Geodesic
Bruhat-Chevalley order in reductive monoids.
Journal of Algebraic Combinatorics, Tome 20 (2004) no. 1, pp. 33-53.

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

Summary: Let $M$ be a reductive monoid with unit group $G$. Let $Lambda$ denote the idempotent cross-section of the $G \times $G-orbits on $M$. If $W$ is the Weyl group of $G$ and $e, fisinLambda$ with $elef$, we introduce a projection map from $WeW$ to $WfW$. We use these projection maps to obtain a new description of the Bruhat-Chevalley order on the Renner monoid of $M$. For the canonical compactification $X$ of a semisimple group $G _{0}$ with Borel subgroup $B _{0}$ of $G _{0}$, we show that the poset of $B _{0} \times B _{0}$-orbits of $X$ (with respect to Zariski closure inclusion) is Eulerian.
Classification : Primary, 20G99,, 20M99,, 06A07
Keywords: reductive monoid, Renner monoid, Bruhat-Chevalley order, projections 
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     title = {Bruhat-Chevalley order in reductive monoids.},
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Putcha, Mohan S. Bruhat-Chevalley order in reductive monoids.. Journal of Algebraic Combinatorics, Tome 20 (2004) no. 1, pp. 33-53. http://geodesic.mathdoc.fr/item/JAC_2004__20_1_a4/