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Slodowy slices and universal Poisson deformations

Part of: Local theory Lie algebras and Lie superalgebras

Published online by Cambridge University Press:  09 November 2011

M. Lehn ,
Y. Namikawa  and
Ch. Sorger
M. Lehn
Affiliation:
Fachbereich Physik, Mathematik u. Informatik, Johannes Gutenberg–Universität Mainz, D-55099 Mainz, Germany (email: lehn@mathematik.uni-mainz.de)
Y. Namikawa
Affiliation:
Department of Mathematics, Faculty of Science, Kyoto University, Kitashirakawa-Oiwakecho, Kyoto, 606-8502, Japan (email: namikawa@math.kyoto-u.ac.jp)
Ch. Sorger
Affiliation:
Laboratoire de Mathématiques Jean Leray (UMR 6629 du CNRS), Université de Nantes, 2, Rue de la Houssinière, BP 92208, F-44322 Nantes Cedex 03, France (email: christoph.sorger@univ-nantes.fr)
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Abstract

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We classify the nilpotent orbits in a simple Lie algebra for which the restriction of the adjoint quotient map to a Slodowy slice is the universal Poisson deformation of its central fibre. This generalises work of Brieskorn and Slodowy on subregular orbits. In particular, we find in this way new singular symplectic hypersurfaces of dimension four and six.

Keywords

nilpotent orbitssymplectic singularitiessymplectic hypersurfacesPoisson deformations

MSC classification

Secondary: 14B07: Deformations of singularities 17B45: Lie algebras of linear algebraic groups 17B63: Poisson algebras
Type
Research Article
Information
Compositio Mathematica , Volume 148 , Issue 1 , January 2012 , pp. 121 - 144
Copyright
Copyright © Foundation Compositio Mathematica 2011

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