Minimal length elements in some double cosets of Coxeter groups

2006/11/02 by He, Xuhua · 1 citation
#20F55 #20G99 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.math/0611055

Abstract

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 \citeGKP.

Cited by

• Centralizers in Hecke Algebras of Any Coxeter Group

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• Elements of minimal length and Bruhat order on fixed point cosets of Coxeter groups
• Maximal length elements of excess zero in finite Coxeter groups
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• Stable reflection length in Coxeter groups
• Coxeter elements of the symmetric groups whose powers afford the longest