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

TL;DR

This paper proves the generic local Langlands correspondence and Arthur packet conjectures for even unitary similitude groups by establishing key equalities of L-functions and describing properties of L-packets.

Contribution

It establishes the generic local Langlands correspondence and proves the Arthur packet conjectures for even unitary similitude groups, advancing understanding of their representation theory.

Findings

Equality of Langlands-Shahidi and Artin L-functions for these groups

Proof of weak and strong Arthur packet conjectures in the specified cases

Description of properties and finiteness of L-packets

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.