Frobenius--Schur indicators of unipotent characters and the twisted involution module
arXiv:1204.3590
Abstract
Let be a finite Weyl group and $\sg$ be a non-trivial graph automorphism of . We show a remarkable relation between the $\sg$-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.
18 pages; the second version corrects some inaccuracies and adds some material in Section 5; the third version corrects a reference