Quantization of Whitney functions and reduction

M. J. Pflaum, H. Posthuma, and X. Tang

Journal of Singularities
volume 13 (2015), 217-228

Received 23 October 2013.

DOI: 10.5427/jsing.2015.13l

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For a possibly singular subset of a regular Poisson manifold we construct a deformation quantization of its algebra of Whitney functions. We then extend the construction of a deformation quantization to the case where the underlying set is a subset of a not necessarily regular Poisson manifold which can be written as the quotient of a regular Poisson manifold on which a compact Lie group acts freely by Poisson maps. Finally, if the quotient Poisson manifold is regular as well, we show a "quantization commutes with reduction" type result. For the proofs, we use methods stemming from both singularity theory and Poisson geometry.

Author(s) information:

Markus J. Pflaum Hessel Posthuma Xiang Tang
Department of Mathematics Korteweg-de Vries Institute for Mathematics Department of Mathematics
University of Colorado University of Amsterdam Washington University
Boulder, USA The Netherlands St. Louis, USA
email: markus.pflaum@colorado.edu email: h.b.posthuma@uva.nl email: xtang@math.wustl.edu