arXiv:2408.04196 Abstract | arXiv Analytics

arXiv:2408.04196 [math.RT]Abstract References Reviews Resources

Growth Problems for Representations of Finite Groups

Published 2024-08-08Version 1

We compute (exact and asymptotic) formulas 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 in addition a general exact formula for the growth rate and give a complete solution to the growth problems in terms of the character table. We also provide code used to compute our formulas.

Comments: 18 pages, many figures, comments welcome

Categories: math.RT, math.CT

Subjects: 11N45, 18M05, 20C15, 20C20

Keywords: finite groups, growth problems, representations, growth rate, general exact formula

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