On cycle spaces of flag domains of \(SL_{n}{\mathbb R}\) (Q2757783)

Wolf's domain \(\Omega_D\) of \(q\)-cycles in an open \(SL_n(\mathbb{R})\) orbit \(D\) in a classical flag manifold \(Z\) [see \textit{J. A. Wolf}, Bull. Am. Math. Soc. 75, 1121-1237 (1969; Zbl 0183.50901)] is studied in detail. Special Schubert varieties which are in particular transversal to the cycles are introduced. It is shown that \(\Omega_D\) is Stein with respect to special rational functions in the image of the Andreotti-Norguet integration transform \(AN:H^q(D, \Omega^P)\to O(\Omega_D)\). For \(n\) fixed with \(Z_1\) and \(Z_2\) any two flag manifolds containing open orbits \(D_1\) and \(D_2\) it is proved that \(\Omega_{D_1}\) and \(\Omega_{D_2}\) are naturally biholomorphic.NEWLINENEWLINENEWLINEThe basic results which are needed from the theory of cycle spaces are sketched in the appendix.