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Götz Pfeiffer and Gerhard Röhrle,

Distributive Coset Graphs of Finite Coxeter Groups.

J. Group Theory 6 (2003), 311-320.


Let W be a finite Coxeter group, WJ a parabolic subgroup of W and XJ the set of distinguished coset representatives of WJ in W equipped with the induced weak Bruhat ordering of W. All instances when XJ is a distributive lattice are known. In this note we present a new short conceptual proof of this result.

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