Semisimple characters for inner forms II: Quaternionic forms of 𝑝-adic classical groups (𝑝 odd)

Abstract

In this article we consider the set G G of rational points of a quaternionic form of a symplectic or an orthogonal group defined over a non-Archimedean local field of odd residue characteristic. We construct all full self-dual semisimple characters for G G and we classify their intertwining classes using endo-parameters. We compute the set of intertwiners between self-dual semisimple characters, and prove an intertwining and conjugacy theorem. Finally we count all G G -intertwining classes of full self-dual semisimple characters which lift to the same G ~ \tilde {G} -intertwining class of a full semisimple character for the ambient general linear group G ~ \tilde {G} for G G .