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

We provide an explicit expression for the first-order -difference system for the Jackson integral of symmetric Selberg type. The q-difference system gives a generalization of the -analog of contiguous relations for the Gauss hypergeometric function. As a basis of the system, we use a set of symmet...

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Bibliographic Details
Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2020
Main Author: Ito, Masahiko
Format: Article
Language:English
Published: Інститут математики НАН України 2020
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/211007
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:q-Difference Systems for the Jackson Integral of Symmetric Selberg Type. Masahiko Ito. SIGMA 16 (2020), 113, 31 pages

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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Summary:We provide an explicit expression for the first-order -difference system for the Jackson integral of symmetric Selberg type. The q-difference system gives a generalization of the -analog of contiguous relations for the Gauss hypergeometric function. As a basis of the system, we use a set of symmetric polynomials introduced by Matsuo in his study of the -KZ equation. Our main result is an explicit expression for the coefficient matrix of the -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.
ISSN:1815-0659