Distributive coset graphs of finite coxeter groups
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Pfeiffer, Götz; Röhrle, Gerhard (2003). Distributive coset graphs of finite coxeter groups. Journal of Group Theory 6 (3), 311-320
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.