The Langlands parameter of a simple supercuspidal representation: Symplectic groups

2018/03/23 by Adrian, Moshe, Kaplan, Eyal
#11S37 #22E50 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1803.08881

Abstract

Let π be a simple supercuspidal representation of the symplectic group Sp_2l(F), over a p-adic field F. In this work, we explicitly compute the Rankin-Selberg γ-factor of rank-1 twists of π. We then completely determine the Langlands parameter of π, if p ≠ 2. In the case that F = ℚ₂, we give a conjectural description of the functorial lift of π, with which, using a recent work of Bushnell and Henniart, one can obtain its Langlands parameter.

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