Changements de base explicites  des représentations supercuspidales de $U(1,1)(F_0)$

Blasco, Laure

Changements de base explicites des représentations supercuspidales de

U (1, 1) (F_{0})

Blasco, Laure

Annales de l'Institut Fourier, Tome 60 (2010), p. 905-938 / Harvested from Numdam

Access to full text
Full (PDF)
Full (DJVU)

Résumé
Abstract

Soit $F_{0}$ un corps local non archimédien de caractéristique nulle et de caractéristique résiduelle impaire. On décrit explicitement les changements de base des représentations supercuspidales de $U (1, 1) (F_{0})$ . C’est une étape vers la description du changement de base des paquets endoscopiques supercuspidaux de $U (2, 1) (F_{0})$ .

Let $F_{0}$ be a nonarchimedean local field of characterisitic 0 and odd residual characteristic. We describe explicitly the two base change lifts of supercuspidal representations of $U (1, 1) (F_{0})$ . This represents a step towards the goal of describing base change of endoscopic supercuspidal $L$ -packets of $U (2, 1) (F_{0})$ .

Publié le : 2010-01-01

MR 2680819 | Zbl 1210.22009

DOI : https://doi.org/10.5802/aif.2542
Classification: 22E50, 11F70
Mots clés: corps local, changement de base, groupe unitaire, représentations supercuspidales,

L

-paquets

@article{AIF_2010__60_3_905_0,
     author = {Blasco, Laure},
     title = {Changements de base explicites  des repr\'esentations supercuspidales de $U(1,1)(F\_0)$},
     journal = {Annales de l'Institut Fourier},
     volume = {60},
     year = {2010},
     pages = {905-938},
     doi = {10.5802/aif.2542},
     zbl = {1210.22009},
     mrnumber = {2680819},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/AIF_2010__60_3_905_0}
}

Blasco, Laure. Changements de base explicites  des représentations supercuspidales de $U(1,1)(F_0)$. Annales de l'Institut Fourier, Tome 60 (2010) pp. 905-938. doi : 10.5802/aif.2542. http://gdmltest.u-ga.fr/item/AIF_2010__60_3_905_0/

Bibliographie

[1] Adler, J.; Lansky, J. Depth-zero base change for unramified $U (2, 1)$ , J. Number Theory, Tome 114 (2005), pp. 324-360 | Article | MR 2167974 | Zbl 1077.22021

[2] Adler, J.; Lansky, J. Depth-zero base change for ramified $U (2, 1)$ (2008) (arXiv :0807.1528v1)

[3] Blasco, L. Description du dual admissible de $U (2, 1) (F)$ par la théorie des types de C. Bushnell et P. Kutzko, Manuscripta Math., Tome 107 (2002), pp. 151-186 | Article | MR 1894738 | Zbl 1108.22011

[4] Blasco, L. Types, paquets et changement de base : l’exemple de $U (2, 1) (F_{0})$ , I, Canadian J. Math., Tome 60 (2008), pp. 790-821 | Article | MR 2423457 | Zbl 1158.22019

[5] Bushnell, C.; Henniart, G. Local tame lifting for GL $(N)$ I : simple characters, Publ. Math. IHES, Tome 83 (1996), pp. 105-233 | Numdam | MR 1423022 | Zbl 0878.11042

[6] Bushnell, C.; Henniart, G. Local tame lifting for GL $(n)$ II : wildly ramified supercuspidals, Astérisque, Soc. Math. France, Tome 254 (1999), pp. vi+105 | MR 1685898 | Zbl 0920.11079

[7] Bushnell, C.; Henniart, G. The local Langlands conjecture for $GL (2)$ , Springer-Verlag, Berlin, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], Tome 335 (2006) | MR 2234120 | Zbl 1100.11041

[8] Ennola, V. On the characters of the finite unitary groups, Ann. Acad. Scien. Fenn., Tome 323 (1963), pp. 1-35 | MR 156900 | Zbl 0109.26001

[9] Flicker, Y. Stable and labile base change for $U (2)$ , Duke Math. J., Tome 49 (1982), pp. 691-729 | Article | MR 672503 | Zbl 0502.12013

[10] Flicker, Y. On distinguished representations, J. Reine Angew. Math., Tome 418 (1991), pp. 134-172 | MR 1111204 | Zbl 0725.11026

[11] Fröhlich, A. Principal orders and embedding of local fields in algebras, Proc. London Math. Soc., Tome 54 (1987), pp. 247-266 | Article | MR 872807 | Zbl 0615.12021

[12] Hakim, J.; Murnaghan, F. Two types of distinguished supercuspidal representations, Int. Math. Res. Not., Tome 35 (2002), pp. 1857-1889 | Article | MR 1920643 | Zbl 0996.22012

[13] Jacquet, H.; Langlands, R. Automorphic forms on $GL (2)$ , Springer-Verlag, Berlin, Lecture Notes in Mathematics, Vol. 114 (1970) | MR 401654 | Zbl 0236.12010

[14] Kottwitz, R. Rational conjugacy classes on reductive groups, Duke Math. J., Tome 49 (1982), pp. 785-806 | Article | MR 683003 | Zbl 0506.20017

[15] Kutzko, P. C.; Sally, P. J. Jr. All supercuspidal representations of $S L_{ℓ}$ over a $p$ -adic field are induced, Representation theory of reductive groups (Park City, Utah, 1982), Birkhäuser, Boston, MA (Progr. Math.) Tome 40 (1983), pp. 185-196 | Zbl 0538.22011

[16] Labesse, J.-P.; Langlands, R. $L$ -indistinguishability for $S L (2)$ , Canadian J. Math., Tome 31 (1979), pp. 726-785 | Article | MR 540902 | Zbl 0421.12014

[17] Morris, L. Tamely ramified supercuspidal representations, Ann. scient. Éc. Norm. Sup., Tome 29 (1996), pp. 639-667 | Numdam | MR 1399618 | Zbl 0870.22012

[18] Rogawski, J. Automorphic representations of unitary groups in three variables, Princeton University Press, Princeton, NJ, Annals of Mathematics Studies, Tome 123 (1990) | MR 1081540 | Zbl 0724.11031

[19] Springer, T. A. Characters of special groups, Seminar on Algebraic Groups and Related Finite Groups (The Institute for Advanced Study, Princeton, N.J., 1968/69), Springer, Berlin (Lecture Notes in Mathematics, Vol. 131) (1970), pp. 121-166 | MR 263943 | Zbl 0259.20039

[20] Stevens, S. Double coset decompositions and intertwining, Manuscripta Math., Tome 106 (2001), pp. 349-364 | Article | MR 1869226 | Zbl 0988.22008