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Paramétrisation d’orbites dans les nappes de Dixmier admissibles. (Parametrization of orbits in admissible Dixmier sheets). (French) Zbl 0574.17006
The purpose of this paper is to prove that the space of orbits in an ”admissible” closed Dixmier sheet (nappes de Dixmier) of a complex semisimple Lie algebra \({\mathfrak g}\) is parametrized by an affine space, in other words, to prove that there exists a section of orbits which is an affine space. The author of this paper introduced the notion of admissibility of a subset \(\theta\) of a basis of the root system of \({\mathfrak g}\) and gave a parametrization of orbits for a suitably defined Dixmier sheet \(X_{\theta}\) when \(\theta\) is an admissible set by utilizing his theory of prehomogeneous vector spaces of parabolic type. This parametrization is a generalization of Kostant’s section of the regular elements.
Reviewer: M.Muro

MSC:
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
17B20 Simple, semisimple, reductive (super)algebras
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