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arXiv · 2609.17280

Concise tensors with maximal symmetries

Annika Holtrup·Jeroen Zuiddam
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Abstract

Conner, Gesmundo, Landsberg and Ventura (2019) determined the largest stabilizer dimension of concise $n\times n \times n$ tensors that are binding, and they determined the corresponding maximizing tensors to be the null algebra tensors. They left as an open problem to extend this to all concise $n \times n \times n$ tensors (i.e. dropping binding). We solve this problem: We prove that the largest stabilizer dimension of concise $n\times n\times n$ tensors is $n^2 + 1$ and the maximizers are the null algebra tensors (as in the binding case) and the skew symmetric tensor $e_1 \wedge e_2 \wedge e_3$. As part of our approach we obtain upper bounds on the stabilizer dimension of matrix tuples under left-right action (generalized Kronecker quiver representations), which we think are of independent interest.

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Annika Holtrup, Jeroen Zuiddam. 2026-09-15. Concise tensors with maximal symmetries. https://arxiv.org/abs/2609.17280

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