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 
@article{10_4007_annals_2010_172_1407,
     author = {Avraham Aizenbud and Dmitry Gourevitch and Stephen Rallis and G\'erard Schiffmann},
     title = {Multiplicity one theorems},
     journal = {Annals of mathematics},
     pages = {1407--1434},
     publisher = {mathdoc},
     volume = {172},
     number = {2},
     year = {2010},
     doi = {10.4007/annals.2010.172.1407},
     mrnumber = {2680495},
     zbl = {1202.22012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2010.172.1407/}
}
TY  - JOUR
AU  - Avraham Aizenbud
AU  - Dmitry Gourevitch
AU  - Stephen Rallis
AU  - Gérard Schiffmann
TI  - Multiplicity one theorems
JO  - Annals of mathematics
PY  - 2010
SP  - 1407
EP  - 1434
VL  - 172
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4007/annals.2010.172.1407/
DO  - 10.4007/annals.2010.172.1407
LA  - en
ID  - 10_4007_annals_2010_172_1407
ER  - 
%0 Journal Article
%A Avraham Aizenbud
%A Dmitry Gourevitch
%A Stephen Rallis
%A Gérard Schiffmann
%T Multiplicity one theorems
%J Annals of mathematics
%D 2010
%P 1407-1434
%V 172
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4007/annals.2010.172.1407/
%R 10.4007/annals.2010.172.1407
%G en
%F 10_4007_annals_2010_172_1407
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. http://geodesic.mathdoc.fr/articles/10.4007/annals.2010.172.1407/

Cité par Sources :