G-modules: Stable Categories and Subcoalgebras - Lecture on Affine Group Scheme Representations

Explore the intricacies of G-modules in this 54-minute lecture presented by Eric Friedlander from the University of Southern California's Mathematics department. Delve into the concept of stable module categories for arbitrary G-modules and their connection to support theory, specifically for representations of affine group schemes over a field. Examine the formulation of these categories for linear algebraic groups and discover how they complement support theory through filtrations of G-modules. These filtrations are associated with ascending, converging sequences of subcoalgebras within the coordinate algebra O(G) of G. Recorded on January 9, 2024, this talk is part of the Symmetric Tensor Categories and Representation Theory Workshop hosted by the Institute for Pure & Applied Mathematics (IPAM) at UCLA.