Description:

This course is an introduction to the geometric approach to representations of real reductive groups through Beilinson-Bernstein localization of (g,K)-modules. We plan to get to the relation between geometric classification and the Langlands classification of irreducible (g,K)-modules, and the geometric description of Langlands parameter spaces due to Adams-Barbasch-Vogan. If time permits, we will discuss recent developments based on interests, such as unitarizability or categorification of Vogan duality.

Prerequisite:

Some knowledge of semisimple Lie algebras, algebraic groups, D-modules. Familiarity with localization will be helpful.

References:

1. Localization and standard modules for real semisimple Lie groups II (by H. Hecht, D. Milicic, W. Schmid, and J. Wolf), available at https://www.math.utah.edu/~milicic/Eprints/hmsw2.pdf

2. The Langlands Classification and Irreducible Characters for Real Reductive Groups (by J. Adams, D. Barbasch, D. Vogan)

Target Audience: Undergraduate students, Graduate students

Teaching Language: English

Registration: https://www.wjx.top/vm/mBWVAsY.aspx#