Geodesic
Multiplicity one theorems
Avraham Aizenbud1 ; Dmitry Gourevitch2 ; Stephen Rallis3 ; Gérard Schiffmann4
1 Faculty of Mathematics and Computer Science<br/>Weizmann Institute of Science<br/>POB 26<br/>Rehovot 76100<br/>Israel
2 School of Mathematics<br/>Intitute for Advanced Study<br/>Einstein Drive<br/>Princeton, NJ 08540<br/>United States
3 The Ohio State University<br/>Department of Mathematics<br/>231 West 18th Avenue<br/>Columbus, OH 43210-1174<br/>United States
4 Institut de Recherche Mathématique Avancée<br/>Université de Strasbourg et CNRS<br/>7 rue René-Descartes<br/>67084 Strasbourg Cedex<br/>France
Annals of mathematics, Tome 172 (2010) no. 2, pp. 1407-1434

Voir la notice de l'article provenant de la source Annals of Mathematics website

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.

DOI : 10.4007/annals.2010.172.1407

Avraham Aizenbud 1 ; Dmitry Gourevitch 2 ; Stephen Rallis 3 ; Gérard Schiffmann 4

1 Faculty of Mathematics and Computer Science<br/>Weizmann Institute of Science<br/>POB 26<br/>Rehovot 76100<br/>Israel
2 School of Mathematics<br/>Intitute for Advanced Study<br/>Einstein Drive<br/>Princeton, NJ 08540<br/>United States
3 The Ohio State University<br/>Department of Mathematics<br/>231 West 18th Avenue<br/>Columbus, OH 43210-1174<br/>United States
4 Institut de Recherche Mathématique Avancée<br/>Université de Strasbourg et CNRS<br/>7 rue René-Descartes<br/>67084 Strasbourg Cedex<br/>France 
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Avraham Aizenbud; Dmitry Gourevitch; Stephen Rallis; Gérard Schiffmann. Multiplicity one theorems. Annals of mathematics, Tome 172 (2010) no. 2, pp. 1407-1434. doi: 10.4007/annals.2010.172.1407

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