English

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

Representation Theory 2012-04-25 v3

Abstract

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

Keywords

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

R2 v1 2026-06-21T20:50:18.370Z