[Research field]
Mathematical Physics: Study on representation theory, difference equations, special functions and combinatorics arising from quantum integrable systems.
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.
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 dimension of the space spanned by MZV's over , and present
an application to MZV.
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.
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 was studied by van Meer and Stokman. We construct an integral
formula for solutions to our compatible system in a special case.
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 version of the singular polynomials studied by Dunkl. We prove
that our solutions contain those obtained as a scaling limit of matrix elements
of the ve...
In the recent study of correlation functions for the infinite XXZ spin chain,
a new pair of anti-commuting operators was introduced. They act on
the space of quasi-local operators, which are local operators multiplied by the
disorder operator. For the inhomogeneous chain with the spectral parameters , these operators have simple poles at . The residues
are d...
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