A note on Bruhat order and double coset representatives
Christophe Hohlweg, Mark Skandera
Abstract
Let W be a finite coxeter group, let WI, WJ be standard parabolic subgroups, let u, v be minimal double cosets representatives of double cosets in WI W / WJ 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.
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