Correspondance de Jacquet-Langlands \'etendue \`a toutes les repr\'esentations

Abstract

We propose a generalisation of the Jacquet-Langlands correspondence to the whole Grothendieck group of finite lenght admissible representations. As an application we prove some particular cases of the global Jacquet-Langlands correspondence, and that a class of representations of a inner form of GL_n over a p-adic field is unitarisable, which agree with some conjecture of Tadic.