Bergman kernel and Geometric quantization (joint with Weiping ...
Bergman kernel and Geometric quantization (joint with Weiping ...
Bergman kernel and Geometric quantization (joint with Weiping ...
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Quantization on symplectic manifolds<br />
<strong>Bergman</strong> <strong>kernel</strong> <strong>and</strong> qeometric <strong>quantization</strong><br />
Transversal index<br />
<strong>Geometric</strong> <strong>quantization</strong><br />
Quantization commutes <strong>with</strong> reduction<br />
Non-compact case : Vergne’s conjecture<br />
◮ Assume X is non-compact <strong>and</strong> µ : X → g ∗ is proper.<br />
◮ We can define a transversally elliptic symbol σ X L,µ in<br />
the sense of Atiyah (1974).<br />
σM L,µ has an index :<br />
Ind σ X <br />
L,µ =<br />
The set {γ ∈ Λ ∗ + : Indγ<br />
γ∈Λ ∗ +<br />
Indγ<br />
X G<br />
σL,µ · Vγ .<br />
<br />
X σL,µ = 0} can be infinite.<br />
Xiaonan Ma <strong>Bergman</strong> <strong>kernel</strong> <strong>and</strong> <strong>Geometric</strong> <strong>quantization</strong> (jo