Comptes Rendus
Algebra/Group Theory
Jacquet modules of ladder representations
[Modules de Jacquet des représentations en échelle]
Comptes Rendus. Mathématique, Volume 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
Arno Kret 1 ; Erez Lapid 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 = {Arno Kret and Erez Lapid},
     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},
}
TY  - JOUR
AU  - Arno Kret
AU  - Erez Lapid
TI  - Jacquet modules of ladder representations
JO  - Comptes Rendus. Mathématique
PY  - 2012
SP  - 937
EP  - 940
VL  - 350
IS  - 21-22
PB  - Elsevier
DO  - 10.1016/j.crma.2012.10.014
LA  - en
ID  - CRMATH_2012__350_21-22_937_0
ER  - 
%0 Journal Article
%A Arno Kret
%A Erez Lapid
%T Jacquet modules of ladder representations
%J Comptes Rendus. Mathématique
%D 2012
%P 937-940
%V 350
%N 21-22
%I Elsevier
%R 10.1016/j.crma.2012.10.014
%G en
%F CRMATH_2012__350_21-22_937_0
Arno Kret; Erez Lapid. Jacquet modules of ladder representations. Comptes Rendus. Mathématique, Volume 350 (2012) no. 21-22, pp. 937-940. doi : 10.1016/j.crma.2012.10.014. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.10.014/

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

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

[4] R.E. Kottwitz 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] M. Rapoport 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] M. Tadić 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] M. Tadić 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] A.V. Zelevinsky 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 :

Commentaires - Politique


Ces articles pourraient vous intéresser

On the relationship between distinction and irreducibility of parabolic induction

Arnab Mitra

C. R. Math (2019)


Positivity of 𝐋(1 2,π) for symplectic representations

Erez Lapid; Stephen Rallis

C. R. Math (2002)