# Thorsten Heidersdorf

## "Pro-Reductive Groups Attached to Representations of the General Linear Supergroup Gl(m|n)"

 Date: Tue, September 20, 2016 Time: 11:00 Place: Seminar Room (120), Research I

Abstract: The tensor category $$\text{Rep}\big(\text{Gl}(m|n)\big)$$ is not semisimple and the decomposition of tensor products into the indecomposable constituents is only known in very special cases. Every nice enough tensor category $$C$$ has a unique proper tensor ideal $$N$$, the negligible morphisms, such that the quotient $$C/N$$ is a semisimple tensor category. I will apply this construction to the tensor category $$C=\text{Rep}\big(\text{Gl}(m|n)\big)$$. The quotient is the representation category of a pro-reductive supergroup scheme. I will show some results about this supergroup scheme and explain what this implies about tensor product decompositions.