A functoriality property for supercusipidal $L$-packets

Adèle Bourgeois and Paul Mezo

Vol. 339 (2025), No. 1, 73–131

DOI: 10.2140/pjm.2025.339.73

Abstract

Kaletha constructed $L$-packets for supercuspidal $L$-parameters of tame $p$-adic groups. These $L$-packets consist entirely of supercuspidal representations, which are explicitly described. In the setting of quasisplit reductive groups, we show that Kaletha’s $L$-packets satisfy a functoriality property for homomorphisms with central kernel and abelian cokernel.

Keywords

supercuspidal representations, Langlands, functoriality, $L$-packets

Mathematical Subject Classification

Primary: 11F70, 11S37, 22E50

Milestones

Received: 28 February 2024

Revised: 23 July 2025

Accepted: 24 July 2025

Published: 1 September 2025