Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-24T17:41:35.240Z Has data issue: false hasContentIssue false
  • English
  • Français

Transfert du pseudo-coefficient de Kottwitz et formules de caractère pour la série discrète de GL(N) sur un corps local

Published online by Cambridge University Press:  20 November 2018

P. Broussous
P. Broussous*
Affiliation:
Université de Poitiers, Laboratoire de Mathématiques et Applications, UMR 7348 du CNRS. courriel: paul.broussous@math.univ-poitiers.fr
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.

Soit $G$ le groupe $\text{GL}\,\left( N,\,F \right)$, où $F$ est un corps localement compact et non archimédien. En utilisant la théorie des types simples de Bushnell et Kutzko, ainsi qu'une idée originale d'Henniart, nous construisons des pseudo-coefficients explicites pour les représentations de la série discrète de $G$. Comme application, nous en déduisons des formules inédites pour la valeur du charactère d'Harish- Chandra de certaines telles représentations en certainséléments elliptiques réguliers.

Keywords

22E50reductive p-adic groupsdiscrete seriesHarish-Chandra characterpseudo-coefficient
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 66 , Issue 2 , 01 April 2014 , pp. 241 - 283
Copyright
Copyright © Canadian Mathematical Society 2014

References

Références

[Ba] Badulescu, I., Un résultat de transfert et un résultat d’intégrabilité locale des caractères en caractéristique non nulle. J. Reine Angew. Math. 565(2003), 1001–124.Google Scholar
[Be] Bernstein, J., On the support of Plancherel measure. J. Geom. Phys. 5(1988), 663–710. http://dx.doi.org/10.1016/0393-0440(88)90024-1 Google Scholar
[BH] Bushnell, C. J. et Henniart, G., Explicit functorial correspondences for level zero representations of p-adic linear groups. J. Number Theory 131(2011), 309–331. http://dx.doi.org/10.1016/j.jnt.2010.09.003 Google Scholar
[BH1] Bushnell, C. J., The essentially tame Jacquet–Langlands correspondence for inner forms of GL(n). Prépublication, 2008.Google Scholar
[BH2] Bushnell, C. J., Local tame lifting for GL(n). III. Explicit base change and Jacquet–Langlands correspondence. J. Reine Angew. Math. 580(2005), 39–100. http://dx.doi.org/10.1515/crll.2005.2005.580.39 Google Scholar
[BH3] Bushnell, C. J., Correspondance de Jacquet–Langlands explicite. II. Le cas de degré égal à la caractéristiquerésiduelle. Manuscripta Math. 102(2000), 211–225. http://dx.doi.org/10.1007/s002291020211 Google Scholar
[BH4] Bushnell, C. J., Local tame lifting for GL(N). I. Simple characters. Inst. Hautes Études Sci. Publ. Math. 83(1996), 105–233.Google Scholar
[BHK] Bushnell, C. J., Henniart, G. et Kutzko, P. C., Types and explicit Plancherel formulae for reductive p-adic groups. In: On certain L-functions, Clay Math. Proc. 13, Amer. Math. Soc., Providence, RI, 2011, 55–80.Google Scholar
[BK] Bushnell, C. J. et Kutzko, P. C., The admissible dual of GL(N) via compact open subgroups. Ann. of Math. Stud. 129, Princeton University Press, 1993.Google Scholar
[BK2] Bushnell, C. J., Smooth representations of p-adic groups: Structure theory via types, Proc. London Math. Soc. (3) 77(1998), 582–634. http://dx.doi.org/10.1112/S0024611598000574 Google Scholar
[DL] Deligne, P. et Lusztig, G., Duality for representations of reductive a group over a finite field. J. Algebra 74(1982), 284–291. http://dx.doi.org/10.1016/0021-8693(82)90023-0 Google Scholar
[DM] Digne, F. et Michel, J., Representations of finite groups of Lie type. London Mathematical Society Student Texts 21, Cambridge University Press, Cambridge, 1991.Google Scholar
[GG] Gel’fand, I. M. et Graev, M. I., Représentations of the group of second order matrices with elements in a locally compact field and spherical functions in locally compact fields. (Russian) Uspehi Mat. Nauk 18(1963), 29–99.Google Scholar
[HM] Howe, R. et Moy, A., Harish-Chandra homomorphisms for p-adic groups. CBMS Regional Conference Series in Mathematics 59, Amer. Math. Soc., Providence, RI, 1985.Google Scholar
[Ka] Kazhdan, D., Cuspidal geometry of p-adic groups. J. d’Analyse Math. 47(1986), 1–36. http://dx.doi.org/10.1007/BF02792530 Google Scholar
[Kott] Kottwitz, R. E., Tamagawa Numbers. Annals of Math. 127(1988), 629–646. http://dx.doi.org/10.2307/2007007 Google Scholar
[La] Laumon, G., Cohomology of Drinfeld modular varieties, Part I: Geometry, counting of points and local harmonic analysis. Cambridge Stud. Adv. Math. 41, Cambridge University Press, 1996.Google Scholar
[ScSt] Schneider, P. et Stuhler, U., Representation theory and sheaves on the Bruhat-Tits building. Inst. Hautes Études Sci. Publ. Math. 85(1997), 97–191.Google Scholar
[SaSp] Sally Jr, P. J. et Spice, L., Character theory of reductive p-adic groups. In: Ottawa lectures on admissible representations of reductive p-adic groups, Fields Institute Monographs 26, Amer. Math. Soc., Providence, RI, 2009.Google Scholar
[SZ] Silberger, A. L. et Zink, E.-W., The character of the generalized Steinberg representations of finitelinear groups on the regular elliptic set. Trans. Amer. Math. Soc. 352(2000), 3339–3356. http://dx.doi.org/10.1090/S0002-9947-00-02454-5 Google Scholar
[SZ2] Silberger, A. L., Weak explicit matching for level zero discrete series of unit groups of p-adic simple algebras. Canad. J. Math. 55(2003), 353–378. http://dx.doi.org/10.4153/CJM-2003-016-4 Google Scholar
[Wa] Waldspurger, J.-L., La formule de Plancherel pour les groupes p-adiques (d’après Harish-Chandra). J. Inst. Math. Jussieu 2(2003), 235–333. http://dx.doi.org/10.1017/S1474748003000082 Google Scholar