Algebra/Group Theory
Disjoint pairs for GLn(R) and GLn(C)
[Paires disjointes pour GL(n,R) et GL(n,C)]
Comptes Rendus. Mathématique, Tome 350 (2012) no. 1-2, pp. 9-11.

Voir la notice de l'article provenant de la source Numdam

We show the disjointness property of Klyachko for GLn(R) and GLn(C).

Nous montrons la propriété de disjonction de Klyachko pour GLn(R) et GLn(C).

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2011.11.011

Aizenbud, Avraham 1 ; Offen, Omer 1 ; Sayag, Eitan 1

1 Technion Mathematics, Department of Mathematics, Haifa, Israel
@article{CRMATH_2012__350_1-2_9_0,
     author = {Aizenbud, Avraham and Offen, Omer and Sayag, Eitan},
     title = {Disjoint pairs for $ {\mathit{GL}}_{n}(\mathbb{R})$ and $ {\mathit{GL}}_{n}(\mathbb{C})$},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {9--11},
     publisher = {Elsevier},
     volume = {350},
     number = {1-2},
     year = {2012},
     doi = {10.1016/j.crma.2011.11.011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2011.11.011/}
}
TY  - JOUR
AU  - Aizenbud, Avraham
AU  - Offen, Omer
AU  - Sayag, Eitan
TI  - Disjoint pairs for $ {\mathit{GL}}_{n}(\mathbb{R})$ and $ {\mathit{GL}}_{n}(\mathbb{C})$
JO  - Comptes Rendus. Mathématique
PY  - 2012
SP  - 9
EP  - 11
VL  - 350
IS  - 1-2
PB  - Elsevier
UR  - http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2011.11.011/
DO  - 10.1016/j.crma.2011.11.011
LA  - en
ID  - CRMATH_2012__350_1-2_9_0
ER  - 
%0 Journal Article
%A Aizenbud, Avraham
%A Offen, Omer
%A Sayag, Eitan
%T Disjoint pairs for $ {\mathit{GL}}_{n}(\mathbb{R})$ and $ {\mathit{GL}}_{n}(\mathbb{C})$
%J Comptes Rendus. Mathématique
%D 2012
%P 9-11
%V 350
%N 1-2
%I Elsevier
%U http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2011.11.011/
%R 10.1016/j.crma.2011.11.011
%G en
%F CRMATH_2012__350_1-2_9_0
Aizenbud, Avraham; Offen, Omer; Sayag, Eitan. Disjoint pairs for $ {\mathit{GL}}_{n}(\mathbb{R})$ and $ {\mathit{GL}}_{n}(\mathbb{C})$. Comptes Rendus. Mathématique, Tome 350 (2012) no. 1-2, pp. 9-11. doi : 10.1016/j.crma.2011.11.011. http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2011.11.011/

[1] Avraham Aizenbud, Dmitry Gourevitch, Smooth transfer of Kloosterman integrals (the archimedean case), Amer. J. Math., in press.

[2] Aizenbud, Avraham; Gourevitch, Dmitry Schwartz functions on Nash manifolds, Int. Math. Res. Not. IMRN, Volume 155 (2008) no. 5, p. 37 (Art. ID rnm)

[3] Aizenbud, Avraham; Gourevitch, Dmitry; Sayag, Eitan (GLn+1(F),GLn(F)) is a Gelfand pair for any local field F, Compos. Math., Volume 144 (2008) no. 6, pp. 1504-1524

[4] Joseph Bernstein, Bernhard Krötz, Smooth fréchet globalizations of Harish–Chandra modules, Preprint.

[5] Fogarty, John Invariant Theory, W.A. Benjamin, Inc., New York–Amsterdam, 1969

[6] Humphreys, James E. Linear Algebraic Groups, Graduate Texts in Mathematics, vol. 21, Springer-Verlag, New York, 1975

[7] Inglis, N.F.J.; Saxl, J. An explicit model for the complex representations of the finite general linear groups, Arch. Math. (Basel), Volume 57 (1991) no. 5, pp. 424-431

[8] Jiang, Dihua; Sun, Binyong; Zhu, Chen-Bo Uniqueness of Ginzburg–Rallis models: the Archimedean case, Trans. Amer. Math. Soc., Volume 363 (2011) no. 5, pp. 2763-2802

[9] Klyachko, A.A. Models for complex representations of groups GL(n,q), Mat. Sb. (N.S.), Volume 120(162) (1983) no. 3, pp. 371-386

[10] Offen, Omer; Sayag, Eitan Uniqueness and disjointness of Klyachko models, J. Funct. Anal., Volume 254 (2008) no. 11, pp. 2846-2865

[11] Sun, Binyong; Zhu, Chen-Bo A general form of Gelfand–Kazhdan criterion, Manuscripta Math., Volume 136 (2011) no. 1–2, pp. 185-197 | DOI

[12] Wallach, Nolan R. Real Reductive Groups II, Pure and Applied Mathematics, vol. 132, Academic Press, Inc., Boston, MA, 1992

Cité par Sources :