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- Title
The Weil-Steinberg character of finite classical groups.
- Authors
G. Hiss; A. Zalesski
- Abstract
We compute the irreducible constitutents of the product of the Weil character and the Steinberg character in those finite classical groups for which a Weil character is defined, namely the symplectic, unitary and general linear groups. It turns out that this product is multiplicity free for the symplectic and general unitary groups, but not for the general linear groups. par As an application we show that the restriction of the Steinberg character of such a group to the subgroup stabilizing a vector in the natural module is multiplicity free. The proof of this result for the unitary groups uses an observation of Brunat, published as an appendix to our paper. par As our ``Weil character'' for the symplectic groups in even characteristic we use the $2$-modular Brauer character of the generalized spinor representation. Its product with the Steinberg character is the Brauer character of a projective module. We also determine its indecomposable direct summands.
- Subjects
WEIL group; FINITE groups; UNITARY groups; LINEAR algebraic groups; BRAUER groups; SPINOR analysis; INDECOMPOSABLE modules
- Publication
Representation Theory, 2009, Vol 13, Issue 20, p427
- ISSN
1088-4165
- Publication type
Article
- DOI
10.1090/S1088-4165-09-00351-3