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

Geck, Meinolf; Malle, Gunter

doi:10.1090/S1088-4165-2013-00430-2

Frobenius–Schur indicators of unipotent characters and the twisted involution module
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by Meinolf Geck and Gunter Malle

Represent. Theory 17 (2013), 180-198

DOI: https://doi.org/10.1090/S1088-4165-2013-00430-2

Published electronically: April 1, 2013

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Abstract:

Let $W$ be a finite Weyl group and $\sigma$ a non-trivial graph automorphism of $W$. We show a remarkable relation between the $\sigma$-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 and 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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