On $A$-packets containing unitary lowest-weight representations of $U(p,q)$

Shuji Horinaga

Vol. 338 (2025), No. 2, 295–324

DOI: 10.2140/pjm.2025.338.295

Abstract

We determine all the Arthur packets containing an irreducible unitary lowest-weight representation $\pi$ of a real unitary group $G=U(p,q)$, including nonscalar cases. Our methods are the Barbasch–Vogan parametrization of representations of $G$ and Trapa’s algorithm to calculate the cohomological inductions. In particular, we show that an Arthur packet has at most one irreducible unitary lowest-weight representation of $G$. As a consequence, if an irreducible unitary lowest-weight representation $\pi$ exists in the Arthur packet of $\psi$, we give an explicit formula for the lowest $K$-type of $\pi$.

Keywords

unitary groups, lowest-weight representations, Arthur classification

Mathematical Subject Classification

Primary: 11F55, 11F70, 17B10, 22E50

Milestones

Received: 10 March 2025

Revised: 19 June 2025

Accepted: 30 June 2025

Published: 24 August 2025