On automorphy of certain Galois representations of GO4-type

Let ρ:Gal(Q‾/Q)→GO4(Q‾p) be a continuous representation. We prove (potential) automorphy theorems for certain types of ρ  . Our results include several cases in which the Hodge–Tate weights are irregular. Finally, we prove (potential) automorphy for certain compatible systems of representations of GO4GO4-type, which includes certain compatible systems constructed from Scholl motives.