Geodesic
Algebraic and combinatorial properties of zircons
Journal of Algebraic Combinatorics, Tome 26 (2007) no. 3, pp. 363-382.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In this paper we introduce and study a new class of posets, that we call zircons, which includes all Coxeter groups partially ordered by Bruhat order. We prove that many of the properties of Coxeter groups extend to zircons often with simpler proofs: in particular, zircons are Eulerian posets and the Kazhdan-Lusztig construction of the Kazhdan-Lusztig representations can be carried out in the context of zircons. Moreover, for any zircon $Z$, we construct and count all balanced and exact labelings (used in the construction of the Bernstein-Gelfand-Gelfand resolutions in the case that $Z$ is the Weyl group of a Kac-Moody algebra).
Keywords: keywords Bruhat order, special matchings, Coxeter groups 
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     title = {Algebraic and combinatorial properties of zircons},
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Marietti, Mario. Algebraic and combinatorial properties of zircons. Journal of Algebraic Combinatorics, Tome 26 (2007) no. 3, pp. 363-382. http://geodesic.mathdoc.fr/item/JAC_2007__26_3_a1/