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Inductive McKay condition for finite simple groups of type $\mathsf {C}$

Authors: Marc Cabanes and Britta Späth
Journal: Represent. Theory 21 (2017), 61-81
MSC (2010): Primary 20C15, 20C33; Secondary 20G40
Published electronically: June 14, 2017
MathSciNet review: 3662374
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Abstract: We verify the inductive McKay condition for simple groups of Lie type $\mathsf {C}$, namely finite projective symplectic groups. This contributes to the program of a complete proof of the McKay conjecture for all finite groups via the reduction theorem of Isaacs-Malle-Navarro and the classification of finite simple groups. In an important step we use a new counting argument to determine the stabilizers of irreducible characters of a finite symplectic group in its outer automorphism group. This is completed by analogous results on characters of normalizers of Sylow $d$-tori in those groups.

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Additional Information

Marc Cabanes
Affiliation: CNRS, IMJ-PRG, Boite 7012, 75205 Paris Cedex 13, France
MR Author ID: 211320

Britta Späth
Affiliation: Bergische Universität Wuppertal, Gaußstr. 20, 42119 Wuppertal, Germany

Keywords: McKay’s conjecture, symplectic groups, action of automorphisms on characters, extended Weyl groups
Received by editor(s): September 16, 2016
Received by editor(s) in revised form: March 29, 2017
Published electronically: June 14, 2017
Article copyright: © Copyright 2017 American Mathematical Society