DAHAs and character varieties
Organizers
Speaker
Oleg Chalykh
Time
Monday, April 15, 2024 11:30 AM - 1:00 PM
Venue
A4-1
Abstract
Consider the spherical subalgebra of the double affine Hecke algebra of type C^\vee C_n. It depends on the quantum parameter q and five couplings t=(t_0, t_1, t_2, t_3, t_4). It is known that for q=1 this algebra becomes commutative, so one may ask for its geometric interpretation. We show that it is isomorphic to the ring of functions on a certain character variety of a 4-punctured Riemann sphere. This proves a conjecture of Etingof-Gan-Oblomkov. As a by-product, we establish that this character variety provides a completed phase space of the classical Koornwinder-van Diejen particle system, and explicitly integrate its dynamics. This is joint work with Bradley Ryan (Leeds).
Speaker Intro
Oleg Chalykh obtained his PhD from Moscow State University in 1992, after which he worked at the Moscow State University and Kolmogorov School, then held visiting research positions at Loughborough University (UK) and Cornell University (USA) before moving to the University of Leeds (UK) in 2004 where he has been since. His interests include integrable systems, mathematical physics, and representation theory.