Linear cycle spaces in flag domains

Abstract.

Let Z = G/Q, a complex flag manifold, where G is a complex semisimple Lie group and Q is a parabolic subgroup. Fix a real form $G_0 \subset G$ and consider the linear cycle spaces $M_D$, spaces of maximal compact linear subvarieties of open orbits $D = G_0(z) \subset Z$. In general $M_D$ is a Stein manifold. Here the exact structure of $M_D$ is worked out when $G_0$ is a classical group that corresponds to a bounded symmetric domain B. In that case $M_D$ is biholomorphic to B if a certain double fibration is holomorphic, is biholomorphic to $B \times \overline{B}$ otherwise. There are also a number of structural results that do not require $G_0$ to be classical.