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Representation Theory

ISSN 1088-4165



Height 0 characters of finite groups of Lie type

Author: Gunter Malle
Journal: Represent. Theory 11 (2007), 192-220
MSC (2000): Primary 20C33, 20G40
Published electronically: December 5, 2007
MathSciNet review: 2365640
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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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Additional Information

Gunter Malle
Affiliation: FB Mathematik, Universität Kaiserslautern, Postfach 3049, D 67653 Kaiserslautern, Germany
MR Author ID: 225462

Received by editor(s): April 7, 2006
Received by editor(s) in revised form: September 16, 2007
Published electronically: December 5, 2007
Dedicated: Dedicated to Professor Toshiaki Shoji on the occasion of his 60th birthday
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.