  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.
