### 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.