666	104	16	integer	integer	NOUN
ap-10666	104	17	n	n	PRON
ap-10666	104	18	is	be	AUX
ap-10666	104	19	related	relate	VERB
ap-10666	104	20	to	to	ADP
ap-10666	104	21	the	the	DET
ap-10666	104	22	n	n	ADV
ap-10666	104	23	-	-	PUNCT
ap-10666	104	24	dimensional	dimensional	ADJ
ap-10666	104	25	representation	representation	NOUN
ap-10666	104	26	of	of	ADP
ap-10666	104	27	the	the	DET
ap-10666	104	28	gl2	gl2	PROPN
ap-10666	104	29	algebra	algebra	PROPN
ap-10666	104	30	.	.	PUNCT
ap-10666	105	1	this	this	DET
ap-10666	105	2	representation	representation	NOUN
ap-10666	105	3	can	can	AUX
ap-10666	105	4	be	be	AUX
ap-10666	105	5	converted	convert	VERB
ap-10666	105	6	to	to	ADP
ap-10666	105	7	the	the	DET
ap-10666	105	8	representations	representation	NOUN
ap-10666	105	9	in	in	ADP
ap-10666	105	10	terms	term	NOUN
ap-10666	105	11	of	of	ADP
ap-10666	105	12	the	the	DET
ap-10666	105	13	first	first	ADJ
ap-10666	105	14	-	-	PUNCT
ap-10666	105	15	order	order	NOUN
ap-10666	105	16	differential	differential	NOUN
ap-10666	105	17	,	,	PUNCT
ap-10666	105	18	finite	finite	ADJ
ap-10666	105	19	-	-	NOUN
ap-10666	105	20	difference	difference	ADJ
ap-10666	105	21	,	,	PUNCT
ap-10666	105	22	discrete	discrete	ADJ
ap-10666	105	23	,	,	PUNCT
ap-10666	105	24	and	and	CCONJ
ap-10666	105	25	complex	complex	ADJ
ap-10666	105	26	(	(	PUNCT
ap-10666	105	27	z	z	NOUN
ap-10666	105	28	,	,	PUNCT
ap-10666	105	29	z̄	z̄	NUM
ap-10666	105	30	)	)	PUNCT
ap-10666	105	31	operators	operator	NOUN
ap-10666	105	32	with	with	ADP
ap-10666	105	33	matrix	matrix	NOUN
ap-10666	105	34	coefficients	coefficient	NOUN
ap-10666	105	35	.	.	PUNCT
ap-10666	106	1	all	all	DET
ap-10666	106	2	these	these	DET
ap-10666	106	3	representations	representation	NOUN
ap-10666	106	4	are	be	AUX
ap-10666	106	5	alternative	alternative	ADJ
ap-10666	106	6	to	to	ADP
ap-10666	106	7	the	the	DET
ap-10666	106	8	standard	standard	ADJ
ap-10666	106	9	gl3	gl3	PROPN
ap-10666	106	10	algebra	algebra	NOUN
ap-10666	106	11	representations	representation	NOUN
ap-10666	106	12	acting	act	VERB
ap-10666	106	13	in	in	ADP
ap-10666	106	14	three	three	NUM
ap-10666	106	15	-	-	PUNCT
ap-10666	106	16	dimensional	dimensional	ADJ
ap-10666	106	17	space	space	NOUN
ap-10666	106	18	(	(	PUNCT
ap-10666	106	19	on	on	ADP
ap-10666	106	20	flag	flag	NOUN
ap-10666	106	21	manifold	manifold	ADJ
ap-10666	106	22	)	)	PUNCT
ap-10666	106	23	.	.	PUNCT
ap-10666	107	1	acknowledgements	acknowledgement	VERB
ap-10666	107	2	the	the	DET
ap-10666	107	3	author	author	NOUN
