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

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dc.creatorHuckleberry, Alan T.
dc.creatorWolf, Joseph A.
dc.date2003-08-29
dc.date.accessioned2026-07-07T05:00:40Z
dc.date.available2026-07-07T05:00:40Z
dc.descriptionThe 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.
dc.identifierhttps://arxiv.org/abs/math/0308285
dc.identifierhttp://arxiv.org/abs/math/0308285
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/68408
dc.subjectRepresentation Theory
dc.subjectMathematical Physics
dc.subjectComplex Variables
dc.subjectDifferential Geometry
dc.subject22E46; 32F10
dc.titleInjectivity of the Double Fibration Transform for Cycle Spaces of Flag Domains
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