Representations of General Linear Groups in the Verlinde Category

Explore a 52-minute lecture on representations of general linear groups in the Verlinde category, presented by Alexandra Utiralova from the University of California, Berkeley. Delve into the semisimplification of finite-dimensional representations of Z/pZ in characteristic p, known as the Verlinde category Ver_p. Examine the work of Coulembier, Etingof, and Ostrik, which demonstrates how pre-Tannakian categories of moderate growth with Frobenius exactness admit fiber functors into Ver_p. Investigate the implications for studying representations of affine group schemes in these categories. Learn about the current understanding of representations of the affine group scheme GL(X) for an object X in Ver_p, including its highest weight structure. Explore open questions in this field of research. Recorded on January 8, 2024, this talk is part of the Symmetric Tensor Categories and Representation Theory Workshop at the Institute for Pure & Applied Mathematics (IPAM).