L-packets and the generic Arthur packet conjectures for even unitary similitude groups

Yeansu Kim, Muthu Krishnamurthy and Freydoon Shahidi

Vol. 344 (2026), No. 2, 367–393

DOI: 10.2140/pjm.2026.344.367

Abstract

We establish the generic local Langlands correspondence by showing the equality of the Langlands–Shahidi $L$-functions and Artin $L$-functions in the case of even unitary similitude groups. As an application, we prove both weak and strong versions of the generic Arthur packet conjectures in the cases of even unitary similitude groups and even unitary groups. We further describe (not necessarily generic) $L$-packets for even unitary similitude groups and establish their expected properties, including Shahidi’s conjecture, the finiteness of $L$-packets, and other related results.

Keywords

$L$-packets, generic Arthur packet conjectures, even unitary similitude groups, Langlands–Shahidi $L$-functions, local Langlands correspondence

Mathematical Subject Classification

Primary: 11F66, 11F70, 22E50, 22E55

Milestones

Received: 3 July 2025

Revised: 29 April 2026

Accepted: 17 May 2026

Published: 8 September 2026