ap-10666	107	4	(	(	PUNCT
ap-10666	107	5	avt	avt	PROPN
ap-10666	107	6	)	)	PUNCT
ap-10666	107	7	partially	partially	ADV
ap-10666	107	8	supported	support	VERB
ap-10666	107	9	by	by	ADP
ap-10666	107	10	dgapa	dgapa	ADJ
ap-10666	107	11	grant	grant	PROPN
ap-10666	107	12	in104125	in104125	PROPN
ap-10666	107	13	(	(	PUNCT
ap-10666	107	14	mexico	mexico	PROPN
ap-10666	107	15	)	)	PUNCT
ap-10666	107	16	.	.	PUNCT
ap-10666	108	1	this	this	DET
ap-10666	108	2	work	work	NOUN
ap-10666	108	3	is	be	AUX
ap-10666	108	4	dedicated	dedicate	VERB
ap-10666	108	5	to	to	ADP
ap-10666	108	6	the	the	DET
ap-10666	108	7	memory	memory	NOUN
ap-10666	108	8	of	of	ADP
ap-10666	108	9	miloslav	miloslav	NOUN
ap-10666	108	10	havlíček	havlíček	PROPN
ap-10666	108	11	–	–	PUNCT
ap-10666	108	12	an	an	DET
ap-10666	108	13	exemplary	exemplary	ADJ
ap-10666	108	14	scientist	scientist	NOUN
ap-10666	108	15	and	and	CCONJ
ap-10666	108	16	citizen	citizen	NOUN
ap-10666	108	17	.	.	PUNCT
ap-10666	109	1	the	the	DET
ap-10666	109	2	present	present	ADJ
ap-10666	109	3	author	author	NOUN
ap-10666	109	4	thinks	think	VERB
ap-10666	109	5	that	that	SCONJ
ap-10666	109	6	the	the	DET
ap-10666	109	7	representation	representation	NOUN
ap-10666	109	8	(	(	PUNCT
ap-10666	109	9	1	1	X
ap-10666	109	10	)	)	PUNCT
ap-10666	109	11	should	should	AUX
ap-10666	109	12	be	be	AUX
ap-10666	109	13	called	call	VERB
ap-10666	109	14	the	the	DET
ap-10666	109	15	havlíček	havlíček	NOUN
ap-10666	109	16	representation	representation	NOUN
ap-10666	109	17	.	.	PUNCT
ap-10666	110	1	564	564	NUM
ap-10666	110	2	vol	vol	NOUN
ap-10666	110	3	.	.	PUNCT
ap-10666	111	1	65	65	NUM
ap-10666	111	2	no	no	NOUN
ap-10666	111	3	.	.	PUNCT
ap-10666	112	1	5/2025	5/2025	NUM
ap-10666	112	2	gl3	gl3	NOUN
ap-10666	112	3	algebra	algebra	NOUN
ap-10666	112	4	in	in	ADP
ap-10666	112	5	mixed	mixed	ADJ
ap-10666	112	6	matrix	matrix	NOUN
ap-10666	112	7	representations	representation	NOUN
ap-10666	112	8	references	reference	NOUN
ap-10666	112	9	[	[	X
ap-10666	112	10	1	1	NUM
ap-10666	112	11	]	]	PUNCT
ap-10666	112	12	m.	m.	NOUN
ap-10666	112	13	havlíček	havlíček	PROPN
ap-10666	112	14	.	.	PUNCT
ap-10666	113	1	personal	personal	ADJ
ap-10666	113	2	communications	communication	NOUN
ap-10666	113	3	,	,	PUNCT
ap-10666	113	4	1988–2010	1988–2010	NUM
ap-10666	113	5	.	.	PUNCT
ap-10666	114	1	[	[	X
ap-10666	114	2	2	2	X
ap-10666	114	3	]	]	X
ap-10666	114	4	y.	y.	PROPN
ap-10666	114	5	f.	f.	PROPN
ap-10666	114	6	smirnov	smirnov	PROPN
