Journal of Lie Theory Vol. 14, No. 2, pp. 509522 (2004) 

Injectivity of the Double Fibration Transform for Cycle Spaces of Flag DomainsAlan T. Huckleberry and Joseph A. WolfAlan T. HuckleberryFakult\" at f\" ur Mathematik RuhrUniversit\" at Bochum D44780 Bochum, Germany ahuck@cplx.ruhrunibochum.de and Joseph A. Wolf Department of Mathematics University of California Berkeley, CA 947203840, USA jawolf@math.berkeley.edu Abstract: 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. Full text of the article:
Electronic version published on: 1 Sep 2004. This page was last modified: 1 Sep 2004.
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