, Volume 172, Issue 2, pp 383-438
Date: 25 Jan 2008

Global Jacquet–Langlands correspondence, multiplicity one and classification of automorphic representations

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Abstract

In this paper we generalize the local Jacquet-Langlands correspondence to all unitary irreducible representations. We prove the global Jacquet-Langlands correspondence in characteristic zero. As consequences we obtain the multiplicity one and strong multiplicity one Theorems for inner forms of GL(n) as well as a classification of the residual spectrum and automorphic representations in analogy with results proved by Mœglin–Waldspurger and Jacquet–Shalika for GL(n).