Centralizers of reflections and reflection-independence of Coxeter groups

Details Centralizers of reflections and reflection-independence of Coxeter groups Centralizers of reflections and reflection-independence of Coxeter groups

2006-02-08

arxiv.org/abs/math/0602165v1

Mathematics

Group Theory

86 pages

Scientific paper

A Coxeter group W is called reflection independent if its reflections are uniquely determined by W only, independently on the choice of the generating set. We give a new sufficient condition for the reflection independence, and examine this condition for Coxeter groups in certain classes, possibly of infinite ranks. We also determine the finite irreducible components of another Coxeter group, that is a subgroup of W generated by the reflections centralizing a given generator of W. Determining such a subgroup makes our criterion efficient.

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