Götz Pfeiffer and Gerhard Röhrle,

Distributive Coset Graphs of Finite Coxeter Groups.

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

Abstract.

Let

W

be a finite Coxeter group,

W

_J a parabolic subgroup of

W

and

X

_J the set of distinguished coset representatives of

W

_J in

W

equipped with the induced weak Bruhat ordering of

W

. All instances when

X

_J is a distributive lattice are known. In this note we present a new short conceptual proof of this result.

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