Almost-commuting variety, D-modules, and Cherednik Algebras
  We study a scheme M closely related to the set of pairs of n by n-matrices with rank 1 commutator. We show that M is a reduced complete intersection with n+1 irreducible components, which we describe.   There is a distinguished Lagrangian subvariety Nil in M. We introduce a category, C, of D-modules whose characteristic variety is contained in Nil. Simple objects of that category are analogous to Lusztig's character sheaves. We construct a functor of Quantum Hamiltonian reduction from category C to the category O for type A rational Cherednik algebra. 
Wee Liang Gan and Victor Ginzburg