Local Langlands Correspondence for Unitary Groups via Theta Lifts

TL;DR

This paper extends the local Langlands correspondence to non quasi-split unitary groups using theta lifts, providing a new classification approach with desirable properties.

Contribution

It introduces a novel method to classify representations of non quasi-split unitary groups via theta correspondence, expanding existing frameworks.

Findings

Classification of non quasi-split unitary groups achieved

The new classification satisfies key properties and is uniquely characterized

Provides an alternative approach to existing classification methods

Abstract

Using the theta correspondence, we extend the classification of irreducible representations of quasi-split unitary groups (the so-called local Langlands correspondence, which was established in an early paper of Mok) 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 Kaletha-Minguez-Shin-White and Moeglin-Renard.