Nonsymmetric interpolation Macdonald polynomials and g_n basic hypergeometric series
Alain Lascoux, Eric M. Rains, S. Ole Warnaar
TL;DR
This paper introduces new hypergeometric series of type g_n using nonsymmetric interpolation Macdonald polynomials, deriving key identities like a q-binomial theorem, q-Gauss sum, and transformation formulas.
Contribution
It develops a novel application of interpolation Macdonald polynomials to define and analyze new basic hypergeometric series of type g_n, including fundamental identities.
Findings
New q-binomial theorem for g_n series
New q-Gauss sum formula for g_n series
Transformation formulas for g_n hypergeometric series
Abstract
The Knop-Sahi interpolation Macdonald polynomials are inhomogeneous and nonsymmetric generalisations of the well-known Macdonald polynomials. In this paper we apply the interpolation Macdonald polynomials to study a new type of basic hypergeometric series of type g_n. Our main results include a new q-binomial theorem, new q-Gauss sum, and several transformation formulae for g_n series.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Nonlinear Waves and Solitons · Advanced Combinatorial Mathematics