
Journal of Lie Theory 14 (2004), No. 2, 509522 Copyright Heldermann Verlag 2004 Injectivity of the Double Fibration Transform for Cycle Spaces of Flag Domains Alan T. Huckleberry Fakultät für Mathematik, RuhrUniversität, 44780 Bochum, Germany, ahuck@cplx.ruhrunibochum.de Joseph A. Wolf Dept. of Mathematics, University of California, Berkeley CA 947203840, U.S.A., jawolf@math.berkeley.edu [Abstractpdf] The basic setup consists of a complex flag manifold $Z=G/Q$ where $G$ is a complex semisimple Lie group and $Q$ is a parabolic subgroup, an open orbit $D = G_0(z) \subset Z$ where $G_0$ is a real form of $G$, and a $G_0$homogeneous holomorphic vector bundle $\mathbb E \to D$. The topic here is the double fibration transform ${\cal P}: H^q(D; {\cal O}(\mathbb E)) \to H^0({\cal M}_D;{\cal O}(\mathbb E'))$ where $q$ is given by the geometry of $D$, ${\cal M}_D$ is the cycle space of $D$, and $\mathbb E' \to {\cal M}_D$ is a certain naturally derived holomorphic vector bundle. Schubert intersection theory is used to show that ${\cal P}$ is injective whenever $\mathbb E$ is sufficiently negative. [FullTextpdf (238 KB)] for subscribers only. 