Asymptotic Growth of Trivial Summands in Tensor Powers

2025/01/19 by Nai-Heng Sheu, Sheu, Nai-Heng · 2 citations
Mathematics · #Meromorphic and Entire Functions #Advanced Topics in Algebra #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2501.11125

Abstract

Given a finite-dimensional representation V over an algebraically closed field of an abstract group G, we consider the number of the trivial summand counted with multiplicity in the direct sum decomposition of V^{⊗ n}. We give necessary and sufficient conditions when the field is of characteristic 0 and when the field is of characteristic p so that (V^{⊗ n})_n has a subsequence (V^{⊗ n_k})_k such that V^{⊗ n_k} contains enough trivial summands when k is sufficiently large.

Cited by

• Tensor Power Asymptotics for Linearly Reductive Groups
• Growth Problems of Quantum Groups

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