Growth Problems for Representations of Finite Groups

2024/08/08 by He, David · 3 citations
#18M05 #20C20 #Category Theory (math.CT) #FOS: Mathematics #Primary: 11N45 #Representation Theory (math.RT) #Secondary: 20C15

paper · doi:10.48550/arxiv.2408.04196

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.

Cited by

• Affine diagram categories, algebras and monoids
• Growth Problems of Quantum Groups
• Tensor powers of representations of (diagram) monoids

Related

• Growth Problems for Representations of Finite Monoids
• Asymptotic Growth of Trivial Summands in Tensor Powers
• Growth problems in diagram categories
• Asymptotics in infinite monoidal categories
• Representation Growth for Linear Groups