In May 2016, I attended a week-long workshop on Branching Problems for Reductive Groups at the Institut Mittag-Leffler (Djursholm, Sweden).
I gave a lecture on An overview of representations of reductive algebraic groups; essentially everything I discussed can be found in the text of Jens Jantzen on the representation theory of algebraic groups. I tried to focus on things that seem to me to be relevant to the difficulties presented by modular representation theory to “branching problems”:
- (Hochschild) cohomology,
- the description of simple representations for reductive groups,
- reduction mod p and
- the Jantzen filtration of Weyl modules Δ(λ).
Here are the slides from my talk.