On the uniqueness of generic representations in an $L$-packet

Abstract

In this paper, we give a simple and short proof of the uniqueness of generic representations in an L-packet for a quasi-split connected classical group over a non-archimedean local field.

On the local Langlands correspondence and Arthur conjecture for even orthogonal groups

“…A simple proof of the other direction is given by the first author [At2]. Also (3) is a special case of Gross-Prasad conjecture [GGP,Conjecture 17.1], which is proven by Waldspurger [W2], [W3], [W5] and [W6].…”

“…(2) In [At2], the first author gave a proof of "only if " part of Proposition 3.5 (3). This proof is essentially the same as the proof of Desideratum 3.9 (3) (Theorem 3.13).…”

Generic representations of metaplectic groups and their theta lifts

“…In the case of generic representations this factor is trivial (cf. [12], Proposition 3.1 and [2]). Thus, let φ : W D F → Sp(2n, C) be the L-parameter of a generic discrete series π of SO(2n+1, F ).…”