ap-10666	114	7	,	,	PUNCT
ap-10666	114	8	a.	a.	NOUN
ap-10666	114	9	turbiner	turbiner	NOUN
ap-10666	114	10	.	.	PUNCT
ap-10666	115	1	gln+1	gln+1	VERB
ap-10666	115	2	algebra	algebra	NOUN
ap-10666	115	3	of	of	ADP
ap-10666	115	4	matrix	matrix	NOUN
ap-10666	115	5	differential	differential	NOUN
ap-10666	115	6	operators	operator	NOUN
ap-10666	115	7	and	and	CCONJ
ap-10666	115	8	matrix	matrix	NOUN
ap-10666	115	9	quasi	quasi	ADJ
ap-10666	115	10	-	-	ADJ
ap-10666	115	11	exactly	exactly	ADV
ap-10666	115	12	-	-	PUNCT
ap-10666	115	13	solvable	solvable	ADJ
ap-10666	115	14	problems	problem	NOUN
ap-10666	115	15	.	.	PUNCT
ap-10666	116	1	acta	acta	PROPN
ap-10666	116	2	polytechnica	polytechnica	PROPN
ap-10666	116	3	53(5):462–469	53(5):462–469	PROPN
ap-10666	116	4	,	,	PUNCT
ap-10666	116	5	2013	2013	NUM
ap-10666	116	6	.	.	PUNCT
ap-10666	117	1	https://doi.org/10.14311/ap.2013.53.0462	https://doi.org/10.14311/ap.2013.53.0462	PROPN
ap-10666	118	1	[	[	X
ap-10666	118	2	3	3	X
ap-10666	118	3	]	]	X
ap-10666	118	4	f.	f.	PROPN
ap-10666	118	5	tremblay	tremblay	PROPN
ap-10666	118	6	,	,	PUNCT
ap-10666	118	7	a.	a.	NOUN
ap-10666	118	8	v.	v.	PROPN
ap-10666	118	9	turbiner	turbiner	NOUN
ap-10666	118	10	,	,	PUNCT
ap-10666	118	11	p.	p.	PROPN
ap-10666	118	12	winternitz	winternitz	PROPN
ap-10666	118	13	.	.	PUNCT
ap-10666	119	1	an	an	DET
ap-10666	119	2	infinite	infinite	ADJ
ap-10666	119	3	family	family	NOUN
ap-10666	119	4	of	of	ADP
ap-10666	119	5	solvable	solvable	ADJ
ap-10666	119	6	and	and	CCONJ
ap-10666	119	7	integrable	integrable	ADJ
ap-10666	119	8	quantum	quantum	NOUN
ap-10666	119	9	systems	system	NOUN
ap-10666	119	10	on	on	ADP
ap-10666	119	11	a	a	DET
ap-10666	119	12	plane	plane	NOUN
ap-10666	119	13	.	.	PUNCT
ap-10666	120	1	journal	journal	PROPN
ap-10666	120	2	of	of	ADP
ap-10666	120	3	physics	physics	PROPN
ap-10666	120	4	a	a	PRON
ap-10666	120	5	:	:	PUNCT
ap-10666	120	6	mathematical	mathematical	ADJ
ap-10666	120	7	and	and	CCONJ
ap-10666	120	8	theoretical	theoretical	ADJ
ap-10666	120	9	42(24):242001	42(24):242001	NUM
ap-10666	120	10	,	,	PUNCT
ap-10666	120	11	2009	2009	NUM
ap-10666	120	12	.	.	PUNCT
ap-10666	121	1	https://doi.org/10.1088/1751-8113/42/24/242001	https://doi.org/10.1088/1751-8113/42/24/242001	X
ap-10666	122	1	[	[	X
ap-10666	122	2	4	4	NUM
ap-10666	122	3	]	]	PUNCT
ap-10666	122	4	a.	a.	NOUN
ap-10666	122	5	v.	v.	PROPN
ap-10666	122	6	turbiner	turbiner	PROPN
ap-10666	122	7	,	,	PUNCT
ap-10666	122	8	j.	j.	PROPN
ap-10666	122	9	c.	c.	PROPN
