1997/09/17 by Alexander Karabegov, Alexander V. Karabegov, Karabegov, Alexander V.
Mathematics · #Advanced Algebra and Geometry #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #dg-ga #math.DG #math.QA #q-alg
paper · pdf · doi:10.48550/arxiv.dg-ga/9709015
32 pages, latex
arxiv created 1997/09/17 · openalex publication_date 1997/09/17 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.