On the global construction of modules over Fedosov deformation quantization algebra

TL;DR

This paper constructs a Fedosov-type star-product on a symplectic manifold that naturally endows functions on a polarization leaf with a module structure over the deformed algebra, extending previous results.

Contribution

It generalizes the construction of modules over Fedosov deformation quantization algebras to arbitrary leaves of a polarization on symplectic manifolds.

Findings

Established a Fedosov-type star-product compatible with polarization leaves.

Defined a natural module structure on functions over polarization leaves.

Extended previous results to more general geometric settings.

Abstract

Let $(M,\omega)$ be a symplectic manifold, $\mathcal{D}\subset TM$ a real polarization on $M$ and $\wp$ a leaf of $\mathcal{D}$. We construct a Fedosov-type star-product $\ast_L$ on $M$ such that $C^\infty (\wp)[[h]]$ has a natural structure of left module over the deformed algebra $(C^\infty (M)[[h]], \ast_L)$. This generalizes the results of 0708.2626.