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arXiv · 1106.3822

Reflection centralizers in Coxeter groups

Daniel Allcock
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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.

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Daniel Allcock. 2013-06-27. Reflection centralizers in Coxeter groups. https://arxiv.org/abs/1106.3822

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