On the Langlands parameter of a simple supercuspidal representation: even orthogonal groups

2019/05/22 by Moshe Adrian, Adrian, Moshe, Eyal Kaplan +1
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Black Holes and Theoretical Physics #FOS: Mathematics #Number Theory (math.NT) #Quantum Chromodynamics and Particle Interactions #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1905.09172

openalex publication_date 2019/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let π be a simple supercuspidal representation of the split even special orthogonal group. We compute the Rankin-Selberg γ-factors for rank 1-twists of π by quadratic tamely ramified characters of F^*. We then use our results to determine the Langlands parameter of π up to its restriction to the wild inertia subgroup, subject to an analogue of a work of Blondel, Henniart, and Stevens for SO_2l. In the particular case of the field ℚ₂, we are able to describe the parameter completely.

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