If we have filtration on D-module compatible with some good filtration on differential operators sheaf then adjoint graded module is module over functions on cotangent bundle. So morally D-module is quantization of something lying on cotangent bundle. There is some rigid statement around this? Some concrete expectations. From here Derived (non-commutative) geometry, geometric constructions in explicit form we could get some dg-algebras for derived categories of D-modules and coherent sheaves on cotangent bundle resp., for their suitable models (~quasi-isomorphism) can we observe first thing as "quantization" of second precisely on the level of differential? Second. Peoples in geometric representation theory often work with coherent sheaves on cotangent bundle of flag varieties, but by the pointed view their constructions must admit quantization, does such thoughts been exploited? It is can be funny if geometric representation construction was connected with some quantum group, because D-modules on flag variety is almost representations of lie algebra

If we have filtration on D-module compatible with some good filtration on differential operators sheaf then adjoint graded module is module over functions on cotangent bundle. So morally D-module is quantization of something lying on cotangent bundle. There is some rigid statement around this? Some concrete expectations. From here Derived (non-commutative) geometry, geometric constructions in explicit form we could get some dg-algebras for derived categories of D-modules and coherent sheaves on cotangent bundle resp., for their suitable models (~quasi-isomorphism) can we observe first thing as "quantization" of second precisely on the level of differential? Second. Peoples in geometric representation theory often work with coherent sheaves on cotangent bundle of flag varieties, but by the pointed view their constructions must admit quantization, does such thoughts been exploited? It is can be funny if geometric representation construction was connected with some quantum group, because D-modules on flag variety is almost representations of lie algebra