Quasi-isolated blocks and Brauer's height zero conjecture

Radha Kessar*, Gunter Malle

*Corresponding author for this work

Research output: Contribution to journalArticle

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Abstract

This paper has two main results. Firstly, we complete the parametrisation of all p-blocks of finite quasi-simple groups by finding the so-called quasi-isolated blocks of exceptional groups of Lie type for bad primes. This relies on the explicit decomposition of Lusztig induction from suitable Levi subgroups. Our second major result is the proof of one direction of Brauer's long-standing height zero conjecture on blocks of finite groups, using the reduction by Berger and Knorr to the quasi-simple situation. We also use our result on blocks to verify a conjecture of Malle and Navarro on nilpotent blocks for all quasi-simple groups.

Original languageEnglish
Pages (from-to)321-384
Number of pages64
JournalAnnals of Mathematics
Volume178
Issue number1
DOIs
Publication statusPublished - Jul 2013

Keywords

  • finite reductive groups
  • defect -groups
  • unitary groups
  • lie type
  • characters
  • subgroups
  • induction
  • Brauer's height 0 conjecture
  • classification of blocks
  • isolated blocks
  • Lusztig induction

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