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Holomorphic Discrete Models of Semisimple Lie Groups and their Symplectic Constructions

✍ Scribed by Meng-Kiat Chuah

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 257 KB
Volume: 175
Category: Article
ISSN: 0022-1236
DOI: 10.1006/jfan.2000.3586

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✦ Synopsis

Let G be a connected real semisimple Lie group which contains a compact Cartan subgroup such that it has non-empty discrete series. A holomorphic discrete model of G is a unitary G-representation consisting of all its holomorphic discrete series with multiplicity one. We perform geometric quantization to a class of G-invariant pseudo-Ka hler manifolds and construct a holomorphic discrete model. The construction of discrete series which are not holomorphic is also discussed.

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