The nilpotent cone for classical Lie superalgebras.

In this paper the authors introduce an analogue of the nilpotent cone, N, for a classical Lie superalgebra, g, that generalizes the definition for the nilpotent cone for semisimple Lie algebras. For a classical simple Lie superalgebra, g = g₀ ⊕ g₁ with Lie G₀ = g₀, it is shown that there are finitely many G₀-orbits on N. Later the authors prove that the Duflo-Serganova commuting variety, X, is contained in N for any classical simple Lie superalgebra. Consequently, our finiteness result generalizes and extends the work of Duflo-Serganova on the commuting variety. Further applications are given at the end of the paper. [ABSTRACT FROM AUTHOR]