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Representation Theory

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

Authors: Meinolf Geck and Gunter Malle
Journal: Represent. Theory 17 (2013), 180-198
MSC (2010): Primary 20C15; Secondary 20C33
Published electronically: April 1, 2013
MathSciNet review: 3037782
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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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Additional Information

Meinolf Geck
Affiliation: Institute of Mathematics, Aberdeen University, Aberdeen AB24 3UE, Scotland, UK.
Address at time of publication: IAZ – Lehrstuhl für Algebra, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
MR Author ID: 272405

Gunter Malle
Affiliation: FB Mathematik, TU Kaiserslautern, Postfach 3049, 67653 Kaiserslautern, Germany.
MR Author ID: 225462

Received by editor(s): April 22, 2012
Received by editor(s) in revised form: October 10, 2012
Published electronically: April 1, 2013
Article copyright: © Copyright 2013 American Mathematical Society