Reversible linear differential equations

Let ? be a meromorphic connection on a vector bundle over a compact Riemann surface Γ. An automorphism $\sigma :\Gamma \to \Gamma$ is called a symmetry of ? if the pullback bundle and the pullback connection can be identified with ?. We study the symmetries by means of what we call the Fano group; and, under the hypothesis that ? has a unimodular reductive Galois group, we relate the differential Galois group, the Fano group and the symmetries by means of an exact sequence.