Abstract

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. By using our description of Z_W(W_I), we will be able to 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.