Holomorphic sections of pre-quantum line bundles on G/(P, P)

Abstract

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