Special involutions and bulky parabolic subgroups in finite Coxeter groups
نویسندگان
چکیده
منابع مشابه
Special Involutions and Bulky Parabolic Subgroups in Finite Coxeter Groups
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...
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 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 کاملOn 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...
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: Journal of the Australian Mathematical Society
سال: 2005
ISSN: 1446-7887,1446-8107
DOI: 10.1017/s1446788700009381