Kaehler-Ricci solitons on homogeneous toric bundles

We deal with homogeneous toric bundles M over generalized flag manifolds Gc/P, where G is a compact semisimple Lie group and P a parabolic subgroup. Using symplectic data, we provide a simple characterization of the homogeneous toric bundles M which are Fano; we then show that a homogeneous toric bundle M admits a Kaehler-Ricci solitonic metric if and only if it is Fano.