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

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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).

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  1. UFR Sciences SP2MI, Département de Mathématiques, Université de Poitiers, Téléport 2, Boulevard Marie et Pierre Curie BP 30179, 86962, Futuroscope Chasseneuil Cedex, France

    Alexandru Ioan Badulescu

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Badulescu, A. Global Jacquet–Langlands correspondence, multiplicity one and classification of automorphic representations . Invent. math. 172, 383–438 (2008). https://doi.org/10.1007/s00222-007-0104-8

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