Inductive McKay condition for finite simple groups of type 𝖢

Cabanes, Marc; Späth, Britta

doi:10.1090/ert/497

Inductive McKay condition for finite simple groups of type $\mathsf {C}$
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by Marc Cabanes and Britta Späth

Represent. Theory 21 (2017), 61-81

DOI: https://doi.org/10.1090/ert/497

Published electronically: June 14, 2017

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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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