Minimal Length Elements in Some Double Cosets of Coxeter Groups
نویسنده
چکیده
We study the minimal length elements in some double cosets of Coxeter groups and use them to study Lusztig’s G-stable pieces and the generalization of G-stable pieces introduced by Lu and Yakimov. We also use them to study the minimal length elements in a conjugacy class of a finite Coxeter group and prove a conjecture in [GKP].
منابع مشابه
Parabolic 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 کاملMinimal and maximal elements in Kazhdan-Lusztig double sided cells of Sn and a Robinson-Schensted correspondance in simply laced Coxeter groups
Let W be a Coxeter group. We generalise the Knuth plactic relations to W and we show that their equivalence classes decompose the Kazhdan-Lusztig cells. In the case of symmetric groups, we show that the set of elements of minimal length in a double sided cell is the set of elements of maximal length in conjugated parabolic (i.e. Young) subgroups. We also give an interpretation of this set with ...
متن کاملMinimal and maximal elements in Kazhdan-Lusztig double sided cells of Sn and Robinson-Schensted correspondance
In symmetric groups, viewed as Coxeter groups, we show that the set of elements of minimal length in a double sided cell is the set of elements of maximal length in conjugated parabolic (i.e. Young) subgroups. We also give an interpretation of this set with tableau, using the RobinsonSchensted correspondance. We show also that the set of elements of maximal length in a two sided cell is the set...
متن کاملA Model for the Double Cosets of Young Subgroups
There are several results concerning double cosets of Young subgroups of symmetric groups which are often proved as corollaries of more general results about Coxeter groups. In this note we give a selection of these results and give them the short combinatorial proofs they deserve. Our replacement for the machinery of Coxeter groups consists of some simple combinatorial arguments involving tabl...
متن کاملA Model for the Double Cosets of Young Subgroups
There are several results concerning double cosets of Young subgroups of symmetric groups which are often proved as corollaries of more general results about Coxeter groups. In this note we give a selection of these results and give them short combinatorial proofs. The replacement for the machinery of Coxeter groups consists of some simple combinatorial arguments involving tableaux. Inevitably ...
متن کامل