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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?

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Essentially people do consider all these things -- when you include twisted D-modules on the flag variety you are essentially studying D-modules on the basic affine space, and D-modules on any partial flag variety are also studied (in relation to singular characters in particular). –  Kevin McGerty Mar 13 '10 at 18:26
Kevin- Come on, you know better than that: D-modules on the base affine space see generalized central characters, those on the flag variety only see representations where the center acts semi-simply. –  Ben Webster Mar 13 '10 at 20:12
Unknown- Your question is very unclear. There are people on this site (such as Kevin and myself) who know many things about the objects you mention but without anything specific to go on, there's not a lot we can tell you. –  Ben Webster Mar 13 '10 at 20:12
@Ben: haha yea sure, but I meant that people often work with the basic affine space without explicitly saying it. –  Kevin McGerty Mar 13 '10 at 21:57
Actually, one should go to flag variety rather than base affine space because of exactness of global section functors. I will elaborate later –  Shizhuo Zhang Mar 14 '10 at 5:15

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