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Holomorphic Discrete Models of Semisimple Lie Groups and their Symplectic Constructions

Authors
Journal
Journal of Functional Analysis
0022-1236
Publisher
Elsevier
Publication Date
Volume
175
Issue
1
Identifiers
DOI: 10.1006/jfan.2000.3586
Keywords
  • Holomorphic Discrete Model
  • Pseudo-Kähler
Disciplines
  • Mathematics

Abstract

Abstract 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-Kähler manifolds and construct a holomorphic discrete model. The construction of discrete series which are not holomorphic is also discussed.

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