Ju l 2 00 3 Functorial quantization and the Guillemin – Sternberg conjecture

@inproceedings{Landsman2008JuL2,
  title={Ju l 2 00 3 Functorial quantization and the Guillemin – Sternberg conjecture},
  author={Nicolaas P. Landsman},
  year={2008}
}
We propose that geometric quantization of symplectic manifolds is the arrow part of a functor, whose object part is deformation quantization of Poisson manifolds. The 'quantiza-tion commutes with reduction' conjecture of Guillemin and Sternberg then becomes a special case of the functoriality of quantization. In fact, our formulation yields almost unlimited generalizations of the Guillemin–Sternberg conjecture, extending it, for example, to arbitrary Lie groups or even Lie groupoids… CONTINUE READING