منابع مشابه
Essays on Coxeter groups Bruhat closures
If G is a split reductive group and B a Borel subgroup then G is the disjoint union of the BwB as w ranges over the Weyl group of a maximal torus in B. The closure of BwB is the union of certain double cosets BxB, where the x that occur can be characterized in purely combinatorial terms. Somewhat surprisingly, this combinatorial definition may be extended to define the Bruhat closure operation ...
متن کاملParabolic Double Cosets in Coxeter Groups
Parabolic subgroups WI of Coxeter systems (W,S), as well as their ordinary and double quotients W/WI and WI\W/WJ , appear in many contexts in combinatorics and Lie theory, including the geometry and topology of generalized flag varieties and the symmetry groups of regular polytopes. The set of ordinary cosets wWI , for I ⊆ S, forms the Coxeter complex of W , and is well-studied. In this article...
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 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...
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ژورنال
عنوان ژورنال: Journal of Group Theory
سال: 2010
ISSN: 1433-5883,1435-4446
DOI: 10.1515/jgt.2009.061