Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-23T18:01:07.975Z Has data issue: false hasContentIssue false
  • English
  • Français

On Mœglin's Parametrization of Arthur Packets for p-adic Quasisplit Sp(N) and SO(N)

Published online by Cambridge University Press:  20 November 2018

Bin Xu
Bin Xu*
Affiliation:
Department of Mathematics and Statistics, University of Calgary, 2500 University Dr. NW Calgary, AB, T2N 1N4 e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We give a survey on Mœglin's construction of representations in the Arthur packets for $p$-adic quasisplit symplectic and orthogonal groups. The emphasis is on comparing Mœglin's parametrization of elements in the Arthur packets with that of Arthur.

Keywords

22E5011F70symplectic and orthogonal groupArthur packetendoscopy
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 69 , Issue 4 , 01 August 2017 , pp. 890 - 960
Copyright
Copyright © Canadian Mathematical Society 2017

References

[ABV92] Adams, J.,Barbasch, D., and Vogan, D., The Langlands classification and irreducible characters for real reductive groups. Progress in Mathematics, 104, Birkhäuser Boston, Inc., Boston, MA, 1992.http://dx.doi.org/10.1007/978-1-4612-0383-4 Google Scholar
[Artl3] Arthur, J., The endoscopie classification of representations: orthogonal and symplectic groups. American Mathematical Society Colloquium Publications, 61, American Mathematical Society, Providence, RI, 2013.http://dx.doi.Org/10.1090/coll/061 Google Scholar
[HenOO] Henniart, G., Une preuve simple des conjectures de Langlands pour GL(n) sur un corps p-adique. Invent. Math. 139(2000), no. 2, 439–455.http://dx.doi.Org/10.1OO7/sOO222OO5OO12 Google Scholar
[HirO4] Hiraga, K., On functoriality ofZelevinski involutions. Compos. Math. 140(2004), no. 6, 1625–1656.http://dx.doi.Org/10.1112/S0010437X04000892 Google Scholar
[HT01] Harris, M. and Taylor, R., The geometry and cohomology of some simple Shimura varieties. Annals of Mathematics Studies, 151, Princeton University Press, Princeton, NJ, 2001.Google Scholar
[Mœg06a] Moeglin, C., Paquets d-Arthur pour les groupes classiques; point de vue combinatoire. arxiv:math/0610189 Google Scholar
[MœgO6b] Moeglin, C., Sur certains paquets d'Arthur et involution d'Aubert-Schneider-Stuhler généralisée. Represent. Theory 10(2006), 86–129.http://dx.doi.org/10.1090/S1088-4165-06-00270-6 Google Scholar
[Mœg09] Moeglin, C., Paquets d'Arthur discrets pour un groupe classique p-adique, Automorphic forms and L-functions II Local aspects. Contemp. Math., 489, American Mathematical Society, Providence, RI, 2009, pp. 179–257.http://dx.doi.Org/10.1090/conm/489/09549 Google Scholar
[Mœgl0] Moeglin, C. , Holomorphie des opérateurs d'entrelacement normalisés à l'aide des paramétres d'Arthur. Canad. J. Math. 62(2010), no. 6,1340–1386.http://dx.doi.org/10.4153/CJM-2010-074-6 Google Scholar
[Mœglla] Moeglin, C., Conjecture d'Adams pour la correspondance de Howe et filtration de Kuala. Arithmetic geometry and automorphic forms, Adv. Lect. Math. (ALM), 19, Int. Press, Somerville, MA, 2011, pp. 445–503.Google Scholar
[Mœgllb] Moeglin, C., Image des opérateurs d'entrelacements normalisés et pôles des séries d'Eisenstein. Adv. Math. 228(2011), no. 2, 1068–1134.http://dx.doi.Org/10.101 6/j.aim.2O11.06.003 Google Scholar
[Mœgllc] Moeglin, C., Multiplicité 1 dans les paquets d'Arthur aux places p-adiques. In: On certain L-functions, Clay Math. Proc. 13, American Mathematical Society, Providence, RI, 2011, pp. 333–374.Google Scholar
[MT02] Mœglin, C. and Tadic, M., Construction of discrete series for classical p-adic groups. J. Amer. Math. Soc. 15(2002), no. 3, 715–786. http://dx.doi.Org/10.1090/S0894-0347-02-00389-2 Google Scholar
[MW89] Mœglin, C. and Waldspurger, J.-L., Le spectre résiduel de GL(n). Ann. Sci. École Norm. Sup. (4) 22(1989), no. 4, 605–674.Google Scholar
[MW06] Mœglin, C., Sur le transfert des traces d'un groupe classique p-adique à un groupe linéaire tordu. Selecta Math. (N.S.) 12(2006), no. 3-4, 433–515.http://dx.doi.org/10.1007/s00029-006-0026-0 Google Scholar
[NgôlO] Ngô, B. C., Le lemme fondamental pour les algébres de Lie. Publ. Math. Inst. Hautes Études Sci. 111(2010), 1–169.http://dx.doi.org/10.1007/s10240-010-0026-7 Google Scholar
[Schl3] Scholze, P., The local Langlands correspondence for GLn over p-adic fields. Invent. Math. 192(2013), 663–715.http://dx.doi.Org/10.1 OO7/sOO222-O12-0420-5 Google Scholar
[Tad86] Tadić, M., Classification of unitary representations in irreducible representations of general linear group (non-Archimedean case). Ann. Sci. École Norm. Sup. (4) 19(1986), no. 3, 335–382.Google Scholar
[Wal95] Waldspurger, J.-L., Une formule des traces locale pour les algébres de Lie p-adiques. J. Reine Angew. Math. 465(1995), 41–99.http://dx.doi.Org/10.1515/crll.1 995.465.41 Google Scholar
[Wal97] Waldspurger, J.-L., Le lemme fondamental implique le transfert. Compositio Math. 105(1997), no. 2,153–236.http://dx.doi.Org/10.1023/A:10001 031122 68 Google Scholar
[WalO6] Waldspurger, J.-L., Endoscopie et changement de caractéristique. J. Inst. Math. Jussieu 5(2006), no. 3, 423–525.http://dx.doi.Org/1 0.101 7/S1474748006000041 Google Scholar
[WalO8] Waldspurger, J.-L., L'endoscopie tordue n'est pas si tordue. Mem. Amer. Math. Soc. 194(2008), no. 908. http://dx.doi.Org/10.1090/memo/0908 Google Scholar
[Xul5] Xu, B., On the cuspidal support of discrete series for p-adic quasisplit Sp( N) and SO(N). arxiv:1 504.08364 Google Scholar