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Whittaker models for  ,  a  -adic field
Authors:
Roberto Johnson and José Pantoja
Journal:
Proc. Amer. Math. Soc. 135 (2007), 579-586
MSC (2000):
Primary 22D30
Posted:
August 4, 2006
MathSciNet review:
2255305
Full-text PDF Free Access
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Abstract: Let  be a non-archimedean local field with odd residual characteristic. Let  be the group  We construct explicit Whittaker models for any supercuspidal representation of  with positive level.
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representations of 𝐺𝐿_{𝑁}, J. Reine Angew.
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(88e:22024), http://dx.doi.org/10.1515/crll.1987.375-376.184
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Johnson, Whittaker models for Carayol representations of
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𝐺𝑙₂, Amer. J. Math. 100
(1978), no. 1, 43–60. MR 0507253
(58 #22411a)
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C. Kutzko, On the supercuspidal representations of
𝐺𝑙₂. II, Amer. J. Math. 100
(1978), no. 4, 705–716. MR 0507254
(58 #22411b)
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(92d:22027)
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C. Kutzko and P.
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𝑆𝐿_{𝑙} over a 𝑝-adic field are
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- C.J. Bushnell, Hereditary orders, Gauss sums and supercuspidal representations of
 , J. Fur Reine und Angew. Math. 375/376, (1987), 184-210. MR 0882297 (88e:22024)
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- 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)
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- W. Casselman, Introduction to the theory of admissible representations of p-adic reductive groups, Preprint.
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- R. Johnson, Some Whittaker Models for
 , 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
 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
 of a supercuspidal representation of  Compositio Mathematica 79, (1991), 139-155. MR 1117337 (92d:22027)
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- P. C. Kutzko and P. Sally, All supercuspidal representations of
 over a p-adic field are induced, Representation Theory of Redactive Groups, Proc. Univ. of Utah Conf. 1982, Birkhäuser. MR 733814 (85i:22029)
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- J. P. Serre, Corps Locaux, Hermann, Paris (1962). MR 0150130 (27:133)
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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:
http://dx.doi.org/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
Article copyright:
© Copyright 2006 American Mathematical Society
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