Complex Asystatic actions of compact Lie Groups

Abstract

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