# Introduction to Geometric Representation Theory - Spring 2024

Here is where we'll post the reading material for the introductory GRT reading group. I'll update this page regularly as the semester progresses.

We meet on Thursdays at 2:00 pm (directly after the GRT seminar) in Evans 961.

Next time we meet (4/18) we'll define lie algebroids and the sheaf of twisted differential operators associated to an arbitrary weight. Then we'll get to the statement of Beilinson-Bernstein localization.

Contact info:

alangoldfarb [AT] berkeley [DOT] edu

shreepranav_varma [AT] berkeley [DOT] edu

## 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 (These are very readable but have some typos).

These very useful lecture notes are from a course on algebraic D-modules taught at Stony Brook.

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

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

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

Representations of Semisimple Lie Algebras in the BGG Category O.

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

Helpful notes from The Automorphic Project.

Notes from a talk at David Nadler's seminar.