Tensor Power Asymptotics for Linearly Reductive Groups

2025/12/28 by Larsen, Michael J.
#17B10 (Primary) 20G05 #60B15 #60J15 (Secondary) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2512.22985

Abstract

Given a finite-dimensional faithful representation V of a linearly reductive group G over a field K= K, we consider the growth of the number of irreducible factors of V^{⊗ n} when n is large. We prove that there exist upper and lower bounds which are constant multiples of n^-u/2 (dim V)ⁿ, where u is the dimension of any maximal unipotent subgroup of G.

Citations

• Asymptotic Growth of Trivial Summands in Tensor Powers
• Fractal behavior of tensor powers of the two dimensional space in prime characteristic

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