Speaker : Tom Gannon (University of Texas at Austin)
Title : Categorical Representation Theory and the Coarse Quotient
Time : 2021-12-08 (Wed) 9:00 - 10:15
Place : Auditorium, 6 Floor, Institute of Mathematics (NTU Campus)
Much of modern geometric representation theory of reductive groups can be interpreted as the study of groups acting on categories and the natural symmetries that the various invariants obtain; for example, the Beilinson-Bernstein localization theorem, the relationship between the BGG category O and Soergel modules, and the study of Harish-Chandra bimodules all fall under this paradigm. It is therefore of natural interest to study the collection of categories with an action of a given reductive group G. The main theorem of this talk is that one can classify a "dense open" subset of categories with a G-action, which we call nondegenerate G-categories, using only the root datum of G.

In this talk, we will review the notion of groups acting on categories and some preliminary results to state the main theorem precisely, and then describe some of the main steps of the proof. Time permitting, we will also discuss a conjecture of Ben-Zvi and Gunningham on the essential image of a parabolic restriction functor and discuss its proof for nondegenerate G-categories.