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Robinson’s conjecture on heights of characters

Part of: Representation theory of groups

Published online by Cambridge University Press:  20 May 2019

Zhicheng Feng ,
Conghui Li ,
Yanjun Liu ,
Gunter Malle  and
Jiping Zhang
Zhicheng Feng
Affiliation:
School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China email zfeng@pku.edu.cn
Conghui Li
Affiliation:
Department of Mathematics, Southwest Jiaotong University, Chengdu 611756, China email liconghui@swjtu.edu.cn
Yanjun Liu
Affiliation:
College of Mathematics and Information Science, Jiangxi Normal University, Nanchang, China email liuyanjun@pku.edu.cn
Gunter Malle
Affiliation:
FB Mathematik, TU Kaiserslautern, Postfach 3049, 67653 Kaiserslautern, Germany email malle@mathematik.uni-kl.de
Jiping Zhang
Affiliation:
School of Mathematical Sciences, Peking University, Beijing 100871, China email jzhang@pku.edu.cn
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Abstract

Geoffrey Robinson conjectured in 1996 that the $p$-part of character degrees in a $p$-block of a finite group can be bounded in terms of the center of a defect group of the block. We prove this conjecture for all primes $p\neq 2$ for all finite groups. Our argument relies on a reduction by Murai to the case of quasi-simple groups which are then studied using deep results on blocks of finite reductive groups.

Keywords

Robinson’s conjectureheights of charactersdefects of characters

MSC classification

Primary: 20C15: Ordinary representations and characters 20C33: Representations of finite groups of Lie type
Type
Research Article
Information
Compositio Mathematica , Volume 155 , Issue 6 , June 2019 , pp. 1098 - 1117
Copyright
© The Authors 2019 

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Footnotes

The first and fourth authors gratefully acknowledge financial support by SFB TRR 195, and the others by NSFC (No. 11631001). In addition, the third author gratefully acknowledges financial support by NSFC (No. 11661042) and the Key Laboratory of Mathematics and Its Applications of Peking University.

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