Reading Seminar
Thursday, 3rd March · 2:30 – 3:45 pm
Google Meet joining info
Video call link:
https://meet.google.com/auv-mwkn-ixh
Title: Modular representations of Algebraic groups,
Abstract:
We have studied the Borel-Weil-Bott theorem and Kempf vanishing theorem. Using Serre duality and Borel-Weil-Bott we will first discuss the irreducibility of the Weyl modules over a field of characteristics 0. Then moving to the prime characteristic field and we will briefly discuss the Steinberg Tensor product theorem. Finally we will wrap up the talk by browsing through some later developments and recent trends.
Here is the link to the notes of all the talks.
https://drive.google.com/file/d/1PNqfriaSWV4QbLAC9xcYuwPAu9xhjP6m/view?usp=sharing
So far the main references have been Jantzen's book ``Representation theory of Algebraic Groups'' and a note by Andersen ``Modular representation of Algebraic groups and Relations to Quantum groups''.
For this talk besides the previous references I would also like to point out the following two articles which discuss a few recent big developments in representation theory of reductive groups in prime characteristics and geometric representation theory.
1. Lectures on Geometry and modular representation theory of algebraic groups by Joshua Ciappara and Geordie Williamson
https://arxiv.org/pdf/2004.14791.pdf
2. Modular representations and reflection subgroups by Geordie Williamson
https://arxiv.org/pdf/2001.04569.pdf