Let G be an even orthogonal or unitary group over a number field. Based on the same observation used in [GI18], we prove the Arthur's multiplicity formula for the generic part of the automorphic discrete spectrum of G by using the theta lift. We also consider a class of non-generic A-parameters and obtain a multiplicity formula in this case. In particular, we obtain a description of the full automorphic discrete spectrum of even orthogonal or unitary groups with Witt index less or equal to one.In the case [E : F ] = 2, we denote by ω E/F the quadratic character of F × (or F × \A × if F is global, and similarly in later paragraph) by class field theory, and we fix a trace zero element δ ∈ E × . Let V = V (n) be a finite dimensional vector space over E equipped with a non-degenerate Hermitian c-sesquilinear form •, • V : V × V −→ E.

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.

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Using the theta correspondence, we extend the classification of irreducible representations of quasi-split unitary groups (the so-called local Langlands correspondence) due to [Mok15] to non quasi-split unitary groups. We also prove that our classification satisfies some good properties, which characterize it uniquely. In particular, this provides an alternative approach to the works of [KMSW14] and [MR18].

In spirit of [GI18], we have established an Arthur's multiplicity formula for even orthogonal or unitary groups with Witt index less than or equal to one. In that multiplicity formula, some local packets defined using the stable range theta lifts are involved. In this paper, we prove that at non-Archimedean places, the definition of the local packets involved in that multiplicity formula is independent of the choice of the dual-pairs used in their construction. Moreover, at those places where the groups are quasi-split, we prove that the local packets involved are the same as the local A-packets defined by Arthur/ Mok.