Height 0 characters of finite groups of Lie type

Malle, Gunter

doi:10.1090/S1088-4165-07-00312-3

Height 0 characters of finite groups of Lie type
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by Gunter Malle

Represent. Theory 11 (2007), 192-220

DOI: https://doi.org/10.1090/S1088-4165-07-00312-3

Published electronically: December 5, 2007

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Abstract:

We give a classification of irreducible characters of finite groups of Lie type of $p’$-degree, where $p$ is any prime different from the defining characteristic, in terms of local data. More precisely, we give a classification in terms of data related to the normalizer of a suitable Levi subgroup, which in many cases coincides with the normalizer of a Sylow $p$-subgroup. The McKay conjecture asserts that there exists a bijection between characters of $p’$-degree of a group and of the normalizer of a Sylow $p$-subgroup. We hope that our result will constitute a major step towards a proof of this conjecture for groups of Lie type, and, in conjunction with a recent reduction result of Isaacs, Malle and Navarro, for arbitrary finite groups.

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