Symplectically Asystatic actions of compact Lie Groups

In the present paper we introduce the notion of symplectically asystatic Hamiltonian action on a K\"ahler manifold. In the algebraic setting we prove that if a complex linear group $G$ acts in a symplectically asystatic fashion on a K\"ahler manifold then the $G$-orbits are spherical. Finally we give the complete classification of symplectically asystatic irreducible representations.