Alexandra Utiralova, UC Berkeley

Title: Representations of general linear groups in the Verlinde category

Abstract: The Verlinde category Verp is the semisimplification of the category of finite-dimensional representations of Z/pZ in characteristic p. In arXiv:2107.02372 Coulembier, Etingof, and Ostrik showed that all pre-Tannakian categories of moderate growth with additional nice property (Frobenius exactness) admit a fiber functor into Verp. Consequently, the study of representations of affine group schemes in such categories reduces to studying representations of affine group schemes in Verp.

I will talk about what is known about the category of representations of the affine group scheme GL(X) for an object X in Verp, and about the highest weight structure on it.