The higher Verlinde category Ver₄⁺ and superLie theory in
characteristic 2
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hu-serinahu-phd-math-2026-thesis.pdf
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Author(s)
Hu, Serina
Advisor(s)
Etingof, Pavel
Date Issued
May 2026
Publisher
Massachusetts Institute of Technology
Abstract
In this thesis, we develop representation theory of the simplest higher Verlinde category in characteristic 2, Ver₄⁺. We consider two perspectives when studying this category. First, Ver₄⁺ is a nontrivial reduction of the category of supervector spaces to characteristic 2, hence studying Lie theory in this category produces a notion of superLie theory in characteristic 2. From this perspective, we analyze supergroups, Lie superalgebras, and superpolynomial functors in characteristic 2, and relate these to existing notions of Lie theory in characteristic 2. Second, the higher Verlinde categories are the conjectured analogs of supervector spaces in characteristic p in Deligne’s theorem, which classifies all moderate growth symmetric tensor categories in characteristic 0 as representation categories of affine supergroup schemes. Benson, Etingof, and Ostrik conjectured that in characteristic p, one replaces supervector spaces with the union of the higher Verlinde categories in characteristic p. Hence, it is conjecturally sufficient to understand representation theory in the higher Verlinde categories in order to characterize symmetric tensor categories of moderate growth, and we develop the theory to do so in Ver₄⁺ as a starting point for more general cases. We first provide some background on symmetric tensor categories and define Ver₄⁺ and its objects of interest. We then define and study Lie algebras and Lie superalgebras in this category, including classifying the low-dimensional Lie (super)algebras and relating them to Lie superalgebras in characteristic 2. Finally, we discuss representation theory of general linear groups in Ver₄⁺, classifying their irreducible representations and their irreducible polynomial representations (hence also the simple polynomial functors in Ver₄⁺) via a highest weight theory.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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