Pseudo-Kaehler Quantization on Flag Manifolds

Details Pseudo-Kaehler Quantization on Flag Manifolds Pseudo-Kaehler Quantization on Flag Manifolds

1997-09-17

arxiv.org/abs/dg-ga/9709015v1

Mathematics

Differential Geometry

32 pages, latex

Scientific paper

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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