Abstract
A fundamental theorem of P. Deligne (2002) states that a pre-Tannakian category over an algebraically closed field of characteristic zero admits a fiber functor to the category of supervector spaces (i.e., is the representation category of an affine proalgebraic supergroup) if and only if it has moderate growth (i.e., the lengths of tensor powers of an object grow at most exponentially). In this paper we prove a characteristic
It follows that any semisimple pre-Tannakian category of moderategrowth has a fiber functor to
In particular, this result applies to semisimplifications of categories of modular representations of finite groups (or, more generally, affine group schemes), which gives new applications to classical modular representation theory. For example, it allows us to characterize, for a modular representation
Citation
Kevin Coulembier. Pavel Etingof. Victor Ostrik. Alexander Kleshchev. "On Frobenius exact symmetric tensor categories." Ann. of Math. (2) 197 (3) 1235 - 1279, May 2023. https://doi.org/10.4007/annals.2023.197.3.5
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