An improvement on a theorem of Ben Martin

Let π be the fundamental group of a Riemann surface of genus g ≥ 2. The group π has a well-known presentation, as the quotient of a free group on generators {a₁, a₂, . . . , a_g, b₁, b₂, . . . , b_g} by the one relation [a₁, b₁][a₂, b₂] ⋯ [a_g, b_g] = 1. This gives two inclusions F π, where F is the free group on g generators; we could map the generators to the a's, or to the b's. Call the images of these inclusions F₁ ⊂ π and F₂ ⊂ π. Given a connected, reductive group G over an algebraically closed field of characteristic 0, any representation π → G restricts to two representations f₁ : F₁ → G, f₂ : F₂ → G. We prove that on a Zariski open, dense subset of the space of pairs of representations {f₁, f₂}, there exists a representation f : π → G lifting them, up to (separate) conjugacy of f₁ and f₂. Ben Martin proved this theorem, with the hypothesis that the semisimple rank of G is > g. We remove the hypothesis.