Linear cycle spaces in flag domains

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 and consider the linear cycle spaces , spaces of maximal compact linear subvarieties of open orbits . In general is a Stein manifold. Here the exact structure of is worked out when is a classical group that corresponds to a bounded symmetric domain B. In that case is biholomorphic to B if a certain double fibration is holomorphic, is biholomorphic to otherwise. There are also a number of structural results that do not require to be classical. 19 March 1999