Frobenius--Schur indicators of unipotent characters and the twisted involution module

Details Frobenius--Schur indicators of unipotent characters and the twisted involution module Frobenius--Schur indicators of unipotent characters and the twisted involution module

2012-04-16

arxiv.org/abs/1204.3590v3

Mathematics

Representation Theory

18 pages; the second version corrects some inaccuracies and adds some material in Section 5; the third version corrects a refe

Scientific paper

Let $W$ be a finite Weyl group and $\sg$ be a non-trivial graph automorphism of $W$. We show a remarkable relation between the $\sg$-twisted involution module for $W$ 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.

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