K-invariant Kaehler structures on K-C/N and the associated line bundles

Abstract

Let K be a compact semi-simple Lie group, and let N be a maximal unipotent subgroup of the complexified group Kc. classify ail the K-invariant Kaehler structures on K-C/N. structure w, let L be the line bundle with connection whose curvature is w. We then study the holomorphic sections of L, which constitute a K-representation space.