On anti-tempered local Arthur packets and a lemma of Arthur

TL;DR

This paper refines the construction of anti-tempered local Arthur packets for classical groups, identifies a gap in Arthur's lemma, and offers a uniform correction inspired by recent work, enhancing the understanding of automorphic representations.

Contribution

It provides a corrected and explicit construction of anti-tempered local Arthur packets, addressing a gap in Arthur's lemma with a uniform modification based on recent advances.

Findings

Explicit examples illustrating the gap in Arthur's lemma

A uniform modification to correct the gap

Enhanced understanding of local Arthur packets

Abstract

In this paper, following Arthur's ideas, we rework the process of constructing the anti-tempered local Arthur packets for quasi-split classical groups and their pure inner forms. In particular, we present explicit examples illustrating certain gap in a consequential lemma of Arthur and provide a uniform modification, based on the work of Moeglin, Waldspurger, and Xu.