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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., Comment: Final version, to appear in IMRN. Introduction expanded, many minor corresctions made, section 7 rewritten, an Appendix added

We show that solving the Maurer-Cartan equations is, essentially, the same thing as performing the Hamiltonian reduction construction. In particular, any differential graded Lie algebra equipped with an even nondegenerate invariant bilinear form gives rise to modular stacks with symplectic structures., Comment: 9 pp., expanded version: more details and comments added

We give a direct proof of (a slight generalization of) the recent result of A. Premet related to generalized Gelfand-Graev representations and of an equivalence due to Skryabin., Comment: An appendix is added providing some details concerning section 3.1