rt.representation theory - Why should we consider D-module on flag variety of Lie algebra?

Why don't we stay at D-module on base affine space but go to study flag variety of Lie algebra?

I remembered there are nice papers of Bernstein-Gelfand-Gelfand and Gelfand-Kirillov discussing the relationship of representation of Lie algebra and correspondence differential operators on base affine space.

What about Grassmannian? Can we consider the D-module on Grassmannian?