Representations of general linear groups in the Verlinde category

Alexandra Utiralova
University of California, Berkeley (UC Berkeley)

The Verlinde category Ver_p 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 Ver_p. Consequently, the study of representations of affine group schemes in such categories reduces to studying representations of affine group schemes in Ver_p.

I will talk about what is known about the category of representations of the affine group scheme GL(X) for an object X in Ver_p, about the highest weight structure on it, and will discuss some questions that yet remain unanswered.

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