Simple supercuspidal L-packets of split special orthogonal groups over dyadic fields

2023/05/16 by Adrian, Moshe, Henniart, Guy, Kaplan, Eyal +1
#11F70 #11L05 #22E50 #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2305.09076

Abstract

We consider the split special orthogonal group SO_N defined over a p-adic field. We determine the structure of any L-packet of SO_N containing a simple supercuspidal representation (in the sense of Gross--Reeder). We also determine its endoscopic lift to a general linear group. Combined with the explicit local Langlands correspondence for simple supercuspidal representations of general linear groups, this leads us to get an explicit description of the L-parameter as a representation of the Weil group of F. Our result is new when p=2 and our method provides a new proof even when p≠2.

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