Positive polarizations and Abelian ideals in Lie algebras

In this paper a theorem on the relative distribution of an Abelian ideal and a positive polarization in a Lie algebra (of general type) is proved. It permits one to extend signficantly the domain of application of a theorem on holomorphically induced representations of Lie groups with an Abelian normal subgroup and a criterion for nontriviality of the representation space given by a polarization, both results obtained earlier by the author.
Bibliography: 4 titles.