4,462 research outputs found
Form factors of SU(N) invariant Thirring model
We obtain a new integral formula for solutions of the rational quantum
Knizhnik-Zamolodchikov equation associated with Lie algebra sl_{N} at level
zero. Our formula contains the integral representation of form factors of SU(N)
invariant Thirring model constructed by F. Smirnov. We write down recurrence
relations arising from the construction of the form factors. We check that the
recurrence relations hold for the form factors of the energy momentum tensor.Comment: 47 page
On solutions of the q-hypergeometric equation with q^{N}=1
We consider the q-hypergeometric equation with q^{N}=1 and . We solve this equation on the space of functions given by
a power series multiplied by a power of the logarithmic function. We prove that
the subspace of solutions is two-dimensional over the field of quasi-constants.
We get a basis for this space explicitly. In terms of this basis, we represent
the q-hypergeometric function of the Barnes type constructed by Nishizawa and
Ueno. Then we see that this function has logarithmic singularity at the origin.
This is a difference between the q-hypergeometric functions with 0<|q|<1 and at
|q|=1.Comment: 9 page
Algebraic construction of multi-species q-Boson system
We construct a stochastic particle system which is a multi-species version of
the q-Boson system due to Sasamoto and Wadati. Its transition rate matrix is
obtained from a representation of a deformation of the affine Hecke algebra of
type GL.Comment: 18 page
Differential equations compatible with boundary rational qKZ equation
We give differential equations compatible with the rational qKZ equation with
boundary reflection. The total system contains the trigonometric degeneration
of the bispectral qKZ equation of type (C_{n}^{\vee}, C_{n}) which in the case
of type GL_{n} was studied by van Meer and Stokman. We construct an integral
formula for solutions to our compatible system in a special case.Comment: 25 pages, no figure; Section 4.2, 4.4 and 4.6 are revised
On the eigenfunctions for the multi-species q-Boson system
In a previous paper a multi-species version of the q-Boson stochastic
particle system is introduced and the eigenfunctions of its backward generator
are constructed by using a representation of the Hecke algebra. In this article
we prove a formula which expresses the eigenfunctions by means of the
q-deformed bosonic operators, which are constructed from the L-operator of
higher rank found in the recent work by Garbali, de Gier and Wheeler. The
L-operator is obtained from the universal R-matrix of the quantum affine
algebra of type A_{r}^{(1)} by the use of the q-oscillator representation. Thus
our formula may be regarded as a bridge between two approaches to studying
integrable stochastic systems by means of the quantum affine algebra and the
affine Hecke algebra.Comment: We added an explanation of the relation between our result and the
previous results due to Borodin, and Motegi and Sakai in Section 5.
A restricted sum formula for a q-analogue of multiple zeta values
We prove a new linear relation for a q-analogue of multiple zeta values. It
is a q-extension of the restricted sum formula obtained by Eie, Liaw and Ong
for multiple zeta values.Comment: 12 pages, no figur
A deformation of affine Hecke algebra and integrable stochastic particle system
We introduce a deformation of the affine Hecke algebra of type GL which
describes the commutation relations of the divided difference operators found
by Lascoux and Schutzenberger and the multiplication operators. Making use of
its representation we construct an integrable stochastic particle system. It is
a generalization of the q-Boson system due to Sasamoto and Wadati. We also
construct eigenfunctions of its generator using the propagation operator. As a
result we get the same eigenfunctions for the (q, \mu, \nu)-Boson process
obtained by Povolotsky.Comment: 18 pages, no fugur
The q-twisted cohomology and the q-hypergeometric function at |q|=1
We construct the q-twisted cohomology associated with the q-multiplicative
function of Jordan-Pochhammer type at |q|=1. In this framework, we prove the
Heine's relations and a connection formula for the q-hypergeometric function of
the Barnes type. We also prove an orthogonality relation of the q-little Jacobi
polynomials at |q|=1.Comment: 16 page
Quadratic relations for a q-analogue of multiple zeta values
We obtain a class of quadratic relations for a q-analogue of multiple zeta
values (qMZV's). In the limit q->1, it turns into Kawashima's relation for
multiple zeta values. As a corollary we find that qMZV's satisfy the linear
relation contained in Kawashima's relation. In the proof we make use of a
q-analogue of Newton series and Bradley's duality formula for finite multiple
harmonic q-series.Comment: 14 page
The integral formula for the solutions of the quantum Knizhnik-Zamolodchikov equation associated with for |q|=1
We write the integral formula of Tarasov-Varchenko type for the solutions to
the quantum Knizhnik-Zamolodchikov associated with a tensor product the of
vector representations of sl_n. We consider the case where the deformation
parameter q satisfies |q|=1. We use the bosonization of the type II vertex
operators in order to find the hypergeometric pairing in this setting.Comment: submitted to the proceedings for SIDE III meeting at Sabaudia near
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