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

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arxiv 2410.23456 v1 pith:VLZSIGX5 submitted 2024-10-30 math.RT

Oleg Chalykh , Bradley Ryan This is my paper · ORCID
classification math.RT
keywords charactertypeaffinealgebraby-productcertainclassicalcompleted
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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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  1. Integrable systems from Poisson reductions of generalized Hamiltonian torus actions

    math-ph 2025-07 unverdicted novelty 7.0 of 10

    Develops sufficient conditions for Poisson reduction of generalized Hamiltonian torus actions to preserve integrability and applies them to open problems on Lie group doubles and flat-connection moduli spaces.

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