Speaker:  Valerio Toledano-Laredo (Northeastern University)

Title:  Pure Braid Group Actions on Category O 

Abstract:  Let g be a symmetrisable Kac-Moody algebra. The corresponding quantum Weyl group operators give an action of the braid group of g on integrable
modules over the quantum group U_hg.  Answering a question of Pavel
Etingof, we prove that the restriction of this action to the pure braid group
extends to all (not necessarily integrable) category O modules for Uhg.
We also show that this action describes the monodromy of the Casimir
connection of g on category O modules. This is joint work with Andrea
Appel, and is based on https://arxiv.org/abs/2208.05331 [1]