Frobenius--Schur indicators of unipotent characters and the twisted involution module
Representation Theory
2012-04-25 v3
Abstract
Let be a finite Weyl group and be a non-trivial graph automorphism of . We show a remarkable relation between the -twisted involution module for and the Frobenius--Schur indicators of the unipotent characters of a corresponding twisted finite group of Lie type. This extends earlier results of Lusztig-Vogan for the untwisted case and then allows us to state a general result valid for any finite group of Lie type. Inspired by recent work of Marberg, we also formally define Frobenius--Schur indicators for "unipotent characters" of twisted dihedral groups.
Cite
@article{arxiv.1204.3590,
title = {Frobenius--Schur indicators of unipotent characters and the twisted involution module},
author = {Meinolf Geck and Gunter Malle},
journal= {arXiv preprint arXiv:1204.3590},
year = {2012}
}
Comments
18 pages; the second version corrects some inaccuracies and adds some material in Section 5; the third version corrects a reference