On exterior powers of reflection representations
Representation Theory
2024-11-20 v2 Combinatorics
Group Theory
Rings and Algebras
Abstract
In 1968, R. Steinberg proved a theorem stating that the exterior powers of an irreducible reflection representation of a Euclidean reflection group are again irreducible and pairwise non-isomorphic. We extend this result to a more general context where the inner product invariant under the group action may not necessarily exist.
Cite
@article{arxiv.2306.16946,
title = {On exterior powers of reflection representations},
author = {Hongsheng Hu},
journal= {arXiv preprint arXiv:2306.16946},
year = {2024}
}
Comments
13 pages, revised version. Comments welcome!