Cayley transforms and orbit structure in complex flag manifolds

Abstract

LetZ=G/Q be a complex flag manifold andG 0 a real form ofG. Suppose thatG 0 is the analytic automorphism group of an irreducible bounded symmetric domain and that some openG 0-orbit onZ is a semisimple symmetric space. Then theG 0-orbit structure ofZ is described explicitly by the partial Cayley transforms of a certain hermitian symmetric sub-flagF⊃Z. This extends the results and simplifies the proof for the classical orbit structure description of [10] and [11], which applies whenF=Z.