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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Unitriangular basic sets, Brauer characters and coprime actions
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by Zhicheng Feng and Britta Späth PDF
Represent. Theory 27 (2023), 115-148 Request permission

Abstract:

We show that the decomposition matrix of a given group $G$ is unitriangular, whenever $G$ has a normal subgroup $N$ such that the decomposition matrix of $N$ is unitriangular, $G/N$ is abelian and certain characters of $N$ extend to their stabilizer in $G$. Using the recent result by Brunat–Dudas–Taylor establishing that unipotent blocks have a unitriangular decomposition matrix, this allows us to prove that blocks of groups of quasi-simple groups of Lie type have a unitriangular decomposition matrix whenever they are related via Bonnafé–Dat–Rouquier’s equivalence to a unipotent block. This is then applied to study the action of automorphisms on Brauer characters of finite quasi-simple groups. We use it to verify the so-called inductive Brauer–Glauberman condition that aims to establish a Glauberman correspondence for Brauer characters, given a coprime action.
References
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Additional Information
  • Zhicheng Feng
  • Affiliation: School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, People’s Republic of China
  • Address at time of publication: SICM and Department of Mathematics, Southern University of Science and Technology, Shenzhen 518055, People’s Republic of China
  • Email: zfeng@pku.edu.cn
  • Britta Späth
  • Affiliation: School of Mathematics and Natural Sciences, University of Wuppertal, Gaußstrasse 20, 42119 Wuppertal, Germany
  • ORCID: 0000-0002-4593-5729
  • Email: bspaeth@uni-wuppertal.de
  • Received by editor(s): November 28, 2021
  • Received by editor(s) in revised form: July 5, 2022, July 18, 2022, September 16, 2022, and October 17, 2022
  • Published electronically: May 1, 2023
  • Additional Notes: The first author was financially supported by NSFC (11901028 and 11631001). The research of the second author was conducted in the framework of the research training group GRK 2240: Algebro-Geometric Methods in Algebra, Arithmetic and Topology, funded by the DFG
  • © Copyright 2023 American Mathematical Society
  • Journal: Represent. Theory 27 (2023), 115-148
  • MSC (2020): Primary 20C20, 20C33
  • DOI: https://doi.org/10.1090/ert/635
  • MathSciNet review: 4582765