Götz Pfeiffer and Gerhard Röhrle,
Distributive Coset Graphs of Finite Coxeter Groups.
J. Group Theory 6 (2003), 311-320.
Let be a finite Coxeter group,
a parabolic subgroup of and
the set of distinguished coset representatives of
in equipped with the induced weak Bruhat ordering of .
All instances when is a distributive lattice are known.
In this note we present a new short conceptual proof of this result.
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