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arXiv · 2502.19232

Quantum spherical functions of type $\chi$ as Macdonald-Koornwinder polynomials

Stein Meereboer
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Abstract

The theory of quantum symmetric pairs is applied to $q$-special functions. Previous work shows the existence of a family $\chi$-spherical functions indexed by the integers for each Hermitian quantum symmetric pair. A distinguished family of such functions, invariant under the Weyl group of the restricted roots, is shown to be a family of Macdonald-Koornwinder polynomials if the restricted root system is reduced or if the Satake diagram is of type $\mathsf{AIII_a}$.

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BibTeXRIS

Stein Meereboer. 2025-02-26. Quantum spherical functions of type $\chi$ as Macdonald-Koornwinder polynomials. https://arxiv.org/abs/2502.19232

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