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A restriction theorem for invariants and nilpotent elements in \(W_ n\). (Russian) Zbl 0737.17006

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.

MSC:

17B50 Modular Lie (super)algebras
17B05 Structure theory for Lie algebras and superalgebras
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