  We attach a Dixmier algebra B to the closure of any nilpotent orbit of G
where G is GL(n,C), O(n,C) or Sp(2n,C). This algebra B is a noncommutative
analog of the coordinate ring R of the orbit closure, in the sense that B has a
G-invariant algebra filtration and gr B=R.
  We obtain B by making a noncommutative analog of the Kraft-Procesi
construction which modeled the orbit closure as the algebraic symplectic
reduction of a finite-dimensional symplectic vector space L. Indeed B is a
subquotient of the Weyl algebra for L.
