A note on parabolic subgroups of a Coxeter group
نویسندگان
چکیده
منابع مشابه
A Note on Parabolic Subgroups of a Coxeter Group
The aim of this note is to prove that the parabolic closure of any subset of a Coxeter group is a parabolic subgroup. To obtain that, several technical lemmas on the root system of a parabolic subgroup are established. MSC 2000 Subject Classifications: Primary 20F55; Secondary 20H15
متن کاملCommensurators of parabolic subgroups of Coxeter groups
Let (W,S) be a Coxeter system, and let X be a subset of S. The subgroup of W generated by X is denoted by WX and is called a parabolic subgroup. We give the precise definition of the commensurator of a subgroup in a group. In particular, the commensurator of WX in W is the subgroup of w in W such that wWXw ∩WX has finite index in both WX and wWXw . The subgroup WX can be decomposed in the form ...
متن کاملNormalizers of Parabolic Subgroups of Coxeter Groups
We improve a bound of Borcherds on the virtual cohomological dimension of the non-reflection part of the normalizer of a parabolic subgroup of a Coxeter group. Our bound is in terms of the types of the components of the corresponding Coxeter subdiagram rather than the number of nodes. A consequence is an extension of Brink’s result that the non-reflection part of a reflection centralizer is fre...
متن کاملOn Boundaries of Parabolic Subgroups of Coxeter Groups
In this paper, we investigate boundaries of parabolic subgroups of Coxeter groups. Let (W, S) be a Coxeter system and let T be a subset of S such that the parabolic subgroup WT is infinite. Then we show that if a certain set is quasi-dense in W , then W∂Σ(WT , T ) is dense in the boundary ∂Σ(W, S) of the Coxeter system (W, S), where ∂Σ(WT , T ) is the boundary of (WT , T ).
متن کاملOn centralizers of parabolic subgroups in Coxeter groups
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. Moreover, by using our description of ZW (WI), we reveal a further...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Expositiones Mathematicae
سال: 2007
ISSN: 0723-0869
DOI: 10.1016/j.exmath.2006.05.001