Concise tensors with maximal symmetries
Abstract
Conner, Gesmundo, Landsberg and Ventura (2019) determined the largest stabilizer dimension of concise n× n × 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 × n × n tensors (i.e. dropping binding). We solve this problem: We prove that the largest stabilizer dimension of concise n× n× n tensors is n2 + 1 and the maximizers are the null algebra tensors (as in the binding case) and the skew symmetric tensor e1 ∧ e2 ∧ e3. 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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BibTeX
@misc{holtrup2026concise,
title = {{Concise tensors with maximal symmetries}},
author = {Annika Holtrup and Jeroen Zuiddam},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.17280},
eprint = {2609.17280},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.17280},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Concise tensors with maximal symmetries
AU - Annika Holtrup
AU - Jeroen Zuiddam
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.17280
UR - https://arxiv.org/abs/2609.17280
AB - Conner, Gesmundo, Landsberg and Ventura (2019) determined the largest stabilizer dimension of concise n× n × 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 × n × n tensors (i.e. dropping binding). We solve this problem: We prove that the largest stabilizer dimension of concise n× n× 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 ∧ e_2 ∧ 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.
ER -