Component groups for non-supercuspidal $L$-parameters for $p$-adic $\mathrm{SL}_3$

Kwangho Choiy; Doyon Kim; Razan Taha; Pan Yan

Component groups for non-supercuspidal $L$-parameters for $p$-adic $\mathrm{SL}_3$

Representation Theory 2025-07-29 v1 Number Theory

Authors: Kwangho Choiy , Doyon Kim , Razan Taha , Pan Yan

Abstract

We explicitly classify all the component groups associated to the non-supercuspidal, tempered $L$ -parameters of $\mathrm{SL}_3(F)$ for a $p$ -adic field $F$ of characteristic $0$ by direct case-by-case computations in $\mathrm{PGL}_3(\mathbb{C})$ , following earlier work for $\mathrm{SL}_2$ by Labesse-Langlands and Shelstad.

Keywords

automorphic representations

Cite

@article{arxiv.2507.20946,
  title  = {Component groups for non-supercuspidal $L$-parameters for $p$-adic $\mathrm{SL}_3$},
  author = {Kwangho Choiy and Doyon Kim and Razan Taha and Pan Yan},
  journal= {arXiv preprint arXiv:2507.20946},
  year   = {2025}
}

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