Reflection centralizers in Coxeter groups

Details Reflection centralizers in Coxeter groups Reflection centralizers in Coxeter groups

2011-06-20

arxiv.org/abs/1106.3822v1

Mathematics

Group Theory

Scientific paper

We give a new proof of Brink's theorem that the non-reflection part of a reflection centralizer in a Coxeter group is free, and make several refinements. In particular we give an explicit finite set of generators for the centralizer and a method for computing the Coxeter diagram for its reflection part. In many cases, our method allows one to compute centralizers quickly in one's head. We also define "Vinberg representations" of Coxeter groups, in order to isolate some of the key properties of the Tits cone.

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