Irreducible Unitary Representations Concerning Homogeneous Holomorphic Line Bundles Over Elliptic Orbits

Nobutaka Boumuki and Tomonori Noda

Journal of Mathematics Research, 2018, vol. 10, issue 4, 65-88

Abstract: In this paper we consider a homogeneous holomorphic line bundle over an elliptic adjoint orbit of a real semisimple Lie group, and set a continuous representation of the Lie group on a certain complex vector subspace of the complex vector space of holomorphic cross-sections of the line bundle. Then, we demonstrate that the representation is irreducible unitary.

Keywords: irreducible unitary representation; homogeneous holomorphic line bundle; elliptic adjoint orbit; complex flag manifold; real semisimple Lie group; maximal vector (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:ibn:jmrjnl:v:10:y:2018:i:4:p:62

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