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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 gG. (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)?
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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)?
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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 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)?
show/hide this revision's text 2 added 3 characters in body; deleted 4 characters in body
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