Abstract
Let G = KAN be the Iwasawa decomposition of a complex connected semi-simple Lie group G. Let P ⊂ G be a parabolic subgroup containing AN, and let (P, P) be its commutator subgroup. In this paper, we characterize the K-invariant Kähler structures on G/(P, P), and study the holomorphic sections of their corresponding pre-quantum line bundles. © 2000 American Mathematical Society.