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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

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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