Unitary Dual of GL_n at archimedean places and global Jacquet-Langlands correspondence

Details Unitary Dual of GL_n at archimedean places and global Jacquet-Langlands correspondence Unitary Dual of GL_n at archimedean places and global Jacquet-Langlands correspondence

2009-05-26

arxiv.org/abs/0905.4143v1

Mathematics

Representation Theory

Scientific paper

In [7], results about the global Jacquet-Langlands correspondence, (weak and strong) multiplicity-one theorems and the classification of automorphic representations for inner forms of the general linear group over a number field are established, under the condition that the local inner forms are split at archimedean places. In this paper, we extend the main local results of [7] to archimedean places so that this assumption can be removed. Along the way, we collect several results about the unitary dual of general linear groups over $\bbR$, $\bbC$ or $\bbH$ of independent interest.

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