## Geometry Seminar

**Date: ** November 23, 2020

**Time: ** 3:00PM - 3:50PM

**Location: ** zoom

**Speaker: **Tom Gannon, University of Texas

**Title: ***Recovering Lie(G)-Modules from the Weyl Group Action*

**Abstract: **Let G be a semisimple group, for example, G = SL_n. One pervasive theme in representation theory is recovering information about representations of Lie(G) from a maximal torus T in G (for example, T may be identified with the diagonal matrices of SL_n) and its natural action by the Weyl group W := N_G(T)/T. In this talk, we will explore historical incarnations of this theme--specifically, finite dimensional Lie(G) representations and the study of the BGG category O--and then discuss a recent theorem which identifies a "varying central character" version of category O with sheaves on a space determined by the action of W on T. No prior knowledge of representation theory will be assumed.