Quantum spherical functions of type χ as Macdonald-Koornwinder polynomials

2025/02/26 by Meereboer, Stein · 1 citation
#43 #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2502.19232

Abstract

The theory of quantum symmetric pairs is applied to q-special functions. Previous work shows the existence of a family χ-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 AIII_a.

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