Pages 1407-1434 from Volume 172 (2010), Issue 2 by Avraham Aizenbud, Dmitry Gourevitch, Stephen Rallis, Gérard Schiffmann
Abstract
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.
Received: 28 September 2007
Accepted: 17 June 2008
Published online: 17 August 2010
Authors
Avraham Aizenbud
Faculty of Mathematics and Computer Science
Weizmann Institute of
Science
POB 26
Rehovot 76100
Israel
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
France
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