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arXiv · 2410.23456

DAHAs of Type $C^\vee C_n$ and Character Varieties

Oleg Chalykh·Bradley Ryan
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Abstract

This paper studies the spherical subalgebra of the double affine Hecke algebra of type $C^\vee C_n$ and relates it, at the classical level $q = 1$, to a certain character variety of the four-punctured Riemann sphere. This establishes a conjecture from math.QA/0504089. As a by-product, we find a completed phase space for the trigonometric van Diejen system, explicitly integrate its dynamics and explain how it can be obtained via Hamiltonian reduction.

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BibTeXRIS

Oleg Chalykh, Bradley Ryan. 2024-10-30. DAHAs of Type $C^\vee C_n$ and Character Varieties. https://arxiv.org/abs/2410.23456

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