Multiplicity one theorems


In the local, characteristic $0$, non-Archimedean case, we consider distributions on ${\rm GL}(n+1)$ which are invariant under the adjoint action of ${\rm GL}(n)$. We prove that such distributions are invariant by transposition. This implies multiplicity at most one for restrictions from ${\rm GL}(n+1)$ to ${\rm GL}(n)$. Similar theorems are obtained for orthogonal or unitary groups.


Avraham Aizenbud

Faculty of Mathematics and Computer Science
Weizmann Institute of Science
POB 26
Rehovot 76100

Dmitry Gourevitch

School of Mathematics
Intitute for Advanced Study
Einstein Drive
Princeton, NJ 08540
United States

Stephen Rallis

The Ohio State University
Department of Mathematics
231 West 18th Avenue
Columbus, OH 43210-1174
United States

Gérard Schiffmann

Institut de Recherche Mathématique Avancée
Université de Strasbourg et CNRS
7 rue René-Descartes
67084 Strasbourg Cedex