A reproducing kernel for nonsymmetric Macdonald polynomials
K. Mimachi, M. Noumi
TL;DR
This paper introduces a new Cauchy-type formula for nonsymmetric Macdonald polynomials, providing an explicit reproducing kernel for these polynomials as joint eigenfunctions of q-Dunkl operators.
Contribution
It offers a novel explicit formula for the reproducing kernel of nonsymmetric Macdonald polynomials, advancing understanding of their structure and properties.
Findings
Derived a new Cauchy-type formula for nonsymmetric Macdonald polynomials
Provided an explicit reproducing kernel for the polynomial ring
Enhanced tools for studying eigenfunctions of q-Dunkl operators
Abstract
We present a new formula of Cauchy type for the nonsymmetric Macdonald polynomials which are joint eigenfunctions of q-Dunkl operators. This gives the explicit formula for a reproducing kernel on the polynomial ring of n variables.
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Taxonomy
TopicsNonlinear Waves and Solitons · Algebraic structures and combinatorial models · Advanced Algebra and Geometry