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.

arXiv comment13 pages, revised version. Comments welcome!

References in corpus (1)

• Reflection Representations of Coxeter Groups and Homology of Coxeter Graphs

Cited by in corpus (1)

• On exterior powers of reflection representations, II