A quantum duality principle for coisotropic subgroups and Poisson quotients

Details A quantum duality principle for coisotropic subgroups and Poisson quotients A quantum duality principle for coisotropic subgroups and Poisson quotients

2004-12-22

arxiv.org/abs/math/0412465v4

Advances in Mathematics 199 (2006), 104-135

Mathematics

Quantum Algebra

27 pages, AMS-TeX file. Final version, with some typoes (also occurring in the printed version) corrected

Scientific paper

We develop a quantum duality principle for coisotropic subgroups of a (formal) Poisson group and its dual. Namely, starting from a quantum coisotropic subgroup (for a quantization of a given Poisson group) we provide functorial recipes to produce quantizations of the dual coisotropic subgroup (in the dual formal Poisson group). By the natural link between subgroups and homogeneous spaces, we argue a quantum duality principle for Poisson homogeneous spaces which are Poisson quotients, i.e. have at least one zero-dimensional symplectic leaf. As an application, we provide an explicit quantization of the homogeneous SL(n)^*-space of Stokes matrices, with the Poisson structure given by Dubrovin and Ugaglia.

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