Beilinson-Bernstein Localization

Date

2024

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Take a complex reductive group G and its lie algebra g. Understanding the representations of g is a major problem within mathematics. A key tool in this direction is try and realize any such representation as some type of generalized functions on a space. This would allow geometric tools to be applied in order to understand the representations of g. This is done so in a theorem of Beilinson and Bernstein where they show that any g representation can be realized as the global sections of a twisted D-module over the flag variety G/B, where B is a Borel subgroup of G. This paper will provide an exposition of some topics in the geometry of Lie algebras and groups necessary to prove part of this theorem.

Department

Description

LCSH Subject Headings

Citation

Collections