Emmy-Noether-Seminar: Minimal tilting complexes and generic direct summands of tensor products for reductive algebraic groups

Minimal tilting complexes and generic direct summands of tensor products for reductive algebraic groups

Jonathan Gruber (York)

Abstract: Let G be a reductive algebraic group over an algebraically closed field of positive characteristic. In this talk, I will explain a new approach to studying tensor products in the category of rational representations of G, via minimal complexes of tilting modules. I will also explain how this approach allows us to define a new class of indecomposable G-modules, called generic direct summands, which appear generically in Krull-Schmidt decompositions of tensor products of simple G-modules.