English

Reflection centralizers in Coxeter groups

Group Theory 2013-06-28 v2

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.

Keywords

Cite

@article{arxiv.1106.3822,
  title  = {Reflection centralizers in Coxeter groups},
  author = {Daniel Allcock},
  journal= {arXiv preprint arXiv:1106.3822},
  year   = {2013}
}

Comments

To appear in Transformation Groups

R2 v1 2026-06-21T18:24:42.443Z