Beilinson-Bernstein localization via wonderfulasymptotics.

Abstract: We explain how a doubled version of theBeilinson-Bernstein localization functor can be understood using the geometryof the wonderful compactification of a group. Specifically, bimodules for theLie algebra give rise to monodromic D-modules on the horocycle space, and tofiltered D-modules on the group that respect a certain matrix coefficientsfiltration. These two categories of D-modules are related via an associatedgraded construction in a way compatible with localization, Verdier specialization,the Vinberg semigroup, and additional structures. This talk is based on jointwork with David Ben-Zvi.

algebraic geometryalgebraic topologycategory theoryrings and algebrasrepresentation theory

Audience: researchers in the topic

Seminar on Representation Theory and Algebraic Geometry