On the Langlands parameter of a simple supercuspidal representation: even orthogonal groups

Abstract

Let π be a simple supercuspidal representation of the split even special orthogonal group. We compute the Rankin-Selberg γ-factors for rank 1-twists of π by quadratic tamely ramified characters of F * . We then use our results to determine the Langlands parameter of π up to its restriction to the wild inertia subgroup, subject to an analogue of a work of Blondel, Henniart and Stevens for SO 2l . In the particular case of the field Q 2 , we are able to describe the parameter completely.