2008-05-01

David Renard, Ecole polytechnique

Jacquet-Langlands correspondence for unitary representations

Recently, A.I Badulescu has obtained definitive results about the global Jacquet-Langlands correspondence, and he has been able to deduce from these multiplicity one theorems and description of the residual spectrum for $GL(n,A)$, $A$ is a central division algebra over a global field $F$, generalizing well-known results in the case $A=F$. We will discuss mostly local aspects of the proof, concerning unitary dual of $GL(n,A)$, and the Jacquet-Langlands correspondence for unitary representations between $GL(nd,F)$ and $GL(n,A)$.