MS Seminar (Mathematics - String Theory)

Speaker: Valerio Toledano Laredo (Northeastern University)
Title: Coxeter categories, the Casimir connection and quantum Weyl groups
Date: Tue, May 14, 2019, 15:30 - 17:00
Place: Seminar Room A
Abstract: I will explain the definition of a Coxeter category C. The latter is to a generalised Braid group B_W what a braided tensor Category is to the tower of Artin braid groups {B_n}. The data which defines the action of B_W is similar in flavor to the associativity constraints in a tensor category, but is related to the coherence of a family of fiber functors on C. I will then outline how to construct such a structure on integrable, category O representations of a symmetrisable Kac-Moody algebra g, in a way that incorporates the monodromy of the KZ and Casimir connections of g. The rigidity of this structure implies in particular that the monodromy of the latter connection is described by Lusztig’s quantum Weyl group operators for the quantum group U_h(g).
Remarks: Blackboard talk