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Journal of Lie Theory 33 (2023), No. 4, 953--963
Copyright Heldermann Verlag 2023

Cohomological Integral Transform Associated to θ-Stable Parabolic Subalgebras of Holomorphic Type

Hideko Sekiguchi
Graduate School of Mathematical Sciences, The University of Tokyo, Japan

Every elliptic adjoint orbit X of a real reductive group carries naturally a complex manifold structure. This article proves a necessary and sufficient condition on X for which the (generalized) Radon-Penrose transform on Dolbeault cohomologies on X maps into the space of holomorphic sections.

Keywords: Reductive Lie groups, coadjoint orbits, indefinite Kaehler manifold, Penrose transform, Dolbeault cohomology.

MSC: 32M15; 53C65, 53C35, 17B20.

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