Growth Problems for Representations of Finite Groups
Representation Theory
2026-05-28 v2 Category Theory
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.
Cite
@article{arxiv.2408.04196,
title = {Growth Problems for Representations of Finite Groups},
author = {David He},
journal= {arXiv preprint arXiv:2408.04196},
year = {2026}
}
Comments
18 pages, many figures, comments welcome; generalized main result for characteristic 0 to arbitrary characteristic; improved based on referee feedback