ap-10666	122	10	lopez	lopez	PROPN
ap-10666	122	11	vieyra	vieyra	PROPN
ap-10666	122	12	,	,	PUNCT
ap-10666	122	13	m.	m.	NOUN
ap-10666	122	14	a.	a.	NOUN
ap-10666	122	15	guadarrama	guadarrama	PROPN
ap-10666	122	16	-	-	PUNCT
ap-10666	122	17	ayala	ayala	NOUN
ap-10666	122	18	.	.	PUNCT
ap-10666	123	1	gl(3	gl(3	VERB
ap-10666	123	2	)	)	PUNCT
ap-10666	123	3	polynomial	polynomial	ADJ
ap-10666	123	4	integrable	integrable	ADJ
ap-10666	123	5	system	system	NOUN
ap-10666	123	6	:	:	PUNCT
ap-10666	123	7	different	different	ADJ
ap-10666	123	8	faces	face	NOUN
ap-10666	123	9	of	of	ADP
ap-10666	123	10	the	the	DET
ap-10666	123	11	3	3	NUM
ap-10666	123	12	-	-	PUNCT
ap-10666	123	13	body	body	NOUN
ap-10666	123	14	/	/	SYM
ap-10666	123	15	a2	a2	PROPN
ap-10666	123	16	elliptic	elliptic	ADJ
ap-10666	123	17	calogero	calogero	PROPN
ap-10666	123	18	model	model	PROPN
ap-10666	123	19	.	.	PUNCT
ap-10666	124	1	symmetry	symmetry	PROPN
ap-10666	124	2	,	,	PUNCT
ap-10666	124	3	integrability	integrability	NOUN
ap-10666	124	4	and	and	CCONJ
ap-10666	124	5	geometry	geometry	NOUN
ap-10666	124	6	:	:	PUNCT
ap-10666	124	7	methods	method	NOUN
ap-10666	124	8	and	and	CCONJ
ap-10666	124	9	applications	application	NOUN
ap-10666	124	10	20:012	20:012	NUM
ap-10666	124	11	,	,	PUNCT
ap-10666	124	12	2024	2024	NUM
ap-10666	124	13	.	.	PUNCT
ap-10666	125	1	https://doi.org/10.3842/sigma.2024.012	https://doi.org/10.3842/sigma.2024.012	PROPN
ap-10666	125	2	[	[	X
ap-10666	125	3	5	5	NUM
ap-10666	125	4	]	]	X
ap-10666	125	5	y.	y.	PROPN
ap-10666	125	6	smirnov	smirnov	PROPN
ap-10666	125	7	,	,	PUNCT
ap-10666	125	8	a.	a.	NOUN
ap-10666	125	9	turbiner	turbiner	NOUN
ap-10666	125	10	.	.	PUNCT
ap-10666	126	1	lie	lie	VERB
ap-10666	126	2	algebraic	algebraic	ADJ
ap-10666	126	3	discretization	discretization	NOUN
ap-10666	126	4	of	of	ADP
ap-10666	126	5	differential	differential	ADJ
ap-10666	126	6	equations	equation	NOUN
ap-10666	126	7	.	.	PUNCT
ap-10666	127	1	modern	modern	ADJ
ap-10666	127	2	physics	physics	NOUN
ap-10666	127	3	letters	letter	NOUN
ap-10666	127	4	a	a	DET
ap-10666	127	5	10(24):1795–1802	10(24):1795–1802	NUM
ap-10666	127	6	,	,	PUNCT
ap-10666	127	7	1995	1995	NUM
ap-10666	127	8	.	.	PUNCT
ap-10666	128	1	https://doi.org/10.1142/s0217732395001927	https://doi.org/10.1142/s0217732395001927	NUM
ap-10666	128	2	[	[	X
ap-10666	128	3	6	6	NUM
ap-10666	128	4	]	]	PUNCT
ap-10666	128	5	c.	c.	PROPN
ap-10666	128	6	chryssomalakos	chryssomalakos	PROPN
ap-10666	128	7	,	,	PUNCT
