SEMISIMPLE CHARACTERS FOR INNER FORMS II: QUATERNIONIC FORMS OF p-ADIC CLASSICAL GROUPS (p ODD)

In this article we consider the set 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 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-intertwining classes of full self-dual semisimple characters which lift to the same (G) over tilde -intertwining class of a full semisimple character for the ambient general linear group (G) over tilde for G.