Let W be an arbitrary Coxeter group, possibly of infinite rank. We describe a decomposition of the centralizer ZW(WI) of an arbitrary parabolic subgroup WI into the center of WI, 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 ZW(WI), 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.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory