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

Symmetry Integrability and Geometry-Methods and Applications

article

Masahiko Ito¹ 

[1] Department of Mathematical Sciences, University of the Ryukyus

关键词: q-difference equations;    Selberg type integral;    contiguous relations;    Gauss decomposition 2020 Mathematics Subject Classification 33D60;    39A13;   

DOI  :  10.3842/SIGMA.2020.113

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown