Premet, A. A. A restriction theorem for invariants and nilpotent elements in \(W_ n\). (Russian) Zbl 0737.17006 Mat. Sb. 182, No. 5, 746-773 (1991). The ring of invariants on the general Lie algebra of Cartan type \(W_ n\) is studied. It is proved that the well-known Chevalley restriction theorem is true for \(W_ n\), if in \(W_ n\) the Cartan subalgebra of the general type is taken, the analogue of the Weyl group being \(GL_ n(p)\). The geometry of the variety of nilpotent elements in \(W_ n\) is investigated. A criterion for the closed orbit in \(W_ n\) is obtained and some results on the stability of the action are achieved. Reviewer: M.Kuznetsov (Nizhnij Novgorod) Cited in 2 ReviewsCited in 2 Documents MSC: 17B50 Modular Lie (super)algebras 17B05 Structure theory for Lie algebras and superalgebras Keywords:ring of invariants; general Lie algebra of Cartan type \(W_ n\); Chevalley restriction theorem PDFBibTeX XMLCite \textit{A. A. Premet}, Mat. Sb. 182, No. 5, 746--773 (1991; Zbl 0737.17006) Full Text: EuDML