Seminar in Algebra, Lie Theory, and Geometry

Thorsten Heidersdorf

(Ohio State University)

"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.