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Quantization of Vector Bundles on Lagrangian Subvarieties

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We consider a smooth Lagrangian subvariety Y in a smooth algebraic variety X with an algebraic symplectic from. For a vector bundle E on Y and a choice Oh of… Click to show full abstract

We consider a smooth Lagrangian subvariety Y in a smooth algebraic variety X with an algebraic symplectic from. For a vector bundle E on Y and a choice Oh of deformation quantization of the structure sheaf of X, we establish when E admits a deformation quantization to a module over Oh. If the necessary conditions hold, we describe the set of equivalence classes of such quantizations.

Keywords: vector; quantization; vector bundles; lagrangian subvarieties; bundles lagrangian; quantization vector

Journal Title: International Mathematics Research Notices
Year Published: 2017

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