Keller VandeBogert, University of Notre Dame
Representation Theory in Positive Characteristic
4:00 pm–4:50 pm
Avery Hall Room: 115
Additional Info: AVH
This talk will be an expository talk on some of the wild behavior that occurs when passing from characteristic 0 representation theory to the “modular” case, with special emphasis on the general linear group. A fundamental question at the heart of representation theory is to understand the building blocks of representations (ie, the irreducibles) and how to decompose a representation into its irreducible pieces. In characteristic 0, the representation theory of the general linear group is well-understood, and the building blocks correspond to classical objects known as Schur modules. Moreover, decomposing representations reduces to verifying polynomial identities, thus spawning the theory of symmetric functions. In positive characteristic, however, the story is totally different and many basic questions are widely regarded as hopelessly open problems. My goal is to compare the characteristic 0 case to the characteristic p case, showing just how bad things can get (while also showcasing some of the results proved over the years to develop a “characteristic-free” representation theory of the general linear group).