Quasi-isolated blocks and Brauer's height zero conjecture.

DOI10.4007/annals.2013.178.1.6zbMath1317.20006arXiv1112.2642OpenAlexW2141528711WikidataQ123026145 ScholiaQ123026145MaRDI QIDQ355139

Gunter Malle, Radha Kessar

Publication date: 24 July 2013

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1112.2642

zbMATH Keywords

exceptional groups of Lie typefinite quasi-simple groupsBrauer height zero conjectureAbelian defect groupsclassification of blocksisolated blocksLusztig inductionordinary irreducible characters

Mathematics Subject Classification ID

Ordinary representations and characters (20C15) Modular representations and characters (20C20) Representations of finite groups of Lie type (20C33)

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Uses Software

• CHEVIE

Cites Work

• Computational proof of the Mackey formula for \(q>2\).
• On a conjecture of G. Malle and G. Navarro on nilpotent blocks.
• Local methods in block theory
• On the \(p\)-blocks of symmetric and alternating groups and their covering groups
• Brauer's height zero conjecture for central quotients of special linear and special unitary groups
• On the local structure of Morita and Rickard equivalences between Brauer blocks
• On blocks of finite reductive groups and twisted induction
• Unipotent blocks of finite reductive groups of a given type
• On unipotent blocks and their ordinary characters
• Block induction, normal subgroups and characters of height zero
• Derived categories and Deligne-Lusztig varieties.
• On the unipotent \(l\)-blocks of finite reductive groups when \(l\) is bad
• The blocks of finite general linear and unitary groups
• On Brauer's height zero conjecture
• Towards a Jordan decomposition of blocks of finite reductive groups.
• The Solomon system \({\mathcal F}_{\text{Sol}}(3)\) does not occur as fusion system of a 2-block.
• Blocks with cyclic defect groups
• Defect groups for finite groups of Lie type
• Some applications of the theory of blocks of characters of finite groups. IV
• Investigations on group characters
• Brauer's height zero conjecture for the 2-blocks of maximal defect
• Blocks with equal height zero degrees
• Conjectures of Alperin and Broué for 2-blocks with elementary abelian defect groups of order 8
• Characters of Reductive Groups over a Finite Field. (AM-107)
• Brauer's Height Conjecture for p-Solvable Groups
• Character Table and Blocks of Finite Simple Triality Groups 3 D 4 (q)
• On Brauer’s height 0 conjecture
• Normalizers of Parabolic Subgroups of Reflection Groups
• The non-principal 2-blocks of sporadic simple groups^*
• Basic Sets of Brauer Characters of Finite Groups of Lie Type II
• Height 0 characters of finite groups of Lie type
• Quasi-Isolated Elements in Reductive Groups
• On Ree's Series of Simple Groups
• Die unipotenten charaktere von ²F₄(q²)
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