Reciprocity theorems for the classical goups. I: The GL (r, k)-subgroup of GL (2r, k).
The intrinsic differential Galois group is a twisted form of the standard differential Galois group, defined over the base differential field. We exhibit several constraints for the inverse problem of differential Galois theory to have a solution in this intrinsic setting, and show by explicit computations that they are sufficient in a (very) special situation.