ap-10666	128	8	a.	a.	NOUN
ap-10666	128	9	turbiner	turbiner	NOUN
ap-10666	128	10	.	.	PUNCT
ap-10666	129	1	canonical	canonical	ADJ
ap-10666	129	2	commutation	commutation	NOUN
ap-10666	129	3	relation	relation	NOUN
ap-10666	129	4	preserving	preserve	VERB
ap-10666	129	5	maps	map	NOUN
ap-10666	129	6	.	.	PUNCT
ap-10666	130	1	journal	journal	PROPN
ap-10666	130	2	of	of	ADP
ap-10666	130	3	physics	physics	PROPN
ap-10666	130	4	a	a	PRON
ap-10666	130	5	:	:	PUNCT
ap-10666	130	6	mathematical	mathematical	ADJ
ap-10666	130	7	and	and	CCONJ
ap-10666	130	8	general	general	ADJ
ap-10666	130	9	34(48):10475	34(48):10475	NUM
ap-10666	130	10	,	,	PUNCT
ap-10666	130	11	2001	2001	NUM
ap-10666	130	12	.	.	PUNCT
ap-10666	131	1	https://doi.org/10.1088/0305-4470/34/48/312	https://doi.org/10.1088/0305-4470/34/48/312	PROPN
ap-10666	131	2	[	[	X
ap-10666	131	3	7	7	X
ap-10666	131	4	]	]	X
ap-10666	131	5	n.	n.	PROPN
ap-10666	131	6	l.	l.	PROPN
ap-10666	131	7	vasilevski	vasilevski	PROPN
ap-10666	131	8	.	.	PUNCT
ap-10666	132	1	poly	poly	ADJ
ap-10666	132	2	-	-	PUNCT
ap-10666	132	3	fock	fock	ADJ
ap-10666	132	4	spaces	space	NOUN
ap-10666	132	5	.	.	PUNCT
ap-10666	133	1	in	in	ADP
ap-10666	133	2	v.	v.	ADP
ap-10666	133	3	m.	m.	PROPN
ap-10666	133	4	adamyan	adamyan	PROPN
ap-10666	133	5	,	,	PUNCT
ap-10666	133	6	i.	i.	PROPN
ap-10666	133	7	gohberg	gohberg	PROPN
ap-10666	133	8	,	,	PUNCT
ap-10666	133	9	m.	m.	NOUN
ap-10666	133	10	gorbachuk	gorbachuk	NOUN
ap-10666	133	11	,	,	PUNCT
ap-10666	133	12	et	et	PROPN
ap-10666	133	13	al	al	PROPN
ap-10666	133	14	.	.	PUNCT
ap-10666	134	1	(	(	PUNCT
ap-10666	134	2	eds	ed	NOUN
ap-10666	134	3	.	.	PUNCT
ap-10666	134	4	)	)	PUNCT
ap-10666	134	5	,	,	PUNCT
ap-10666	134	6	differential	differential	NOUN
ap-10666	134	7	operators	operator	NOUN
ap-10666	134	8	and	and	CCONJ
ap-10666	134	9	related	related	ADJ
ap-10666	134	10	topics	topic	NOUN
ap-10666	134	11	,	,	PUNCT
ap-10666	134	12	pp	pp	ADJ
ap-10666	134	13	.	.	PUNCT
ap-10666	135	1	371–386	371–386	NUM
ap-10666	135	2	.	.	PUNCT
ap-10666	136	1	birkhäuser	birkhäuser	PROPN
ap-10666	136	2	basel	basel	PROPN
ap-10666	136	3	,	,	PUNCT
ap-10666	136	4	basel	basel	PROPN
ap-10666	136	5	,	,	PUNCT
ap-10666	136	6	2000	2000	NUM
ap-10666	136	7	.	.	PUNCT
ap-10666	137	1	https://doi.org/10.1007/978-3-0348-8403-7_28	https://doi.org/10.1007/978-3-0348-8403-7_28	NOUN
ap-10666	138	1	[	[	X
ap-10666	138	2	8	8	NUM
ap-10666	138	3	]	]	X
ap-10666	138	4	a.	a.	NOUN
ap-10666	138	5	v.	v.	PROPN
