Complex Asystatic actions of compact Lie Groups

摘要

In the present paper we introduce the notion of complex asystatic Hamiltonianaction on a K\"ahler manifold. In the algebraic setting we prove that if acomplex linear group $G$ acts complex asystatically on a K\"ahler manifold thenthe $G$-orbits are spherical. Finally we give the complete classification ofcomplex asystatic irreducible representations.