Watch out that there are more simple objects than it looks like at first glance, even for sl_n, coming from IC extensions of nontrivial local systems on the orbits.

I have heard that the general problem of writing down the intersection homology D-module is weirdly difficult. Kari Vilonen's thesis was about this in the case of isolated singularities. For the nilpotent cone I wonder how well Ben's suggestion works in practice. Is it a simple matter to pick out the isotypic components of a semisimple D-module?

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, they can carry nontrivial local systems whose intermediate extensions to the nilpotent cone will be new simple D-modules.

I have heard that the general problem of writing down intermediate extensions explicitly, say by generators and relations, is weirdly difficult. Kari Vilonen did this for isolated singularities in his thesis. For the nilpotent cone I wonder how well Ben's suggestion works: 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 D-module you know how to decompose?