English

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 CCnC^\vee C_n and relates it, at the classical level q=1q = 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.

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!)