Journal of Lie Theory 33 (2023), No. 3, 713--718
Copyright Heldermann Verlag 2023
Elliptic Coadjoint Orbits of Holomorphic Type
Hideko Sekiguchi
Graduate School of Mathematical Sciences, The University of Tokyo, Japan
hseki@ms.u-tokyo.ac.jp
This article proves that any elliptic coadjoint orbit of a semisimple Lie group carries a holomorphic bundle structure over a flag variety if the polarization is given by a θ-stable parabolic subalgebra of holomorphic type. An application to the Penrose transform is given.
Keywords: Reductive Lie groups, coadjoint orbits, Borel embedding, Harish-Chandra decomposition, indefinite Kaehler manifold.
MSC: 32M15; 53C65, 53C35, 17B20.
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