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Representations of the general linear group in the Verlinde category.
Algebraic Geometry and Number Theory| Speaker: | Alexandra Utiralova, UC Berkeley |
| Location: | 2112 MSB |
| Start time: | Thu, Apr 17 2025, 1:10PM |
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 the classification of representations of the general linear group GL(X) for X in Ver_p and the related combinatorics.