TITLE: Cartan subgroups of p-adic groups.
QUESTION [6 upvotes]: Does anyone know about any reference describing the structure of Cartan subgroups in the case of  connected p-adic reductive (or let's say semi-simple) groups?
I would like to know how different is this from the real case.
Thanks in advance,
Jim Riel

REPLY [6 votes]: just stumbled upon this old thread and decided to contribute my 2 cents (though I completely agree with Moshe's answer): J.-L. Waldspurger has a very explicit description of conjugacy classes of semisimple elements in the classical groups, in his Asterisque volume "Integrales orbitales nilpotentes et endoscopie pour les groupes classiques non ramifies", I believe in Section I.7. This is, essentially, Moshe's examples 1 --3 but done in a systematic way for every classical group. One can get a parametrization of tori from this description of semisimple conjugacy classes by looking at centralizers.