Unitriangular basic sets, Brauer characters and coprime actions
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Published:2023-05-01
Issue:6
Volume:27
Page:115-148
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ISSN:1088-4165
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Container-title:Representation Theory of the American Mathematical Society
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language:en
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Short-container-title:Represent. Theory
Author:
Feng Zhicheng,Späth Britta
Abstract
We show that the decomposition matrix of a given groupGGis unitriangular, wheneverGGhas a normal subgroupNNsuch that the decomposition matrix ofNNis unitriangular,G/NG/Nis abelian and certain characters ofNNextend to their stabilizer inGG. 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-calledinductive Brauer–Glauberman conditionthat aims to establish a Glauberman correspondence for Brauer characters, given a coprime action.
Funder
Deutsche Forschungsgemeinschaft
Publisher
American Mathematical Society (AMS)
Subject
Mathematics (miscellaneous)
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