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Zbl 1163.53056
Paradan, Paul-Émile
Formal geometric quantization. (English)
[J] Ann. Inst. Fourier 59, No. 1, 199-238 (2009). ISSN 0373-0956; ISSN 1777-5310/e

The aim of this remarkable article is to study the functorial properties of the {\it formal geometric quantization} process which is defined on non-compact Hamiltonian manifolds endowed with a proper momentum map. For this purpose, a technique of symplectic cutting is introduced and a central theme is an extension of the ``quantization commutes with reduction" theorem to the singular setting; here the singular manifolds are those obtained by symplectic reduction.
[Mircea Crâşmăreanu (Iaşi)]

MSC 2000:: *53D50 Geometric quantization
57S15 Compact Lie groups of differentiable transformations
19L47 Equivariant K-theory
19L10 Riemann-Roch theorems, etc.

Keywords: geometric quantization; moment map; symplectic reduction; index; transversally elliptic

Cited in: Zbl 1235.53093

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