# Introduction to Geometric Representation Theory - Spring 2024

**Time and Location:** Every Thursday at 2:00 pm in Evans 961 during the Spring 2024 semester.

**Contact info:**

alangoldfarb [AT] berkeley [DOT] edu

shreepranav_varma [AT] berkeley [DOT] edu

Below is the reading material for the seminar. This page will be updated as the semester progresses.

### Borel-Weil-Bott theorem

The best reference in my opinion is Several Complex Variables with Connections to Algebraic Geometry and Lie Groups - Chapter 16.

If you have trouble accessing the above, this note is a very similar presentation.

Section 6.5 of these notes from a course taught at the University of Toronto provides a nice introductory perspective to the Borel-Weil theorem.

An abridged proof of Borel-Weil-Bott written by Jacob Lurie.

### D-modules and Beilinson-Bernstein localization

Introductory notes on D-modules and Beilinson-Bernstein - Chapters 1-4 (3 is not strictly necessary).

The first few sections of these lecture notes from a course taught at Stony Brook give motivation for the definition of D-modules.

Sections 3-9 of these notes cover Beilinson-Bernstein localization and the prerequisite material.

Bernstein's notes on D-modules might also be a helpful reference.

### Category O and the Chevalley and Harish-Chandra isomorphisms

Notes from a talk at David Nadler's seminar introducing the Chevalley and Harish-Chandra isomorphisms to motivate category O.
Representations of Semisimple Lie Algebras in the BGG Category O is a standard refrence on this topic.

Some notes on chapters 1-3 of the above book.

Helpful notes from The Automorphic Project.

Thanks to David Nadler for mentoring this seminar.