The generic dual of p-adic groups and applications

Abstract

In this paper, we give a uniform classification of the generic dual of quasi-split classical groups, their similitude counterparts, and general spin groups. As applications, for quasi-split classical groups, we show that the functorial lifting maps constructed by Cogdell, Kim, Piatetski-Shapiro and Shahidi are surjective. We also analyze structures of general local Langlands parameters and explicitly construct a distinguished element for each local L-packet.