Available in electronic format
Available in print format		 Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Previous Article | Next Article
     

Whittaker models for $ SL_{2}(F)$, $ F$ a $ p$-adic field

Author(s): Roberto Johnson; José Pantoja
Journal: Proc. Amer. Math. Soc. 135 (2007), 579-586.
MSC (2000): Primary 22D30
Posted: August 4, 2006
Retrieve article in: PDF DVI PostScript

Abstract | References | Similar articles | Additional information

Abstract: Let $ F$ be a non-archimedean local field with odd residual characteristic. Let $ G$ be the group $ SL_{2}(F).$ We construct explicit Whittaker models for any supercuspidal representation of $ G$ with positive level.

References:

[B]
C.J. Bushnell, Hereditary orders, Gauss sums and supercuspidal representations of $ GL_{N}(F)$, J. Fur Reine und Angew. Math. 375/376, (1987), 184-210. MR 0882297 (88e:22024)

[B-F]
C.J. Bushnell and A. Fröhlich, Non abelian congruence, Gauss sums and p-adic simple algebras, Proc. London Math. Soc. 50, (1985), 207-264. MR 0772712 (86g:11071)

[B-K]
C.J. Bushnell and P. C. Kutzko, The admissible dual of GL(N) via compact open subgroups, Annals of Mathematics Studies, 1993, Princeton University Press. MR 1204652 (94h:22007)

[Cr]
P. Cartier, Representations of p-adic groups: a survey, Proc. of Symposia in Pure Math., Amer. Math. Soc. 23, (1979), 111-155. MR 0546593 (81e:22029)

[Cs]
W. Casselman, Introduction to the theory of admissible representations of p-adic reductive groups, Preprint.

[J]
R. Johnson, Some Whittaker Models for $ GL_{N}(F)$, Geometry and representation theory of real and p-adic groups, Progress in Mathematics, v. 158, Birkhäuser, 1998. MR 1486140 (98k:22071)

[K1]
P. C. Kutzko, Mackey's theorem for nonunitary representations, Proc. Amer. Math. Soc. 64, (1977), 173-175. MR 0442145 (56:533)

[K2]
P. C. Kutzko, On the supercuspidal representations of GL$ _{2},$ I, II, Amer. J. Math. 100, (1978), 43-60, 705-716. MR 0507253 (58:22411a), MR 0507254 (58:22411b)

[K-P]
P. C. Kutzko and J. Pantoja, The restriction to $ SL_{2} $ of a supercuspidal representation of $ GL_{2},$ Compositio Mathematica 79, (1991), 139-155. MR 1117337 (92d:22027)

[K-S]
P. C. Kutzko and P. Sally, All supercuspidal representations of $ SL_{l}$ over a p-adic field are induced, Representation Theory of Redactive Groups, Proc. Univ. of Utah Conf. 1982, Birkhäuser. MR 733814 (85i:22029)

[R]
F. Rodier, Whittaker models for admissible representations of reductive p-adic split groups, Proc. of Symposia in Pure Math., Amer. Math. Soc. 26, (1973), 425-430. MR 0354942 (50:7419)

[Se]
J. P. Serre, Corps Locaux, Hermann, Paris (1962). MR 0150130 (27:133)

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 22D30

Retrieve articles in all Journals with MSC (2000): 22D30

Additional Information:

Roberto Johnson
Affiliation: Instituto de Matemáticas, Pontificia Universidad Católica de Valparaíso, Casilla 4059, Valparaíso, Chile
Email: rjohnson@ucv.cl

José Pantoja
Affiliation: Instituto de Matemáticas, Pontificia Universidad Católica de Valparaíso, Casilla 4059, Valparaíso, Chile
Email: jpantoja@ucv.cl

DOI: 10.1090/S0002-9939-06-08480-2
PII: S 0002-9939(06)08480-2
Received by editor(s): March 21, 2005
Received by editor(s) in revised form: August 26, 2005
Posted: August 4, 2006
Additional Notes: The first author was partially supported by Pontificia Universidad Catolica de Valparaiso (Project DI 124.796/2004)
The second author was partially supported by FONDECYT (Project 1030907) and Pontificia Universidad Catolica de Valparaiso
Communicated by: Wen-Ching Winnie Li
Copyright of article: Copyright 2006, American Mathematical Society

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2008, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google