3
votes
2answers
551 views

How is this observation related to Koszul duality?

Let $X$ be a smooth variety, $\mathcal D$ the sheaf of algebraic differentail operators, $\Omega$ the algebraic deRham complex and $\mathcal M$ a quasi coherent $\mathcal O_X$-module. Now there is a ...
0
votes
2answers
491 views

What is a Module over a Lie algebroid?

Let $\alpha: \mathfrak g_A \to T_{A/k}$ be a Lie algebroid over a $k$-algebra $A$. Numerous facts about and its universal enveloping algebra comes from the theory of ring differential operators on ...
10
votes
1answer
1k views

What is the recent development of D-module and representation theory of Kac-Moody algebra?

I just started to collect the papers of this field and know little things. So if I make stupid mistake, please correct me. It seems that there are several approaches to localize Kac-Moody algebra(in ...
7
votes
3answers
726 views

Making D-modules on affine varieties more explicit

This is a follow up to my question about D-modules supported on the nilpotent cone. I got some good answers there but now I have a more basic question. Consider an affine algebraic variety X, a ...
11
votes
3answers
993 views

D-modules supported on the nilpotent cone

I am reading some papers which involve D-modules on a Lie algebra g, which are supported on the nilpotent cone n. They are equivariant for the action of G. (In particular, I consider g=sl_n). It ...