Nov. 18, 2023. The 16th National Conference on Algebra.
Huaqiao University. Quanzhou, Fujian Province, China.
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.
Moreover, generically two exterior powers of non-isomorphic reflection representations are also non-isomorphic.
This result applies to an arbitrary Coxeter group, whose reflection representations can be classified explicitly.
In this way, a large class of irreducible representations of Coxeter groups is obtained.