Generalized blocks of unipotent characters in the finite general linear group

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Abstract

In an article of 2003, Külshammer, Olsson, and Robinson defined l-blocks for the symmetric groups, where l > 1 is an arbitrary integer, and proved that they satisfy an analogue of the Nakayama Conjecture. Inspired by this work and the definitions of generalized blocks and sections given by the authors, we give in this article a definition of d-sections in the finite general linear group, and construct d-blocks of unipotent characters, where d = 1 is an arbitrary integer. We prove that they satisfy one direction of an analogue of the Nakayama Conjecture, and, in some cases, prove the other direction. We also prove that they satisfy an analogue of Brauer's Second Main Theorem.
Original languageEnglish
Pages (from-to)4132-4162
Number of pages31
JournalCommunications in Algebra
Volume36
Issue number11
DOIs
Publication statusPublished - 2 Dec 2008

Keywords

  • block theory
  • finite general linear group
  • generalized blocks
  • Nakayama conjecture
  • representation theory
  • unipotent characters

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