A combinatorial solution to M{\oe}glin's parametrization of Arthur packets for p-adic quasisplit $Sp(N)$ and $O(N)$

TL;DR

This paper introduces a combinatorial method to analyze Arthur packets for p-adic quasisplit symplectic and orthogonal groups, providing new insights into their structure and size.

Contribution

It develops a general combinatorial framework to study Arthur packets for p-adic quasisplit Sp(N) and O(N), extending M{\

Findings

Determines the size of Arthur packets for these groups.

Provides a systematic approach to study the combinatorial structure of Arthur packets.

Answers previously delicate questions about the properties of Arthur packets.

Abstract

We develop a general procedure to study the combinatorial structure of Arthur packets for $p$-adic quasisplit $Sp(N)$ and $O(N)$ following the works of M{\oe}glin. This allows us to answer many delicate questions concerning the Arthur packets of these groups, for example the size of the packets.