Abstract: Let G be a quasi-split form of a symplectic, unitary or orthogonal group defined over a non-archimedean local field of odd residue characteristic. Every smooth irreducible representation of a p-adic classical group G contains a semisimple character, a certain arithmetic character which is suitable for the study and handling of the category of smooth representations of G. (These characters were introduced by Bushnell–Kutzko and Stevens). Two of those characters contained in the same irreducible representation intertwine.

In the flavor of Bushnell–Henniart (local tame lifting) we generalize the notion of Endo–equivalence from simple characters to semisimple characters and parametrize intertwining classes of semisimple characters for G using new developed parameters, the so-called endo-parameters.(joint with R. Kurinczuk and S. Stevens).

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