A note on Bruhat order and double coset representatives

Christophe Hohlweg; Mark Skandera

A note on Bruhat order and double coset representatives

Combinatorics 2007-05-23 v1 Group Theory

Authors: Christophe Hohlweg , Mark Skandera

Abstract

Let $W$ be a finite coxeter group, let $W_I$ , $W_J$ be standard parabolic subgroups, let $u$ , $v$ be minimal double cosets representatives of double cosets in $W_I W / W_J$ and let $u'$ , $v'$ be the maximal representatives of those same two cosets. We show that $u < v$ if and only if $u' < v'$ for the Bruhat order.

Cite

@article{arxiv.math/0511611,
  title  = {A note on Bruhat order and double coset representatives},
  author = {Christophe Hohlweg and Mark Skandera},
  journal= {arXiv preprint arXiv:math/0511611},
  year   = {2007}
}

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4 pages

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