Local Langlands Correspondence for Even Orthogonal Groups via Theta Lifts

TL;DR

This paper classifies irreducible representations of even orthogonal groups using theta correspondence, deriving it from known results for symplectic groups, and confirms its consistency with Arthur and Atobe-Gan's established local Langlands correspondence.

Contribution

It extends the local Langlands correspondence to all even orthogonal groups via theta lifts, connecting it with existing classifications for symplectic groups.

Findings

Classification of irreducible representations of even orthogonal groups.

Confirmation that the new classification aligns with Arthur and Atobe-Gan's results.

Demonstration of the effectiveness of theta correspondence in this context.

Abstract

Using theta correspondence, we obtain a classification of irreducible representations of an arbitrary even orthogonal group (i.e. the local Langlands correspondence) by deducing it from the local Langlands correspondence for symplectic groups due to Arthur. Moreover,we show that our classifications coincide with the local Langlands correspondence established by Arthur and formulated precisely by Atobe-Gan for quasi-split even orthogonal groups.