Algebra/Group Theory
Jacquet modules of ladder representations
[Modules de Jacquet des représentations en échelle]
Comptes Rendus. Mathématique, Tome 350 (2012) no. 21-22, pp. 937-940.

On calcule les modules de Jacquet pour une certaine classe de représentations irréductibles du groupe linéaire général sur un corps local non-archimédien. Cette classe contient les représentations de Speh.

We compute the Jacquet modules for a certain class of irreducible representations of the general linear group over a non-Archimedean local field. This class contains the Speh representations.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2012.10.014
Kret, Arno 1 ; Lapid, Erez 2

1 Université Paris-sud, UMR 8628, mathématique, bâtiment 425, 91405 Orsay cedex, France
2 Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
@article{CRMATH_2012__350_21-22_937_0,
     author = {Kret, Arno and Lapid, Erez},
     title = {Jacquet modules of ladder representations},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {937--940},
     publisher = {Elsevier},
     volume = {350},
     number = {21-22},
     year = {2012},
     doi = {10.1016/j.crma.2012.10.014},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2012.10.014/}
}
TY  - JOUR
AU  - Kret, Arno
AU  - Lapid, Erez
TI  - Jacquet modules of ladder representations
JO  - Comptes Rendus. Mathématique
PY  - 2012
SP  - 937
EP  - 940
VL  - 350
IS  - 21-22
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2012.10.014/
DO  - 10.1016/j.crma.2012.10.014
LA  - en
ID  - CRMATH_2012__350_21-22_937_0
ER  - 
%0 Journal Article
%A Kret, Arno
%A Lapid, Erez
%T Jacquet modules of ladder representations
%J Comptes Rendus. Mathématique
%D 2012
%P 937-940
%V 350
%N 21-22
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2012.10.014/
%R 10.1016/j.crma.2012.10.014
%G en
%F CRMATH_2012__350_21-22_937_0
Kret, Arno; Lapid, Erez. Jacquet modules of ladder representations. Comptes Rendus. Mathématique, Tome 350 (2012) no. 21-22, pp. 937-940. doi : 10.1016/j.crma.2012.10.014. http://www.numdam.org/articles/10.1016/j.crma.2012.10.014/

[1] Bernstein, I.N.; Zelevinsky, A.V. Induced representations of reductive p-adic groups. I, Ann. Sci. École Norm. Sup. (4), Volume 10 (1977) no. 4, pp. 441-472 MR 0579172 (58 #28310)

[2] Chenevier, G.; Renard, David Characters of Speh representations and Lewis Caroll identity, Represent. Theory, Volume 12 (2008), pp. 447-452 MR MR2465802 (2010f:22014)

[3] Jantzen, C. Jacquet modules of p-adic general linear groups, Represent. Theory, Volume 11 (2007), pp. 45-83 (electronic). MR 2306606 (2008g:22023)

[4] Kottwitz, R.E. Points on some Shimura varieties over finite fields, J. Amer. Math. Soc., Volume 5 (1992) no. 2, pp. 373-444 MR 1124982 (93a:11053)

[5] A. Kret, The basic stratum of some simple Shimura varieties, Math. Ann., in press, . | arXiv

[6] E. Lapid, A. Mínguez, On a determinantal formula of Tadić, Amer. J. Math., in press, available at http://www.ma.huji.ac.il/~erezla/publications.html.

[7] Rapoport, M. A guide to the reduction modulo p of Shimura varieties. Automorphic forms. I, Astérisque, Volume 298 (2005), pp. 271-318 MR MR2141705 (2006c:11071)

[8] Tadić, M. On characters of irreducible unitary representations of general linear groups, Abh. Math. Sem. Univ. Hamburg, Volume 65 (1995), pp. 341-363 MR 1359141 (96m:22039)

[9] Tadić, M. Classification of unitary representations in irreducible representations of general linear group (non-Archimedean case), Ann. Sci. École Norm. Sup. (4), Volume 19 (1986) no. 3, pp. 335-382 MR 870688 (88b:22021)

[10] Zelevinsky, A.V. Induced representations of reductive p-adic groups. II. On irreducible representations of GL(n), Ann. Sci. École Norm. Sup. (4), Volume 13 (1980) no. 2, pp. 165-210 MR 584084 (83g:22012)

Cité par Sources :