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

Abstract

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 $\mathbb{R}$, $\mathbb{C}$ or $\bbH$ of independent interest.

References in corpus (1)

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

Cited by in corpus (1)

• Periods and nonvanishing of central L-values for GL(2n)