Height 0 characters of finite groups of Lie type
Author:
Gunter Malle
Journal:
Represent. Theory 11 (2007), 192-220
MSC (2000):
Primary 20C33, 20G40
DOI:
https://doi.org/10.1090/S1088-4165-07-00312-3
Published electronically:
December 5, 2007
MathSciNet review:
2365640
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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
Email:
malle@mathematik.uni-kl.de
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.