Remarks on automorphy of residually dihedral representations

We prove automorphy lifting results for geometric representations rho: G(F) -> GL(2)(O), with F a totally real field, and O the ring of integers of a finite extension of Q(p) with p an odd prime, such that the residual representation (rho) over bar is totally odd and induced from a character of the absolute Galois group of the quadratic subfield K of F(zeta(p))/F. Such representations fail the Taylor-Wiles hypothesis and the patching techniques to prove automorphy do not work. We apply this to automorphy of elliptic curves E over F, when E has no F rational 7-isogeny and such that the image of G(F) acting on E[7] normalizes a split Cartan subgroup of GL(2)(F-7).