Hamiltonian diffeomorphisms of toric manifolds and flag manifolds

If ss and nn are integers relatively prime and Ham(Gs(Cn)) is the group of Hamiltonian symplectomorphisms of the Grassmannian manifold Gs(Cn)Gs(Cn), we prove that ♯π1(Ham(Gs(Cn)))≥n.We prove that π1(Ham(M)) contains an infinite cyclic subgroup, when MM is the one point blow up of CP3CP3. We give a sufficient condition for the group π1(Ham(M)) to contain a subgroup isomorphic to ZpZp, when MM is a general toric manifold.