Mathematics – Representation Theory
Scientific paper
2006-11-02
Mathematics
Representation Theory
35 pages
Scientific paper
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 \cite{GKP}.
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