Stable partitions and Alperin's weight conjecture for the symmetric groups in characteristic two

Radha Kessar, L. Valero-Elizondo

Research output: Contribution to journalArticle

Abstract

Alperin's weight conjecture for the symmetric groups has been proved using an enumeration of the weights and the simple modules (see [2]), but so far there is no explicit way to associate weights with simple modules. Based on data obtained using an algorithm for finding weights for small symmetric groups in characteristic two (see [16]), we put forward a combinatorial conjecture which, if true, would provide explicit bijections between weights and irreducible modules for the symmetric groups in characteristic two. We prove some results towards the proof of this combinatorial conjecture.

Original languageEnglish
Pages (from-to)53-62
Number of pages9
JournalBoletin Sociedad Matematica Mexicana
Volume10
Issue number1
Publication statusPublished - 2004

Keywords

  • group representation
  • Alperin's conjecture
  • weight
  • Brauer quotient
  • symmetric group
  • partition
  • GENERAL LINEAR-GROUPS
  • HECKE ALGEBRAS
  • 2-WEIGHTS

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