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arXiv · 1309.0353

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

Charlene Coniglio-Guilloton
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Abstract

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

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Charlene Coniglio-Guilloton. 2014-06-02. Correspondance de Jacquet-Langlands et distinction : cas des representations cuspidales de niveau 0. https://arxiv.org/abs/1309.0353

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