On localization of quantized hypertoric algebras and microlocal analysis

Starting from a well-known and easy example of the Beilinson-Bernstein
correspondence for the case of U(sl_2), I will explain how we consider
"localization" for some noncommutative algebras, which I will call quantized
hypertoric algebras in this talk.
The quantized hypertoric algebras are defined as quantization
(non-commutative deformation) of hypertoric variety by I. Musson and
M. Van der Burgh. By introducing quantization of the structure sheaves
of symplectic manifolds, we obtain sheaves of noncommutative algebras l
ocalizing the quantized hypertoric algebras.
This talk is based on the joint work with G. Bellamy.