Depth Zero Supercuspidal Representations of Classical Groups into L-packets: the Typically Almost Symmetric Case

2023/12/07 by Geo Kam-Fai Tam, Tam, Geo Kam-Fai
Mathematics · #11F70 #20G05 #22E50 #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2312.04061

openalex publication_date 2023/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We classify what we call ``typically almost symmetric'' depth zero supercuspidal representations of classical groups into L-packets. Our main results resolve an ambiguity in the paper of Lust-Stevens \citeLust-Stevens in this case, where they could only classify these representations in two or four, if not one, L-packets. By assuming the expected numbers of supercuspidal representations in the L-packets, we employ only simple properties of the representations to prove the main results. In particular, we do not require any deep calculations of character values.

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