The fundamental conjecture for homogeneous Kähler manifolds (Q1113339)

The authors prove a conjecture first stated by \textit{S. G. Gindikin} and \textit{Eh. B. Vinberg} [Math. USSR, Sb. 3(1967), 333-351 (1969); translation from Mat. Sb., n. Ser. 74(116), 357-377 (1967; Zbl 0153.399)]: Every homogeneous Kähler manifold is a holomorphic fiber bundle over a homogeneous bounded domain in which the fiber is the product of a flat homogeneous Kähler manifold and a compact simply connected homogeneous Kähler manifold. Homogeneous Kähler manifolds have a long history, going back to the work of A. Borel, Y. Matsushima, and H. C. Wang in the 1950's. In the 1970's the structure of bounded homogeneous domains and their infinitesimal automorphisms were classified by various authors. More recently, the efforts of the two authors of this paper led to the solution of the fundamental conjecture under several different additional assumptions. This latter work and the knowledge of the detailed structure of bounded homogeneous domains play important parts in the proof of the general conjecture.