A bilateral extension of the 𝑞-Selberg integral

Ito, Masahiko; Forrester, Peter

doi:10.1090/tran/6851

A bilateral extension of the $q$-Selberg integral
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by Masahiko Ito and Peter J. Forrester PDF

Trans. Amer. Math. Soc. 369 (2017), 2843-2878 Request permission

Abstract:

A multi-dimensional bilateral $q$-series extending the $q$-Selberg integral is studied using concepts of truncation, regularization and connection formulae. Following Aomoto’s method, which involves regarding the $q$-series as a solution of a $q$-difference equation fixed by its asymptotic behavior, an infinite product evaluation is obtained. The $q$-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 $q$-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.

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