Unitary dual of quasi-split $PGSO_8^E$

TL;DR

This paper explicitly classifies the Langlands parameters and determines the unitary dual of the quasi-split group $PGSO_8^E$, advancing the understanding of its representation theory.

Contribution

It provides the first explicit Langlands classification and unitary dual description for $PGSO_8^E$ using Casselman-Tadi$ ext{c}$'s Jacquet module method.

Findings

Explicit Langlands classification for $PGSO_8^E$ established

Unitary dual of $PGSO_8^E$ determined

Aubert duality computed for the group

Abstract

In this paper, we first determine the explicit Langlands classification for the quasi-split group $PGSO_8^E$ by following Casselman-Tadi$\acute{c}$'s Jacquet module machine. Based on the classification, we furthur sort out the unitary dual of $PGSO_8^E$ and compute the Aubert duality.