  It is known that any primitive ideal I of U(g) whose associated variety
contains a nilpotent element e in its open G-orbit admits a finite generalised
Gelfand-Graev model which is a finite dimensional irreducible module over the
finite W-algebra U(g,e). We prove that if V is such a model for I, then the
Goldie rank of the primitive quotient U(g)/I always divides the dimension of V.
For g=sl(n), we use a result of Joseph to show that the Goldie rank of U(g)/I
equals the dimension of V and we show that the equality conntinues to hold
outside type A provided that the Goldie field of U(g)/I is isomorphic to a Weyl
skew-field. As an application of this result, we disprove Joseph's conjecture
on the structure of the Goldie fields of primitive quotients of U(g) formulated
in the mid-70s.
