Component groups for non-supercuspidal L-parameters for p-adic SL₃

2025/07/28 by Choiy, Kwangho, Kim, Doyon, Taha, Razan +1
#11F70 (Secondary) #22E50 (Primary) 22E35 #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2507.20946

Abstract

We explicitly classify all the component groups associated to the non-supercuspidal, tempered L-parameters of SL₃(F) for a p-adic field F of characteristic 0 by direct case-by-case computations in PGL₃(ℂ), following earlier work for SL₂ by Labesse-Langlands and Shelstad.

Citations

• Global rigid inner forms and multiplicities of discrete automorphic representations
• On multiplicity in restriction of tempered representations of p-adic\n groups
• The local Langlands correspondence for GL(n) over p-adic fields
• Une preuve simple des conjectures de Langlands pour GL(n) sur un corps p-adique

Related

• Modulo ℓ-representations of p-adic groups SL_n(F)
• Connected components of the moduli space of L-parameters
• Supercuspidal representations in non-defining characteristics
• Simple supercuspidal L-packets of quasi-split classical groups
• Bruhat-Tits buildings, representations of p-adic groups and Langlands correspondence