Journal of Lie Theory

no. 2
Injectivity of the Double Fibration Transform for Cycle Spaces of Flag Domains<!-- Anfang Autor -->
Journal of Lie Theory, Volume 14 (2004) no. 2, pp. 509-522
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.
DOI: 10.5802/jolt.348
Classification: 22E10, 32L25, 22E46
Keywords: double fibration transform, Schubert intersection theory 
@article{JOLT_2004_14_2_a8,
     author = {A. T. Huckleberry and J. A. Wolf},
     title = {Injectivity of the {Double} {Fibration} {Transform} for {Cycle} {Spaces} of {Flag} {Domains<!--} {Anfang} {Autor} -->},
     journal = {Journal of Lie Theory},
     pages = {509--522},
     year = {2004},
     volume = {14},
     number = {2},
     doi = {10.5802/jolt.348},
     zbl = {1057.22007},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.348/}
}
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A. T. Huckleberry; J. A. Wolf. Injectivity of the Double Fibration Transform for Cycle Spaces of Flag Domains. Journal of Lie Theory, Volume 14 (2004) no. 2, pp. 509-522. doi: 10.5802/jolt.348

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