an:03916516
Zbl 0574.17006
Rubenthaler, Hubert
Param??trisation d'orbites dans les nappes de Dixmier admissibles. (Parametrization of orbits in admissible Dixmier sheets)
FR
M??m. Soc. Math. Fr., Nouv. S??r. 15, 255-275 (1984).
00150091
1984
j
17B10 17B20
space of orbits; Dixmier sheet; complex semisimple Lie algebra; affine space; admissibility; parametrization; prehomogeneous vector spaces of parabolic type
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.
M.Muro