Abstract
Let K be a compact semi-simple Lie group, and let N be a maximal unipotent subgroup of the complexified group K C . In this paper, we classify all the K-invariant Kaehler structures on K C /N. For each Kaehler structure ω, let L be the line bundle with connection whose curvature is ω. We then study the holomorphic sections of L, which constitute a K-representation space. ©1996 American Mathematical Society.