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arXiv · 2606.27901

Zonal Spherical Functions of Quantum Symmetric Pairs

Philip Schlösser
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Abstract

We identify the zonal and character spherical functions for quantum symmetric pairs with the symmetric Koornwinder--Macdonald polynomials. To this end, the methods of Letzter's 2004 paper are translated to modern conventions and right coideal subalgebras, and extended to non-standard cases and cases with non-reduced restricted root systems. For the last elusive Satake type, FII, a conjecture is provided.

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Philip Schlösser. 2026-06-26. Zonal Spherical Functions of Quantum Symmetric Pairs. https://arxiv.org/abs/2606.27901

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