Title: Singular localization of g-modules
2013.11.01 |
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.