On exterior powers of reflection representations
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- June 2023
- DOI:
- arXiv:
- arXiv:2306.16946
- Bibcode:
- 2023arXiv230616946H
- Keywords:
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- Mathematics - Representation Theory;
- Mathematics - Combinatorics;
- Mathematics - Group Theory;
- Mathematics - Rings and Algebras;
- 15A75;
- 05E10;
- 20C15;
- 20F55;
- 51F15
- E-Print:
- 13 pages, revised version. Comments welcome!