DAHAs of Type $C^\vee C_n$ and Character Varieties
Representation Theory
2024-11-01 v1
Abstract
This paper studies the spherical subalgebra of the double affine Hecke algebra of type and relates it, at the classical level , 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.
Keywords
Cite
@article{arxiv.2410.23456,
title = {DAHAs of Type $C^\vee C_n$ and Character Varieties},
author = {Oleg Chalykh and Bradley Ryan},
journal= {arXiv preprint arXiv:2410.23456},
year = {2024}
}
Comments
39 pages; preliminary version (comments are welcome!)