Reversible linear differential equations

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

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