A bilateral extension of the $q$-Selberg integral
Abstract
A multi-dimensional bilateral -series extending the -Selberg integral is studied using concepts of truncation, regularization and connection formulae. Following Aomoto's method, which involves regarding the -series as a solution of a -difference equation fixed by its asymptotic behavior, an infinite product evaluation is obtained. The -difference equation is derived applying the shifted symmetric polynomials introduced by Knop and Sahi. As a special case of the infinite product formula, Askey--Evans's -Selberg integral evaluation and its generalization by Tarasov--Varchenko and Stokman is reclaimed, and an explanation in the context of Aomoto's setting is thus provided.
Keywords
Cite
@article{arxiv.1309.0001,
title = {A bilateral extension of the $q$-Selberg integral},
author = {Masahiko Ito and Peter J. Forrester},
journal= {arXiv preprint arXiv:1309.0001},
year = {2017}
}
Comments
36 pages. V6: minor corrections. arXiv admin note: text overlap with arXiv:1308.6650