Functorial quantization and the Guillemin-Sternberg conjecture

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dc.creatorLandsman, N. P.
dc.date2003-07-29
dc.date.accessioned2026-07-07T04:30:25Z
dc.date.available2026-07-07T04:30:25Z
dc.descriptionWe propose that geometric quantization of symplectic manifolds is the arrow part of a functor, whose object part is deformation quantization of Poisson manifolds. The `quantization 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. Technically, this involves symplectic reduction and Weinstein's dual pairs on the classical side, and Kasparov's bivariant K-theory for C*-algebras (KK-theory) on the quantum side.
dc.description15 pages. Proc. Bialowieza 2002
dc.identifierhttps://arxiv.org/abs/math-ph/0307059
dc.identifierhttp://arxiv.org/abs/math-ph/0307059
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/57459
dc.subjectMathematical Physics
dc.subjectSymplectic Geometry
dc.subject46L65
dc.titleFunctorial quantization and the Guillemin-Sternberg conjecture
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