On centralizers of parabolic subgroups in Coxeter groups

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2 Citations (Scopus)

Abstract

Let W be an arbitrary Coxeter group, possibly of infinite rank. We describe a decomposition of the centralizer ZW(WI) of an arbitrary parabolic subgroup WI into the center of WI, a Coxeter group and a subgroup defined by a 2-cell complex. Only information about finite parabolic subgroups is required in an explicit computation. By using our description of ZW(WI), we will be able to reveal a further strong property of the action of the third factor on the second factor, in particular on the finite irreducible components of the second factor.

Original languageEnglish
Pages (from-to)891-930
Number of pages40
JournalJournal of Group Theory
Volume14
Issue number6
DOIs
Publication statusPublished - Nov 2011
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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