Some fast-growing tensor categories
arXiv:2305.18230
Abstract
Given a semi-simple pre-Tannakian category over a finite field, we show that (a slight modification of) its linearization over a field of characteristic 0 is also semi-simple and pre-Tannakian. The key input is a result of Kuhn on the generic representation theory of finite fields. The resulting pre-Tannakian categories have substantially faster growth than previously known examples.
10 pages