On centralizers of parabolic subgroups in Coxeter groups

Details On centralizers of parabolic subgroups in Coxeter groups On centralizers of parabolic subgroups in Coxeter groups

2005-01-05

arxiv.org/abs/math/0501061v5

Journal of Group Theory 14 (2011) 891-930

Mathematics

Group Theory

33 pages; improved version, notations changed (ver. 2); inappropriate Eq. (4.7) was removed (ver. 3); Theorem 7.1 was improved

Scientific paper

10.1515/JGT.2010.088

Let $W$ be an arbitrary Coxeter group, possibly of infinite rank. We describe a decomposition of the centralizer $Z_W(W_I)$ of an arbitrary parabolic subgroup $W_I$ into the center of $W_I$, a Coxeter group and a subgroup defined by a 2-cell complex. Only information about finite parabolic subgroups is required in an explicit computation. Moreover, by using our description of $Z_W(W_I)$, we reveal a further strong property of the action of the third factor on the second factor, in particular on the finite irreducible components of the second factor.

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