Title: The Finkelberg-Ginzburg Mirabolic Monodromy Conjecture
Speaker: Robin Walters (Northeastern University)
Abstract: This is a joint work-in-progress with Valerio Toledano Laredo. We study the monodromy of the trigonometric $KZ$ connection associated to the covariant representation $J _{\theta}$ of the trigonometric Cherednik algebra $H_c$. This is motivated by Finkelberg and Ginzburg's study of a mirabolic version $G_{\theta,c}$ of the Harish-Chandra $D$-module defined by Hotta and Kashiwara. Through Hamiltonian reduction and the $KZ$ functor, $G_{\theta,c}$ can be understood by the above monodromy problem. The monodromy of $J_{\theta}$ was computed by Opdam, Heckman, and Cherednik for values of $\theta$ and $c$ when the connection is non-resonant. Our aim is to compute monodromy for all values of the parameters. Our tools are Opdam's shift operators in c as well as shift operators in \theta arising from a commuting copy of the difference Cherednik algebra. In this talk, I will focus on the example of the rank one case, which is easier to illustrate and fully proved.
Seminar URL: https://research.math.osu.edu/reps/