  Given a knot K in an integral homology sphere with exterior N_K, there is a
natural action of the cyclic group Z/n on the space of SL(n,C) representations
of the knot group \pi_1(N_K), and this induces an action on the SL(n,C)
character variety. We identify the fixed points of this action in terms of
characters of metabelian representations, and we apply this to show that the
twisted Alexander polynomial associated to an irreducible metabelian SL(n,C)
representation is actually a polynomial in t^n.
