Geodesic
Nilpotent variety of a reductive monoid.
Journal of Algebraic Combinatorics, Tome 27 (2008) no. 3, pp. 275-292.

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

Summary: In this paper we study the variety $M _{ nil }$ of nilpotent elements of a reductive monoid $M$. In general this variety has a completely different structure than the variety $G _{ uni }$ of unipotent elements of the unit group $G$ of $M$. When $M$ has a unique non-trivial minimal or maximal $G\times $G-orbit, we find a precise description of the irreducible components of $M _{ nil }$ via the combinatorics of the Renner monoid of $M$ and the Weyl group of $G$. In particular for a semisimple monoid $M$, we find necessary and sufficient conditions for the variety $M _{ nil }$ to be irreducible.
Classification : 20M10, 20G99
Keywords: keywords reductive monoid, nilpotent variety, unipotent variety, Renner monoid, Weyl group 
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     title = {Nilpotent variety of a reductive monoid.},
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Putcha, Mohan S. Nilpotent variety of a reductive monoid.. Journal of Algebraic Combinatorics, Tome 27 (2008) no. 3, pp. 275-292. http://geodesic.mathdoc.fr/item/JAC_2008__27_3_a6/