Geodesic
Lattices and bases of Coxeter groups
The electronic journal of combinatorics, The Foata Festschrift volume, Tome 3 (1996) no. 2
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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.
DOI : 10.37236/1285
Classification : 06A07, 20F55
Mots-clés : lattice, Coxeter groups, Bruhat order, enveloping lattices 
@article{10_37236_1285,
     author = {Alain Lascoux and Marcel-Paul Sch\"utzenberger},
     title = {Lattices and bases of {Coxeter} groups},
     journal = {The electronic journal of combinatorics},
     year = {1996},
     volume = {3},
     number = {2},
     doi = {10.37236/1285},
     zbl = {0885.05111},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1285/}
}
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Alain Lascoux; Marcel-Paul Schützenberger. Lattices and bases of Coxeter groups. The electronic journal of combinatorics, The Foata Festschrift volume, Tome 3 (1996) no. 2. doi: 10.37236/1285

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