scientific article

zbMath1171.32001MaRDI QIDQ3545511

Xiaonan Ma, Weiping Zhang

Publication date: 11 December 2008

Full work available at URL: http://smf4.emath.fr/Publications/Asterisque/2008/318/html/smf_ast_318.html

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zbMATH Keywords

Dirac operatorBergman kernelsymplectic reductionBerezin-Toeplitz quantization

Mathematics Subject Classification ID

Research exposition (monographs, survey articles) pertaining to several complex variables and analytic spaces (32-02) Momentum maps; symplectic reduction (53D20) Sheaves and cohomology of sections of holomorphic vector bundles, general results (32L10) Research exposition (monographs, survey articles) pertaining to global analysis (58-02) Geometric quantization (53D50) Research exposition (monographs, survey articles) pertaining to differential geometry (53-02) Integral representations; canonical kernels (Szeg?, Bergman, etc.) (32A25) Perturbations of PDEs on manifolds; asymptotics (58J37)

Related Items (16)

Reduction and coherent states ⋮ Equivariant fixed point formulae and Toeplitz operators under Hamiltonian torus actions and remarks on equivariant asymptotic expansions ⋮ Local scaling asymptotics for the Gutzwiller trace formula in Berezin-Toeplitz quantization ⋮ Asymptotics of eigensections on toric varieties ⋮ Scaling asymptotics of Szegö kernels under commuting Hamiltonian actions ⋮ Geometric quantization on CR manifolds ⋮ Commutativity of quantization with conic reduction for torus actions on compact CR manifolds ⋮ Toeplitz operators and the full asymptotic torsion forms ⋮ Equivariant asymptotics of Szegö kernels under Hamiltonian \(U(\mathbf{2})\)-actions ⋮ Superconnection and family Bergman kernels ⋮ Unitarity in ``Quantization commutes with reduction ⋮ \(G\)-invariant Szegő kernel asymptotics and CR reduction ⋮ \(G\)-invariant holomorphic Morse inequalities ⋮ On the coefficients of the equivariant Szegő kernel asymptotic expansions ⋮ Toeplitz operators on CR manifolds and group actions ⋮ Quantization and isotropic submanifolds

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