Soit un corps local non archimédien de caractéristique nulle et de caractéristique résiduelle impaire. On décrit explicitement les changements de base des représentations supercuspidales de . C’est une étape vers la description du changement de base des paquets endoscopiques supercuspidaux de .
Let be a nonarchimedean local field of characterisitic 0 and odd residual characteristic. We describe explicitly the two base change lifts of supercuspidal representations of . This represents a step towards the goal of describing base change of endoscopic supercuspidal -packets of .
@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/
[1] Depth-zero base change for unramified , J. Number Theory, Tome 114 (2005), pp. 324-360 | Article | MR 2167974 | Zbl 1077.22021
[2] Depth-zero base change for ramified (2008) (arXiv :0807.1528v1)
[3] Description du dual admissible de 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] Types, paquets et changement de base : l’exemple de , I, Canadian J. Math., Tome 60 (2008), pp. 790-821 | Article | MR 2423457 | Zbl 1158.22019
[5] Local tame lifting for GL I : simple characters, Publ. Math. IHES, Tome 83 (1996), pp. 105-233 | Numdam | MR 1423022 | Zbl 0878.11042
[6] Local tame lifting for GL II : wildly ramified supercuspidals, Astérisque, Soc. Math. France, Tome 254 (1999), pp. vi+105 | MR 1685898 | Zbl 0920.11079
[7] The local Langlands conjecture for , Springer-Verlag, Berlin, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], Tome 335 (2006) | MR 2234120 | Zbl 1100.11041
[8] On the characters of the finite unitary groups, Ann. Acad. Scien. Fenn., Tome 323 (1963), pp. 1-35 | MR 156900 | Zbl 0109.26001
[9] Stable and labile base change for , Duke Math. J., Tome 49 (1982), pp. 691-729 | Article | MR 672503 | Zbl 0502.12013
[10] On distinguished representations, J. Reine Angew. Math., Tome 418 (1991), pp. 134-172 | MR 1111204 | Zbl 0725.11026
[11] 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] Two types of distinguished supercuspidal representations, Int. Math. Res. Not., Tome 35 (2002), pp. 1857-1889 | Article | MR 1920643 | Zbl 0996.22012
[13] Automorphic forms on , Springer-Verlag, Berlin, Lecture Notes in Mathematics, Vol. 114 (1970) | MR 401654 | Zbl 0236.12010
[14] Rational conjugacy classes on reductive groups, Duke Math. J., Tome 49 (1982), pp. 785-806 | Article | MR 683003 | Zbl 0506.20017
[15] All supercuspidal representations of over a -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] -indistinguishability for , Canadian J. Math., Tome 31 (1979), pp. 726-785 | Article | MR 540902 | Zbl 0421.12014
[17] Tamely ramified supercuspidal representations, Ann. scient. Éc. Norm. Sup., Tome 29 (1996), pp. 639-667 | Numdam | MR 1399618 | Zbl 0870.22012
[18] 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] 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] Double coset decompositions and intertwining, Manuscripta Math., Tome 106 (2001), pp. 349-364 | Article | MR 1869226 | Zbl 0988.22008