Nilpotent Orbits and Complex Dual Pairs Andrzej

Let (W, 〈 , 〉) be a complex symplectic vector space and let Sp(W) be the symplectic group. Let G, G ′ ⊆ Sp(W) be a complex reductive dual pair (see Howe [H1]), i. e. G and G ′ are centralizers of each other in Sp(W) and both act completely reductively on W. Let g and g′ be the Lie algebras of G and G′. We have the (unnormalized) moment map