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
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 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 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 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...
We studied the rational quantum Knizhnik-Zamolodchikov (rational qKZ) equation, which is a difference equation playing an important role in the theory of massive integrable quantum field theories. We obtained special solutions and constructed a sy...