Admissible Embeddings of L-Tori and the Essentially Tame Local Langlands Correspondence

2012/05/31 by Geo Kam-Fai Tam, Kam-Fai Tam
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Field (mathematics) #Langlands dual group #Langlands program #Local field #Mathematical Analysis and Transform Methods #Torus #math.RT

paper · pdf · doi:10.1093/imrn/rnv183

revised version of previous submission, typos corrected

arxiv created 2012/08/16 · openalex publication_date 2015/06/19 · arxiv updated 2015/10/16 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

Let |F| be a non-Archimedean local field of characteristic 0 and |G| be the general linear group |\mathrm GL_n| over |F|⁠. Bushnell and Henniart described the essentially tame local Langlands correspondence for |G(F)| using admissible characters, with their rectifiers, of tamely ramified elliptic maximal tori of |G(F)|⁠. The main result of this article is to relate these rectifiers to |χ |-data in the theory of endoscopy of Kottwitz, Langlands, and Shelstad. Therefore, we can describe the essentially tame local Langlands correspondence using admissible embeddings of L-tori.

Citations

• The Local Langlands Conjecture for GL(2)
• Linear Representations of Finite Groups
• Une preuve simple des conjectures de Langlands pour GL(n) sur un corps p-adique
• D -elliptic sheaves and the langlands correspondence
• Algebraic Number Theory