# Seminar by Erik Backelin (Universidad de los Andes, Colombia)

Title: Singular localization of g-modules

2013.11.01 | Christine Dilling

 Date Wed 13 Apr Time 15:15 — 16:15 Location Aud D3

Abstract:

(Joint with K. Kremnizer) Let $\mathfrak{g}$ be a complex reductive Lie algebra. We prove a Beilinson-Bernstein localization theorem for the category of $\mathfrak{g}$-modules at a singular central character using a sheaf of extended differential operators on a parabolic flagmanifold. This has earlier been done in finite characteristic by Bezrukavninkov, Mircovic and Rumynin. As an application we generalize an equivalence of Soergel between a regular block in category $\mathcal{O}$ and a category of Harish-Chandra bimodules to singular blocks.

In subsequent talks we will do singular localization for quantum groups using quantized versions of the constructions giving here.

Seminar