Pseudo-Kaehler Quantization on Flag Manifolds

A unified approach to geometric, symbol and deformation quantizations on a generalized flag manifold endowed with an invariant pseudo-Kaehler structure is proposed. The Hilbert space of states is realized via the Bott-Borel-Weil theorem in the sheaf cohomology of the geometric quantization line bund...

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Bibliographic Details
Published in:arXiv.org 1997-09
Main Author: Karabegov, Alexander V
Format: Article
Language:English
Subjects:
Deformation
Hilbert space
Homology
Measurement
Online Access:Get full text
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Summary:A unified approach to geometric, symbol and deformation quantizations on a generalized flag manifold endowed with an invariant pseudo-Kaehler structure is proposed. The Hilbert space of states is realized via the Bott-Borel-Weil theorem in the sheaf cohomology of the geometric quantization line bundle. The corresponding deformation quantization is a quantization with separation of variables. In particular cases we arrive at Berezin's quantization via covariant and contravariant symbols.
ISSN:2331-8422