Langlands parameters associated to special maximal parahoric spherical representations - Mishra, Manish (Proceedings of the American Mathematical Society, 2015)
We describe the image, under the local Langlands correspondence for tori, of the characters of a torus which are trivial on its Iwahori subgroup. Let be a non-archimedian local field. Let be a connected reductive group defined over , which is quasi-split and split over a tamely ramified extension. Let be a special maximal parahoric subgroup of . To the class of representations of having a non-zero vector fixed under , we establish a bijection, in a natural way, with the twisted semisimple conjugacy classes of the inertia fixed subgroup of the dual group . These results generalize the well known classical results to the ramified case.