Article Dans Une Revue Representation theory : An Electronic Journal of the American Mathematical Society Année : 2009

Invariant deformations of orbit closures in $\mathfrak{sl}_n$

Résumé

We study deformations of orbit closures for the action of a connected semisimple group $G$ on its Lie algebra $\mathfrak{g}$, especially when $G$ is the special linear group. The tools we use are on the one hand the invariant Hilbert scheme and on the other hand the sheets of $\mathfrak{g}$. We show that when $G$ is the special linear group, the connected components of the invariant Hilbert schemes we get are the geometric quotients of the sheets of $\mathfrak{g}$. These quotients were constructed by Katsylo for a general semisimple Lie algebra $\mathfrak{g}$; in our case, they happen to be affine spaces.

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Dates et versions

hal-00157519 , version 1 (26-06-2007)
hal-00157519 , version 2 (20-07-2007)

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Sébastien Jansou, Nicolas Ressayre. Invariant deformations of orbit closures in $\mathfrak{sl}_n$. Representation theory : An Electronic Journal of the American Mathematical Society, 2009, 13 (5), pp.50-62. ⟨10.1090/S1088-4165-09-00331-8⟩. ⟨hal-00157519v2⟩
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