Reflection centralizers in Coxeter groups

2011/06/20 by Allcock, Daniel
#20F55 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1106.3822

Abstract

We refine Brink's theorem, that the non-reflection part of a reflection centralizer in a Coxeter group W is a free group. We give an explicit set of generators for centralizer, which is finitely generated when W is. And we give a method for computing the Coxeter diagram for its reflection subgroup. In many cases, our method allows one to compute centralizers in one's head.

Related

• Centralizers of reflections and reflection-independence of Coxeter groups
• The centralizer of a Coxeter element
• A characterization of finitely generated reflection subgroups of Coxeter groups orthogonal to a reflection
• On non-conjugate Coxeter elements in well-generated reflection groups
• Centralizers in the Hecke algebras of complex reflection groups