%0 Journal Article %T Complex Asystatic actions of compact Lie Groups %A Anna Gori %A Fabio Podesta %J Mathematics %D 2004 %I arXiv %X In the present paper we introduce the notion of complex asystatic Hamiltonian action on a K\"ahler manifold. In the algebraic setting we prove that if a complex linear group $G$ acts complex asystatically on a K\"ahler manifold then the $G$-orbits are spherical. Finally we give the complete classification of complex asystatic irreducible representations. %U http://arxiv.org/abs/math/0411204v1