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Pseudo-Kaehler Quantization on Flag Manifolds

Alexander V. Karabegov
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Abstract

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.

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BibTeXRIS

Alexander V. Karabegov. 1997-09-17. Pseudo-Kaehler Quantization on Flag Manifolds. https://arxiv.org/abs/dg-ga/9709015

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