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Representation Theory

ISSN 1088-4165



Invariant deformations of orbit closures in $ \mathfrak{sl}(n)$

Authors: Sébastien Jansou and Nicolas Ressayre
Journal: Represent. Theory 13 (2009), 50-62
MSC (2000): Primary 14D22, 14L24
Published electronically: March 5, 2009
MathSciNet review: 2485792
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Abstract: 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 the invariant Hilbert scheme and 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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Additional Information

Sébastien Jansou
Affiliation: Le Mas des Landes, 87170 Isle, France

Nicolas Ressayre
Affiliation: Department of Mathematics, University of Montpellier II, Place Eugène Bataillon, Montpellier, France

Received by editor(s): July 23, 2007
Received by editor(s) in revised form: March 12, 2008
Published electronically: March 5, 2009
Article copyright: © Copyright 2009 American Mathematical Society