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On the inductive McKay condition in the defining characteristic

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Abstract

This note is concerned with the McKay conjecture in the representation theory of finite groups. Recently, Isaacs–Malle–Navarro have shown that, in order to prove this conjecture in general, it is sufficient to establish certain properties of all finite simple groups. In this note, we develop some new methods for dealing with these properties for finite simple groups of Lie type in the defining characteristic case. We apply these methods to show that the Suzuki and Ree groups, G 2(q), F 4(q) and E 8(q) have the required properties.

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  1. Ruhr-Universität Bochum, Fakultät für Mathematik, Universitätsstrasse 150, 44780, Bochum, Germany

    Olivier Brunat

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  1. Olivier Brunat
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Correspondence to Olivier Brunat.

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Brunat, O. On the inductive McKay condition in the defining characteristic. Math. Z. 263, 411–424 (2009). https://doi.org/10.1007/s00209-008-0423-5

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  • DOI: https://doi.org/10.1007/s00209-008-0423-5

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