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Distributive coset graphs of finite Coxeter groups. (English) Zbl 1062.20045
Summary: 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 short conceptual proof of this result.
##### MSC:
 20F55 Reflection and Coxeter groups (group-theoretic aspects) 05E15 Combinatorial aspects of groups and algebras (MSC2010) 06A07 Combinatorics of partially ordered sets
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##### References:
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