Let be a symplectic group over a nonarchimedean local field of characteristic zero and odd residual characteristic. Given an irreducible cuspidal representation of , we determine its Langlands parameter (equivalently, its Jordan blocks in the language of Mœglin) in terms of the local data from which the representation is explicitly constructed, up to a possible unramified twist in each block of the parameter. We deduce a ramification theorem for , giving a bijection between the set of endoparameters for and the set of restrictions to wild inertia of discrete Langlands parameters for , compatible with the local Langlands correspondence. The main tool consists in analyzing the Hecke algebra of a good cover, in the sense of Bushnell–Kutzko, for parabolic induction from a cuspidal representation of , seen as a maximal Levi subgroup of a bigger symplectic group, in order to determine reducibility points; a criterion of Mœglin then relates this to Langlands parameters.
"Jordan blocks of cuspidal representations of symplectic groups." Algebra Number Theory 12 (10) 2327 - 2386, 2018. https://doi.org/10.2140/ant.2018.12.2327