ap-10666	138	6	turbiner	turbiner	PROPN
ap-10666	138	7	,	,	PUNCT
ap-10666	138	8	n.	n.	NOUN
ap-10666	138	9	vasilevski	vasilevski	NOUN
ap-10666	138	10	.	.	PUNCT
ap-10666	139	1	poly	poly	ADJ
ap-10666	139	2	-	-	PUNCT
ap-10666	139	3	analytic	analytic	ADJ
ap-10666	139	4	functions	function	NOUN
ap-10666	139	5	and	and	CCONJ
ap-10666	139	6	representation	representation	NOUN
ap-10666	139	7	theory	theory	NOUN
ap-10666	139	8	.	.	PUNCT
ap-10666	140	1	complex	complex	ADJ
ap-10666	140	2	analysis	analysis	NOUN
ap-10666	140	3	and	and	CCONJ
ap-10666	140	4	operator	operator	NOUN
ap-10666	140	5	theory	theory	NOUN
ap-10666	140	6	15(7):110	15(7):110	PROPN
ap-10666	140	7	,	,	PUNCT
ap-10666	140	8	2021	2021	NUM
ap-10666	140	9	.	.	PUNCT
ap-10666	141	1	https://doi.org/10.1007/s11785-021-01154-y	https://doi.org/10.1007/s11785-021-01154-y	PROPN
ap-10666	141	2	565	565	NUM
ap-10666	141	3	https://doi.org/10.14311/ap.2013.53.0462	https://doi.org/10.14311/ap.2013.53.0462	PROPN
ap-10666	141	4	https://doi.org/10.1088/1751-8113/42/24/242001	https://doi.org/10.1088/1751-8113/42/24/242001	PROPN
ap-10666	141	5	https://doi.org/10.3842/sigma.2024.012	https://doi.org/10.3842/sigma.2024.012	PROPN
ap-10666	141	6	https://doi.org/10.1142/s0217732395001927	https://doi.org/10.1142/s0217732395001927	PROPN
ap-10666	141	7	https://doi.org/10.1088/0305-4470/34/48/312	https://doi.org/10.1088/0305-4470/34/48/312	PROPN
ap-10666	141	8	https://doi.org/10.1007/978-3-0348-8403-7_28	https://doi.org/10.1007/978-3-0348-8403-7_28	NOUN
ap-10666	141	9	https://doi.org/10.1007/s11785-021-01154-y	https://doi.org/10.1007/s11785-021-01154-y	PROPN
ap-10666	141	10	acta	acta	PROPN
ap-10666	141	11	polytechnica	polytechnica	PROPN
ap-10666	141	12	65(5):562–565	65(5):562–565	PROPN
ap-10666	141	13	,	,	PUNCT
ap-10666	141	14	2025	2025	NUM
ap-10666	141	15	1	1	NUM
ap-10666	141	16	introduction	introduction	NOUN
ap-10666	141	17	2	2	NUM
ap-10666	141	18	gl3	gl3	NOUN
ap-10666	141	19	mixed	mix	VERB
ap-10666	141	20	representation	representation	NOUN
ap-10666	141	21	in	in	ADP
ap-10666	141	22	a	a	DET
ap-10666	141	23	fock	fock	ADJ
ap-10666	141	24	space	space	NOUN
ap-10666	141	25	3	3	NUM
ap-10666	141	26	three	three	NUM
ap-10666	141	27	canonical	canonical	ADJ
ap-10666	141	28	pairs	pair	NOUN
ap-10666	141	29	3.1	3.1	NUM
ap-10666	141	30	translation	translation	NOUN
ap-10666	141	31	-	-	PUNCT
ap-10666	141	32	invariant	invariant	ADJ
ap-10666	141	33	canonical	canonical	ADJ
