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arXiv · 2512.22985

Tensor Power Asymptotics for Linearly Reductive Groups

Michael J. Larsen
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Abstract

Given a finite-dimensional faithful representation $V$ of a linearly reductive group $G$ over a field $K=\bar K$, we consider the growth of the number of irreducible factors of $V^{\otimes n}$ 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 $G$.

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Michael J. Larsen. 2025-12-28. Tensor Power Asymptotics for Linearly Reductive Groups. https://arxiv.org/abs/2512.22985

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