Construction of Local Arthur Packets for Metaplectic Groups and the Adams Conjecture

TL;DR

This paper constructs explicit local Arthur packets for metaplectic groups over non-Archimedean fields, generalizing previous work for classical groups and proving multiplicity-free properties, while extending the Adams conjecture to these groups.

Contribution

It provides a new explicit construction of local Arthur packets for metaplectic groups and extends the Adams conjecture to this setting.

Findings

Local Arthur packets for metaplectic groups are multiplicity free.

The construction generalizes Atobe's work for classical groups.

The Adams conjecture is extended to metaplectic groups.

Abstract

In this article, we explicitly construct local Arthur packets for metaplectic groups over non-Archimedean local fields of characteristic zero. Our construction is a generalization of Atobe's construction of local Arthur packets for classical groups. As a result, we prove that the local Arthur packets are multiplicity free. Moreover, we generalize Moeglin's earlier work about the Adams conjecture to metaplectic groups.