Geometry Seminar

Verlinde categories are defined as the semisimplification of the category of representations of Z/pZ in characteristic p. As shown by Coulembier, Etingof and Ostrik in arXiv:2107.02372, these categories play the role of the target category for the fiber functor for a large class of symmetric tensor categories (Frobenius exact, of moderate growth) in char p (usually played by the category of super vector spaces in char 0).

Consequently, Tannakian reconstruction tells us that any category with a fiber functor to Ver_p (and hence any Frobenius exact category of moderate growth) is equivalent to the category of representations of some group scheme in Ver_p.

I will talk about representations of the general linear group GL(X) for X in Ver_p and the related combinatorics with a focus on translation functors and the related categorical type A action.