NILPOTENT ORBITS, NORMALITY, AND HAMILTONIAN GROUP-ACTIONS

Let M be a G-covering of a nilpotent orbit in g where G is a complex semisimple Lie group and g = Lie(G). We prove that under Poisson bracket the space R[21 of homogeneous functions on M of degree 2 is the unique maximal semisimple Lie subalgebra of R = R(M) containing g. The action of g' congruent-to R[2] exponentiates to an action of the corresponding Lie group G' on a G'-cover M' of a nilpotent orbit in g' such that M is open dense in M'. We determine all such pairs (g subset-of g') .