Watch out that there are more simple objects than it looks like at first glance, even for sl_n. Although the orbits are parameterized by partitions, coming from IC extensions of they can carry nontrivial local systems on whose intermediate extensions to the orbitsnilpotent cone will be new simple D-modules.
I have heard that the general problem of writing down the intersection homology D-module intermediate extensions explicitly, say by generators and relations, is weirdly difficult. Kari Vilonen's thesis was about Vilonen did this in the case of for isolated singularities in his thesis. For the nilpotent cone I wonder how well Ben's suggestion worksin practice. Is : is it a simple matter to pick out the isotypic components of this pushforward D-module, using the bare fact (geometric magic) that it's an intermediate extension of a semisimple D-module you know how to decompose?
