Abstract

Oligomorphic groups and tensor categories

Andrew Snowden
University of Michigan

I will explain joint work with Nate Harman in which we attach a symmetric tensor category to an oligomorphic group G equipped with a measure mu. The simplest example is when G is the infinite symmetric group; in this case, there is a 1-parameter family of measures, and the resulting tensor categories are Deligne's interpolation categories Rep(S_t). Other choices for G lead to interesting new categories: for example, we obtain the first semi-simple pre-Tannakian category in positive characteristic with superexponential growth, and the first pre-Tannakian category with doubly exponential growth.