TITLE: D-modules supported on the nilpotent cone
QUESTION [13 upvotes]: 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 was explained to me (the statement, not the proof) that the category of such D-modules is semisimple, and that the simple objects are given by (the intermediate extension) of the constant sheaf sheaf of functions on each g-orbit on n, so they are in bijection with Jordan decompositions with all zeroes, so just partitions of n.
I'm not strong with D-modules (I'm learning!).  My question is this:  Since g is affine, D(g) is an associative algebra, namely the Weyl algebra on the vector space g.  How can I describe the D(g)-module M corresponding to partition \lambda explicitly as a module over D(g)?

REPLY [2 votes]: This is a very old question, but for future visitors, I would like to point out that the answer is described in section 3 of:
T. Levasseur, "Equivariant D-modules attached to nilpotent orbits in a semisimple Lie algebra", 1998.
It isn't clear to me that all of the simple objects are covered by the constructions in this paper, but at least it seems that the type you're considering are - i.e. those arising from minimal extension of functions on a nilpotent orbit.