  Given a knot K and an irreducible metabelian SL(n,C) representation we
establish an equality for the dimension of the first twisted cohomology. In the
case of equality, we prove that the representation must have finite image and
that it is conjugate to an SU(n) representation. In this case we show it
determines a smooth point x in the SL(n,C) character variety, and we use a
deformation argument to establish the existence of a smooth (n-1)-dimensional
family of characters of irreducible SL(n,C) representations near x.
  Combining this with our previous existence results, we deduce the existence
of large families of irreducible SU(n) and SL(n,C) non-metabelian
representation for knots K in homology 3-spheres S with nontrivial Alexander
polynomial.
  We then relate the condition on twisted cohomology to a more accessible
condition on untwisted cohomology of a certain metabelian branched cover of S
branched along K.
