  Let R(N,G) be the connected component of the identity of the variety of
representations of a finitely generated nilpotent group N into a connected
compact Lie group G, and let X(N,G) be the corresponding moduli space. We show
that there exists a natural Out(N)-invariant measure on X(N,G) and that
whenever Out(N) has at least one hyperbolic element, the action of Out(N) on
X(N,G) is mixing with respect to this measure.
