We give a classification of irreducible metabelian representations from a
knot group into SL(n,C) and GL(n,C). If the homology of the n-fold branched
cover of the knot is finite, we show that every irreducible metabelian SL(n,C)
representation is conjugate to a unitary representation and that the set of
conjugacy classes of such representations is finite. In that case, we give a
formula for this number in terms of the Alexander polynomial of the knot. These
results are the higher rank generalizations of a result of Nagasato, who
recently studied irreducible, metabelian SL(2,C) representations of knot
groups. Finally we deduce the existence irreducible metabelian SL(n,C)
representations of the knot group for any knot with nontrivial Alexander
polynomial.