Antoine Touzé (Lille), Functorial Steinberg tensor product theorems.

Abstract:

R. Steinberg has proved several tensor decomposition theorems, which are of fundamental importance in the representation theory of algebraic groups and finite groups of Lie type.

In this talk, we will explain similar tensor product theorems in the context of generic representation theory (aka representations of small additive categories - in the spirit of some work of N. Kuhn or M. Auslander). As an application of this approach, we obtain new proofs of the classical decomposition theorems of Steinberg for GLn, as well as generalizations for more general finite dimensional algebras.