Treillis et bases des groupes de Coxeter

Abstract

Finite lattices possess a basis, as well as a cobasis, from which the elements of the lattice can be recovered by sup or inf. We extend this construction to finite ordered sets, and then apply it to Coxeter groups, considered as ordered sets (Bruhat order). This amounts to embedding Coxeter groups into their enveloping lattices. These lattices are distributive in the cases of types An and Bn.