Sur la classification des séries discrètes des groupes classiques p-adiques: paramètres de Langlands et exhaustivité

Abstract

In this paper, we are giving parameters for discrete series of classical p-adic groups. We first define: the analogous of the Langlands morphism of WF in the L-group, part of the analogous of the character of the centralizer of that morphism and, to supply the missing part of the full definition of that character, the cuspidal support of the representation. Then, we state an hypothesis on the reducibility points for induced of cuspidal representations. And we prove that, under this hypothesis, the 3 data characterize discrete series.