Nilpotent Orbits and Complex Dual Pairs

Given a complex dual pair G, G', there are natural unnormalized moment maps t, t', from the symplectic space to the Lie algebras g, g' of G, G'.
We prove that the image under  t' of the preimage under t  of the closure of a nilpotent orbit in g is the closure of a single nilpotent orbit in g'.

Appeared in Journal of Algebra, 190, 518--539 (1997)