Some endoscopic properties of the essentially tame Jacquet-Langlands correspondence

  • Kam-Fai Tam

Some endoscopic properties of the essentially tame Jacquet-Langlands correspondence cover
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Abstract

Let FF be a non-Archimedean local field of characteristic 0 and GG be an inner form of the general linear group G=GLG^*=GL_n over FF. We show that the rectifying character appearing in the essentially tame Jacquet-Langlands correspondence of Bushnell and Henniart for GG and GG^* 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 GG can be described using admissible embeddings of L-tori.

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Kam-Fai Tam, Some endoscopic properties of the essentially tame Jacquet-Langlands correspondence. Doc. Math. 21 (2016), pp. 345–389

DOI 10.4171/DM/536