Geodesic
Symplectic slices for actions of reductive groups
Sbornik. Mathematics, Tome 197 (2006) no. 2, pp. 213-224 
I. V. Losev. Symplectic slices for actions of reductive groups. Sbornik. Mathematics, Tome 197 (2006) no. 2, pp. 213-224. http://geodesic.mathdoc.fr/item/SM_2006_197_2_a4/
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     url = {http://geodesic.mathdoc.fr/item/SM_2006_197_2_a4/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $G$ be a reductive algebraic group over the field $\mathbb C$, $X$ a symplectic smooth affine algebraic variety, $G:X$ a Hamiltonian action, $x$ a point in $X$ with closed orbit. The structure of the variety $X$ in some invariant neighbourhood of the point $x$ is described. The neighbourhood is taken in the complex topology. Bibliography: 6 titles.

[1] D. Luna, “Slices étales”, Bull. Soc. Math. France, 33 (1973), 81–105 | MR | Zbl

[2] V. Guillemin, S. Sternberg, Symplectic techniques in physics, Cambridge Univ. Press, Cambridge, 1984 | MR | Zbl

[3] F. Knop, Weyl groups of Hamiltonian manifolds, I, , 1997 dg-ga/9712010

[4] E. B. Vinberg, V. L. Popov, “Teoriya invariantov”, Itogi nauki i tekhniki. Sovr. probl. matem. Fund. napr., 55, VINITI, M., 1989, 137–309 | MR

[5] E. B. Vinberg, “Kommutativnye odnorodnye prostranstva i koizotropnye simplekticheskie deistviya”, UMN, 56:1 (2001), 3–62 | MR | Zbl

[6] N. Burbaki, Gruppy i algebry Li. Gl. 7, 8. Podalgebry Kartana, regulyarnye elementy, rasscheplyaemye poluprostye algebry Li, Mir, M., 1978 | MR