A remark on automorphisms of tensor spaces
Representation Theory
2025-07-21 v1
Abstract
A tensor space is a vector space equipped with a finite collection of multi-linear forms. In recent years, a rich theory of infinite dimensional tensor spaces has emerged. In this note, we show that a large class of permutation groups can occur as the automorphism groups of such tensor spaces. Using this, we show that a tensor space can behave somewhat pathologically as a representation of its automorphism group.
Cite
@article{arxiv.2507.13521,
title = {A remark on automorphisms of tensor spaces},
author = {Alessandro Danelon and Andrew Snowden},
journal= {arXiv preprint arXiv:2507.13521},
year = {2025}
}
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5 pages