Local Langlands correspondence for even orthogonal groups via theta lifts

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 Unitary Groups via Theta Lifts

“…In this paper, we "turn the table around", namely, imitating the prediction of Prasad conjecture, we construct a Vogan version LLC for unitary groups. We also write a parallel paper [CZ20], in which we use the same method to deal with the even orthogonal groups (we write it separately to avoid making notations too complicated). In a sequel to this paper, we carry out the global counterpart of this paper and establish an Arthur multiplicity formula for the tempered part of automorphic discrete spectra of even orthogonal groups/ unitary groups.…”