2012/04/16 by Meinolf Geck, Geck, Meinolf, Gunter Malle +1
Mathematics · #20C15 (Primary) 20C33 (Secondary) #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT) #math.RT #msc:20C15 #msc:20C33
paper · pdf · doi:10.48550/arxiv.1204.3590
18 pages; the second version corrects some inaccuracies and adds some material in Section 5; the third version corrects a reference
openalex publication_date 2012/04/16 · arxiv created 2012/04/24 · arxiv updated 2012/04/25 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
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.