On Arthur packets containing a fixed tempered representation

TL;DR

This paper counts the number of local Arthur packets containing a specific fixed tempered representation for classical p-adic groups, using the theory of intersections of such packets and extended multi-segments.

Contribution

It provides a precise enumeration of Arthur packets containing a given tempered representation based on extended multi-segments and intersection operators.

Findings

Count of Arthur packets for fixed tempered representations determined

Method involves extended multi-segments and intersection operators

Advances understanding of the structure of local Arthur packets

Abstract

We determine the number of local Arthur packets containing a certain fixed tempered representation for classical $p$-adic groups. More specifically, given a tempered extended multi-segment supported in the integers, we determine a count for all extended multi-segments which arise from it through applications of the operators arising from the theory of intersections of local Arthur packets.