English

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.

Keywords

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}
}

Comments

5 pages

R2 v1 2026-07-01T04:06:59.234Z