ap-10666	141	34	pair	pair	NOUN
ap-10666	141	35	3.2	3.2	NUM
ap-10666	141	36	dilatation	dilatation	NOUN
ap-10666	141	37	-	-	PUNCT
ap-10666	141	38	invariant	invariant	ADJ
ap-10666	141	39	canonical	canonical	ADJ
ap-10666	141	40	pair	pair	NOUN
ap-10666	141	41	3.3	3.3	NUM
ap-10666	141	42	complex	complex	NOUN
ap-10666	141	43	(	(	PUNCT
ap-10666	141	44	z	z	NOUN
ap-10666	141	45	,	,	PUNCT
ap-10666	141	46	)	)	PUNCT
ap-10666	141	47	canonical	canonical	ADJ
ap-10666	141	48	pair	pair	NOUN
ap-10666	141	49	4	4	NUM
ap-10666	141	50	gl3	gl3	ADV
ap-10666	141	51	mixed	mix	VERB
ap-10666	141	52	representations	representation	NOUN
ap-10666	141	53	in	in	ADP
ap-10666	141	54	matrix	matrix	NOUN
ap-10666	141	55	operators	operator	NOUN
ap-10666	141	56	4.1	4.1	NUM
ap-10666	141	57	matrix	matrix	NOUN
ap-10666	141	58	representation	representation	NOUN
ap-10666	141	59	of	of	ADP
ap-10666	141	60	the	the	DET
ap-10666	141	61	gl3	gl3	ADJ
ap-10666	141	62	algebra	algebra	NOUN
ap-10666	141	63	of	of	ADP
ap-10666	141	64	finite	finite	ADJ
ap-10666	141	65	-	-	PUNCT
ap-10666	141	66	difference	difference	ADJ
ap-10666	141	67	operators	operator	NOUN
ap-10666	141	68	4.2	4.2	NUM
ap-10666	141	69	matrix	matrix	NOUN
ap-10666	141	70	representation	representation	NOUN
ap-10666	141	71	of	of	ADP
ap-10666	141	72	the	the	DET
ap-10666	141	73	gl3	gl3	ADJ
ap-10666	141	74	algebra	algebra	NOUN
ap-10666	141	75	of	of	ADP
ap-10666	141	76	discrete	discrete	ADJ
ap-10666	141	77	operators	operator	NOUN
ap-10666	141	78	4.3	4.3	NUM
ap-10666	141	79	matrix	matrix	NOUN
ap-10666	141	80	representation	representation	NOUN
ap-10666	141	81	of	of	ADP
ap-10666	141	82	the	the	DET
ap-10666	141	83	gl3	gl3	ADJ
ap-10666	141	84	algebra	algebra	NOUN
ap-10666	141	85	of	of	ADP
ap-10666	141	86	mixed	mixed	ADJ
ap-10666	141	87	finite	finite	NOUN
ap-10666	141	88	-	-	PUNCT
ap-10666	141	89	difference	difference	NOUN
ap-10666	141	90	/	/	SYM
ap-10666	141	91	discrete	discrete	ADJ
ap-10666	141	92	operators	operator	NOUN
ap-10666	141	93	4.4	4.4	NUM
ap-10666	141	94	matrix	matrix	NOUN
ap-10666	141	95	representation	representation	NOUN
ap-10666	141	96	of	of	ADP
ap-10666	141	97	complex	complex	ADJ
ap-10666	141	98	(	(	PUNCT
ap-10666	141	99	z	z	NOUN
ap-10666	141	100	,	,	PUNCT
ap-10666	141	101	)	)	PUNCT
ap-10666	141	102	generators	generator	NOUN
ap-10666	141	103	5	5	NUM
ap-10666	141	104	conclusion	conclusion	NOUN
ap-10666	141	105	acknowledgements	acknowledgement	NOUN
ap-10666	141	106	references	reference	NOUN