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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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Invariant deformations of orbit closures in $\mathfrak {sl}(n)$
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by Sébastien Jansou and Nicolas Ressayre PDF
Represent. Theory 13 (2009), 50-62 Request permission


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
  • © Copyright 2009 American Mathematical Society
  • Journal: Represent. Theory 13 (2009), 50-62
  • MSC (2000): Primary 14D22, 14L24
  • DOI:
  • MathSciNet review: 2485792