References
J. Arthur andL. Clozel,Simple algebras, base change, and the advanced theory of the trace formula, Annals of Math. Studies,120, Princeton University Press, 1989.
C. J. Bushnell andP. C. Kutzko,The admissible dual of GL(N)via compact open subgroups, Annals of Math. Studies,129, Princeton University Press, 1993.
C. J. Bushnell andP. C. Kutzko, The admissible dual of SL(N) II,Proc. London Math. Soc., (3),68 (1992), 317–379.
C. J. Bushnell andP. C. Kutzko, Simple types in GL(N): computing conjugacy classes, inRepresentation theory and analysis on homogeneous spaces (S. Gindikin et al., eds),Contemp. Math.,177, Amer. Math. Soc., 1995, 107–135.
C. J. Bushnell andP. C. Kutzko,Semisimple types in GL(N), Preprint, 1995.
P. Cartier, Representations of p-adic groups: a survey, inAutomorphic forms, representations and L-functions (A. Borel andW. Casselman, ed.),Proc. Symposia in Pure Math., XXXIII, part 1, Amer. Math. Soc. (Providence RI), 1979, 111–156.
L. Clozel, Characters of non-connected, reductivep-adic groups,Can. J. Math.,39 (1987), 149–167.
P. Deligne, D. Kazhdan, M.-F. Vignéras, Représentations des algèbres centrales simplesp-adiques, inReprésentations des groupes réductifs sur un corps local, Hermann, Paris, 1984, 33–117.
D. Flath, Decomposition of representations into tensor products, inAutomorphic forms, representations and L-functions (A. Borel andW. Casselman, ed.),Proc. Symposia in Pure Math., XXXIII, part 1, Amer. Math. Soc. (Providence RI), 1979, 179–183.
A. Fröhlich, Local fields, inAlgebraic Number Theory (J. Cassels andA. Fröhlich, ed.), London, 1967, 1–41.
P. Gérardin, Weil representations associated to finite fields,J. Alg.,46 (1977), 54–101.
G. Glauberman, Correspondences of characters for relatively prime operator groups,Canad. J. Math.,20 (1968), 1465–1488.
Harish-Chandra,Harmonic analysis on reductive p-adic groups (notes byG. Van Dijk),Lecture Notes in Math.,162, Springer, Berlin, 1970.
Harish-Chandra, A submersion principle and its applications,Proc. Ind. Acad. Sci.,90 (1981), 95–102;Collected Papers, IV, Springer, Berlin, 1984, 439–446.
Harish-Chandra, Admissible invariant distributions on reductivep-adic groups, inLie theories and their applications, Queen’s papers in pure and applied math.,48, Queen’s University, Kingston Ontario, 1978, 281–347;Collected Papers, IV, Springer, Berlin, 1984, 371–437.
G. Henniart andR. Herb, Automorphic induction for GL(n) (over local non-archimedean fields),Duke Math. J., to appear.
R. Howe, On the character of Weil’s representation,Trans. Amer. Math. Soc.,177 (1973), 287–298.
H. Jacquet andJ. Shalika, On Euler products and the classification of automorphic representations II,Amer. J. Math.,103 (1981), 777–815.
R. Kottwitz, Base change for unit elements of Hecke algebras,Compositio Math.,60 (1986), 237–250.
P. Kutzko, The Langlands conjecture for GL2 of a local field,Ann. Math.,112 (1980), 381–412.
P. Kutzko andA. Moy, On the local Langlands conjecture in prime dimension,Ann. Math.,121 (1985), 495–517.
P. C. Kutzko andJ. Pantoja, The restriction to SL2 of a supercuspidal representation of GL2,Compositio Math.,79 (1991), 139–155.
R. P. Langlands,Base change for GL(2),Annals of Math. Studies,96, Princeton, 1980.
R. P. Langlands, On the notion of an automorphic representation, inAutomorphic forms, representations and L-functions (A. Borel andW. Casselman, ed.),Proc. Symposia in Pure Math., XXXIII, part 1, Amer. Math. Soc. (Providence RI), 1979, 203–207.
J. Pantoja, Liftings of supercuspidal representations of GL2,Pacific J. Math.,116 (1985), 307–351.
C. Rader andA. Silberger, Some consequences of Harish-Chandra’s submersion principle,Proc. Amer. Math. Soc.,118 (1993), 1271–1279.
J. Rogawski, Representations of GL(n) and division algebras over a local field,Duke Math. J.,50 (1983), 161–196.
H. Saito,Automorphic forms and algebraic extensions of number fields, Lectures in Math.,8, Kyoto University, 1975.
P. Sally Jr., Some remarks on discrete series characters for reductive p-adic groups, inRepresentations of Lie groups, Adv. Studies in Pure Math.,14, Kyoto, 1986, 337–348.
T. Shintani, On liftings of holomorphic cusp forms, inAutomorphic forms, representations and L-functions (A. Borel andW. Casselman, ed.),Proc. Symposia Pure Math., XXXIII, part 2, Amer. Math. Soc. (Providence, RI), 1979, 97–110.
A. Weil, Exercices dyadiques,Invent. Math.,27 (1974), 1–22;Œuvres scientifiques, III, Berlin, 1980, 343–364.
A. V. Zelevinsky, Induced representations of reductivep-adic groups II: On irreducible representations of GL(n),Ann. Scient. Éc. Norm. Sup. (4),13 (1980), 165–210.
Author information
Authors and Affiliations
Additional information
The research for part of this paper was done, and a preliminary draft written, while the authors were on sabbatical leave and enjoying the hospitality, facilities and partial financial support of IHES. Earlier stages of the work were aided by a grant from the University of London Centre for Mathematics and the support of the Isaac Newton Institute for the Mathematical Sciences. It is a pleasure to acknowledge the contribution of all these bodies.
About this article
Cite this article
Bushnell, C.J., Henniart, G. Local tame lifting for GL(N) I: Simple characters. Publications Mathématiques de l’Institut des Hautes Études Scientifiques 83, 105–233 (1996). https://doi.org/10.1007/BF02698646
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02698646