Restrictions of representations of a surface group to a pair of free subgroups

Let Π be the fundamental group of a compact orientable genus m surface, and let G be a connected reductive algebraic group over an algebraically closed field of characteristic zero. Define two free rank m subgroups of Π by A = a1, …, am and B = b1, …, bm , where Π = a1, …, am, b1, …, bm Πj=1m[aj, bj] is the standard presentation of Π. We consider representations of Π, of A and of B into G. Restriction of representations induces a morphism from C(Π, G), the variety of closed conjugacy classes of representations of Π, to C(A, G)C(B, G). We prove that if m is greater than the semisimple rank of G then this morphism is dominant and almost all fibers are finite.