[Modules de Jacquet des représentations en échelle]
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.
Accepté le :
Publié le :
Arno Kret 1 ; Erez Lapid 2
@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}, }
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] Induced representations of reductive -adic groups. I, Ann. Sci. École Norm. Sup. (4), Volume 10 (1977) no. 4, pp. 441-472 MR 0579172 (58 #28310)
[2] Characters of Speh representations and Lewis Caroll identity, Represent. Theory, Volume 12 (2008), pp. 447-452 MR MR2465802 (2010f:22014)
[3] Jacquet modules of p-adic general linear groups, Represent. Theory, Volume 11 (2007), pp. 45-83 (electronic). MR 2306606 (2008g:22023)
[4] 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] 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] 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] 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] Induced representations of reductive -adic groups. II. On irreducible representations of , Ann. Sci. École Norm. Sup. (4), Volume 13 (1980) no. 2, pp. 165-210 MR 584084 (83g:22012)
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