We consider an eigenvalue problem for a discrete analogue of the Hamiltonian
of the non-ideal Bose gas with delta-potentials on a circle. It is a
two-parameter deformation of the discrete Hamiltonian for joint moments of the
partition function of ...
We prove some relations for the -multiple zeta values (MZV). They are
-analogues of the cyclic sum formula, the Ohno relation and the Ohno-Zagier
relation for the multiple zeta values (MZV). We discuss the problem to
determine the dimensi...
We introduce an algebra which describes the multiplication structure of a
family of q-series containing a q-analogue of multiple zeta values. The double
shuffle relations are formulated in our framework. They contain a q-analogue of
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...
Proceedings of the Infinite Analysis 09 -- New Trends in Quantum Integrable Systems 421-450 Nov 2010 [Refereed]
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 which in the case
of type $G...
We construct special solutions to the rational quantum Knizhnik-Zamolodchikov
equation associated with the Lie algebra . The main ingredient is a
special class of the shifted non-symmetric Jack polynomials. It may be regarded
as a shifted ve...