On the Cohomology of Coxeter Groups and Their Finite Parabolic Subgroups
نویسندگان
چکیده
منابع مشابه
On the Cohomology of Coxeter Groups and Their Finite Parabolic Subgroups Ii
In this paper, we study the relation between the cohomology of Coxeter groups and their parabolic subgroups of nite order. Let W be a Coxeter group and k a commutative ring with identity. We investigate the natural map : H (W; k) ! lim:inv: H (W F ; k), where W F runs all parabolic subgroups of nite order, and prove that the kernel and the cokernel of consist of nilpotent elements. This general...
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In [3] Felder and Veselov considered the standard and twisted actions of a finite Coxeter group W on the cohomology H(MW ) of the complement of the complexified hyperplane arrangement MW of W . The twisted action is obtained by combining the standard action with complex conjugation; we refer the reader to [3] for precise statements. In a case by case argument, Felder and Veselov obtain a formul...
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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 ...
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 ).
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ژورنال
عنوان ژورنال: Tokyo Journal of Mathematics
سال: 1995
ISSN: 0387-3870
DOI: 10.3836/tjm/1270043616