Published on *Max Planck Institute for Mathematics* (http://www.mpim-bonn.mpg.de)

Posted in

- Talk [1]

Speaker:

Thorsten Heidersdorf
Affiliation:

MPIM
Date:

Tue, 2018-05-15 14:00 - 15:00 Given two irreducible finite-dimensional representations of the general linear supergroup $GL(m|n)$, how does their tensor product decompose into indecomposable representations? The answer is largely unknown. I will explain in this talk how to obtain the decomposition up to superdimension zero in the $GL(n|n)$-case: Given two irreducible representations of non-vanishing superdimension, the indecomposable representations of non-vanishing superdimension in the tensor product decomposition can be found by the Littlewood-Richardson rule or its variants for the simple algebraic groups of type ABCD.

The approach is rather abstract: The quotient of $Rep(Gl(n|n))$ by its largest proper tensor ideal (the negligible morphisms) 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.

**Links:**

[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39

[2] http://www.mpim-bonn.mpg.de/node/3444

[3] http://www.mpim-bonn.mpg.de/node/5312