  We obtain an explicit characterization of the stable points of the action of
G=SL(2,C) on the cartesian product G^n by simultaneous conjugation on each
factor, in terms of the corresponding invariant functions, and derive from it a
simple criterion for irreducibility of representations of finitely generated
groups into G. We also obtain analogous results for the action of SL(2,C) on
the vector space of n-tuples of 2 by 2 complex matrices. For a free group F_n
of rank n, we show how to generically reconstruct the 2^{n-2} conjugacy classes
of representations F_n -> G from their values under the map T_n : G^n =
Hom(F_n,G) -> C^{3n-3} considered in [M], defined by certain 3n-3 traces of
words of length one and two.
