English

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.

Keywords

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

R2 v1 2026-06-28T18:07:16.715Z