Correspondance de Jacquet-Langlands et distinction : cas des\n representations cuspidales de niveau 0

2013/09/02 by Charlène Coniglio-Guilloton, Coniglio-Guilloton, Charlene
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1309.0353

openalex publication_date 2013/09/02 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

Let K/F be a tamely ramified quadratic extension of non-archimedean locally\ncompact fields. Let GL_m (D) be an inner form of GL_n (F) and GLp(R) = (M_m (D)\n\⊗ K)^\× . Then GLp(R) is an inner form of GL_n (K). In this work,\nwe determine conditions of GL_m (D)-distinction for level zero cuspidal\nrepresentations of GL_p (R) which are the image of a level zero cuspidal\nrepresentation by the Jacquet-Langlands correspondence, and we also prove that\na level zero cuspidal representation of GL_n (K) is GL_n (F) distinguished if\nand only if its image by the Jacquet-Langlands correspondance is GL_m\n(D)-distinguished.\n

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