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

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

2007-04-23

arxiv.org/abs/0704.2920v1

Mathematics

Representation Theory

49 pages; Appendix by N. Grbac

Scientific paper

10.1007/s00222-007-0104-8

In this paper we show a local Jacquet-Langlands correspondence for 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 Moeglin-Waldspurger and Jacquet-Shalika for GL(n).

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