DAHAs and character varieties
组织者
演讲者
Oleg Chalykh
时间
2024年04月15日 11:30 至 13:00
地点
A4-1
摘要
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).