  We study the orbit structure and the geometric quantization of a pair of
mutually commuting hamiltonian actions on a symplectic manifold. If the pair of
actions fulfils a symplectic Howe condition, we show that there is a canonical
correspondence between the orbit spaces of the respective moment images.
Furthermore, we show that reduced spaces with respect to the action of one
group are symplectomorphic to coadjoint orbits of the other group. In the
Kaehler case we show that the linear representation of a pair of compact Lie
groups on the geometric quantization of the manifold is then equipped with a
representation-theoretic Howe duality.
