Local Langlands correspondence for unitary groups via theta lifts

Abstract

Using the theta correspondence, we extend the classification of irreducible representations of quasi-split unitary groups (the so-called local Langlands correspondence, which is due to Mok) to non quasi-split unitary groups. We also prove that our classification satisfies some good properties, which characterize it uniquely. In particular, this paper provides an alternative approach to the works of Kaletha-Mínguez-Shin-White and Mœglin-Renard.

Twisted Gan–gross–prasad Conjecture for Certain Tempered L-Packets

“…(2) In later proofs of our main result, we will only use A-packets of unitary groups in some special cases; those A-packets are the Zelevinsky-Aubert dual of some tempered L-packets. Since the LLC for unitary groups has been fully established (see [Mok15,KMSW14,MR18,CZ21a]), all the properties of those A-packets that we need can be easily checked using the properties of the LLC and the Zelevinsky-Aubert duality. Hence, our main result in this paper is not conditional on the construction of A-packets for unitary groups.…”

The Local Langlands Conjecture for

“…Building upon this, the LLC has now been shown for the quasi-split classical groups (i.e. symplectic, special orthogonal and unitary groups) by the work of Arthur [A], Moeglin and Mok [M], as a consequence of the theory of twisted endoscopy using the stable twisted trace formula of , and extended to pure inner forms by various authors by various means (see for example [KMSW, MR, CZ1, CZ2]). It has also been shown for the group and its inner forms in [GT] and [GTW] using theta correspondence as the main tool.…”

Local Langlands Correspondence for Even Orthogonal Groups via Theta Lifts

“…Moreover, we shall show that our LLC is the same as Arthur's LLC in the quasi-split case. We also write a parallel paper [CZ20], in which we deal with the unitary group case (We write it separately to avoid making notations too complicated). In a sequel to this paper, with these LLC at hand, we shall investigate the Arthur's conjecture for automorphic discrete spectra of even orthogonal groups and unitary groups.…”