$q$-Difference Systems for the Jackson Integral of Symmetric Selberg Type

Abstract

We provide an explicit expression for the first order $q$-difference system for the Jackson integral of symmetric Selberg type. The $q$-difference system gives a generalization of $q$-analog of contiguous relations for the Gauss hypergeometric function. As a basis of the system we use a set of the symmetric polynomials introduced by Matsuo in his study of the $q$-KZ equation. Our main result is an explicit expression for the coefficient matrix of the $q$-difference system in terms of its Gauss matrix decomposition. We introduce a class of symmetric polynomials called interpolation polynomials, which includes Matsuo's polynomials. By repeated use of three-term relations among the interpolation polynomials we compute the coefficient matrix.

References in corpus (4)

• Construction of $R$-matrices for symmetric tensor representations related to $U_q(\widehat{s{l}_n})$
• Matrix product solution to the reflection equation associated with a coideal subalgebra of $U_q(A_{n-1}^{(1)})$
• AFLT-type Selberg integrals
• Connection Formula for the Jackson Integral of Type $A_n$ and Elliptic Lagrange Interpolation

Cited by in corpus (1)

• Non-Stationary Difference Equation and Affine Laumon Space II: Quantum Knizhnik-Zamolodchikov Equation