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The generic dual of p-adic groups and applications
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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.
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On sharpness in Local Converse Theorems for classical groups and $G_2$
The optimal standard local converse theorem for Sp_{2N}, SO_{2N}, SO_{2N+1}, and G2 requires twisting up to roughly half the dual group's standard representation dimension, except for an improved SO_{2N} bound for odd N.
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