Deformation quantization modules on complex symplectic manifolds

Details Deformation quantization modules on complex symplectic manifolds Deformation quantization modules on complex symplectic manifolds

2007-04-23

arxiv.org/abs/0704.3007v2

Mathematics

Quantum Algebra

To appear in the Proceedings of the Poisson 2006 (Tokyo), AMS Contemporary Mathematics

Scientific paper

We study modules over the algebroid stack $\W[\stx]$ of deformation quantization on a complex symplectic manifold $\stx$ and recall some results: construction of an algebra for $\star$-products, existence of (twisted) simple modules along smooth Lagrangian submanifolds, perversity of the complex of solutions for regular holonomic $\W[\stx]$-modules, finiteness and duality for the composition of ``good'' kernels. As a corollary, we get that the derived category of good $\W[\stx]$-modules with compact support is a Calabi-Yau category. We also give a conjectural Riemann-Roch type formula in this framework.

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