In this paper we start by defining what an algebroid stack is, and how it is locally described. We then discuss the algebroid stack of WKB operators on a complex symplectic manifold X and define the deformation quantization of an involutive submanifold V of X by means of simple WKB modules along V . Finally, we relate this deformation quantization to that given by WKB operators on the quotient of V by its bicharacteristic leaves.
Deformation quantization of complex involutive submanifolds
D'AGNOLO, ANDREA;POLESELLO, PIETRO
2005
Abstract
In this paper we start by defining what an algebroid stack is, and how it is locally described. We then discuss the algebroid stack of WKB operators on a complex symplectic manifold X and define the deformation quantization of an involutive submanifold V of X by means of simple WKB modules along V . Finally, we relate this deformation quantization to that given by WKB operators on the quotient of V by its bicharacteristic leaves.File in questo prodotto:
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