Journal of Lie Theory EMIS ELibM Electronic Journals Journal of Lie Theory
Vol. 14, No. 2, pp. 509--522 (2004)

Previous Article

Next Article

Contents of this Issue

Other Issues

ELibM Journals

ELibM Home



Injectivity of the Double Fibration Transform for Cycle Spaces of Flag Domains

Alan T. Huckleberry and Joseph A. Wolf

Alan T. Huckleberry
Fakult\" at f\" ur Mathematik
Ruhr--Universit\" at Bochum
D--44780 Bochum, Germany
Joseph A. Wolf
Department of Mathematics
University of California
Berkeley, CA 94720--3840, USA

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.

© 2004 Heldermann Verlag
© 2004 ELibM and FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition