Homogeneous connections with special symplectic holonomy

We classify all homogeneous symplectic manifolds with a torsion free connection of special symplectic holonomy, i.e. a connection whose holonomy is an absolutely irreducible proper subgroup of the full symplectic group. Thereby, we obtain many new explicit descriptions of manifolds with special symplectic holonomies. We also show that manifolds with such a connection are homogeneous iff they contain no symmetric points and their symplectic scalar curvature is constant.SCOPUS: ar.j