Speaker: Vera Serganova (University  of California, Berkeley)

Abstract:  Let F denote the Fock representation for sl(\infty). We describe the structure of the tensor product of F with its restricted dual F^*. In particular we prove that this module has a decreasing filtration with simple quotients and show that such filtration is unique. The proof uses categorification of the abelian envelope of Deligne category GL(t) for integer t and the category of finite-dimensional representations of the supergroup GL(m|n) with m-n=t.