Kazuhiko Aomoto

On Elliptic Product Formulas for Jackson Integrals Associated with Reduced Root Systems

In this note, we state certain product formulae for Jackson integrals associated with any root systems, involved in elliptic theta functions which appear as connection coefficients. The fomulae arise naturally in case of arbitrary root systems by extending the connection problem which has been investigated in [1, 4] in case ofA type root system. This is also connected with the Macdonald-Morris constant term identity investigated by I. Cherednik [6], and K. Kadell [15] on the one hand, and of the Askey-Habsieger-Kadells q-Selberg integral formula and its extensions [4, 8, 12, 14, 15] on the other. This is also related with some of the results due to R.A. Gustafson [10, 11], although our integrands are different from his.

INTEGRAL REPRESENTATION FOR THE GR AND PARTITION FUNCTION IN QUANTUM STATISTICAL MECHANICS OF EXCLUSION STATISTICS

We derive an exact integral representation for the gr and partition function for an ideal gas with exclusion statistics. Using this we show how the Wus equation for the exclusion statistics appears in the problem. This can be an alternative proof for the Wus equation. We also discuss that singularities are related to the existence of a phase transition of the system.

On a Jacobian Identity Associated with Real Hyperplane Arrangements

AbstractFor

Derivation of q-difference equation from connection matrix for selberg type jackson integrals

x \in (a_{j - 1} ,a_j )(j = ,...,p + 1;a_0 : = - \infty ,a_{p + 1} : = \infty )

Introduction: the Euler−Gauss Hypergeometric Function

the mapping

Holonomic Difference Equations and Asymptotic Expansion

T_j :w = x - \sum {_{l = 1}^p {\lambda }_l /(x - a_l )({\lambda }_l >0,a_l } \in {R)}