On corank 4 unitary representations of classical groups

TL;DR

This paper classifies specific unitary representations of classical groups over non-Archimedean fields, confirming a recent conjecture and advancing understanding of the unitary dual in representation theory.

Contribution

It provides an explicit classification of corank 4 unitary representations for symplectic and split odd orthogonal groups, verifying a recent conjecture in the field.

Findings

Complete classification of corank 4 unitary representations.

Verification of the unitary dual conjecture for these groups.

Advancement in understanding the structure of unitary duals.

Abstract

In this paper, we explicitly classify the corank 4 unitary representations of symplectic or split odd special orthogonal groups over non-Archimedean local fields of characteristic zero, by classifying Arthur representations of corank 4 and verifying the corresponding unitary dual conjecture recently proposed by Hazeltine-Jiang-Liu-Lo-Zhang in [HJLLZ24].