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