The Langlands parameter of a simple supercuspidal representation: symplectic groups

Let π be a simple supercuspidal representation of the symplectic group Sp _{2 l}(F) , over a p-adic field F. In this work, we explicitly compute the Rankin–Selberg γ-factor of rank-1 twists of π. We then completely determine the Langlands parameter of π, if p≠ 2. In the case that F= Q₂, we give a conjectural description of the functorial lift of π, with which, using a recent work of Bushnell and Henniart, one can obtain its Langlands parameter.