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By 1968 Gindikin, P. Shapiro and E.B. Vinberg stated the
conjecture that a homogeneous Kaehlerian manifold is the total space
of an analytical fibration over a bounded domain whose fibers are
products of simply connected homogeneous Kaehlerian manifolds and
compact homogenous Kaehlerian manifolds.\\
This conjecture has become a Theorem proved by J. Dorfmeister. The
proof is base on the notion of j-algebra which had been initiated by
Jean-Louis Koszul. The aim of my talk is to use the linearization of
some lagrangian webs in order to reduce to conjecture in Riemann
surfaces and then to proceed by induction.
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