Let be a non-Archimedean local field of characteristic 0 and be an inner form of the general linear group _n over . We show that the rectifying character appearing in the essentially tame Jacquet-Langlands correspondence of Bushnell and Henniart for and can be factorized into a product of some special characters, called zeta-data in this paper, in the theory of endoscopy of Langlands and Shelstad. As a consequence, the essentially tame local Langlands correspondence for can be described using admissible embeddings of L-tori.
Cite this article
Kam-Fai Tam, Some endoscopic properties of the essentially tame Jacquet-Langlands correspondence. Doc. Math. 21 (2016), pp. 345–389DOI 10.4171/DM/536