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.
Symplectically Asystatic actions of compact Lie Groups / A. Gori, F. Podestà. - In: TRANSFORMATION GROUPS. - ISSN 1083-4362. - 11:2(2006), pp. 177-184.
Symplectically Asystatic actions of compact Lie Groups
A. GoriPrimo
;
2006
Abstract
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.
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