On finite factors of centralizers of parabolic subgroups in Coxeter groups
نویسندگان
چکیده
منابع مشابه
On 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...
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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 ...
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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...
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ژورنال
عنوان ژورنال: Tsukuba Journal of Mathematics
سال: 2013
ISSN: 0387-4982
DOI: 10.21099/tkbjm/1358777001