Asai cube L-functions and the local Langlands conjecture

2017/01/06 by Guy Henniart, Henniart, G., Luis Lomelí +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1701.01516

openalex publication_date 2017/01/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let F be a non-archimedean locally compact field. We study a class of Langlands-Shahidi pairs (\bf H,\bf L), consisting of a quasi-split connected reductive group \bf H over F and a Levi subgroup \bf L which is closely related to a product of restriction of scalars of \rm GL₁'s or \rm GL₂'s. We prove the compatibility of the resulting local factors with the Langlands correspondence. In particular, let E be a cubic separable extension of F. We consider a simply connected quasi-split semisimple group \bf H over F of type D₄, with triality corresponding to E, and let \bf L be its Levi subgroup with derived group \rm Res_E/F \rm SL₂. In this way we obtain Asai cube local factors attached to irreducible smooth representations of \rm GL₂(E); we prove that they are Weil-Deligne factors obtained via the local Langlands correspondence for \rm GL₂(E) and tensor induction from E to F. A consequence is that Asai cube γ- and ε-factors become stable under twists by highly ramified characters.

Citations

• On Certain L-Functions

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