Local Jacquet-Langlands correspondence for regular supercuspidal representations

2023/03/04 by Tokimoto, Kazuki
#11F70 #11S37 #22E50 #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2303.02354

Abstract

We prove that Kaletha's local Langlands correspondence for regular supercuspidal representations gives the classical local Jacquet--Langlands correspondence due to Deligne--Kazhdan--Vigneras and Badulescu. As in a former joint paper with Oi, where a similar result is proved for the local Langlands correspondence for the general linear group, the key ingredients in our proof are the work of Bushnell--Henniart explicitly describing the local Jacquet--Langlands correspondence for essentially tame supercuspidal representations and its reinterpretation due to Tam in terms of Langlands--Shelstad's \(ζ\)-data. While, under suitable assumptions, this result follows from more general theorems either in the recent work of Fintzen--Kaletha--Spice or that of Chan--Oi, our proof does not require any assumptions. We also complement a few points on the proof in the former paper with Oi.

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