Growth Problems for Representations of Finite Groups

Abstract

We give a general asymptotic formula for the growth rate of the number of indecomposable summands in the tensor powers of representations of finite groups, over a field of arbitrary characteristic. In characteristic zero we obtain additional results, including an exact formula for the growth rate. We compute various examples and also provide code used to compute our formulas.

18 pages, many figures, comments welcome; generalized main result for characteristic 0 to arbitrary characteristic; improved based on referee feedback