Skip to main content
Log in

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. 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.

  2. 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.

  3. C. J. Bushnell andP. C. Kutzko, The admissible dual of SL(N) II,Proc. London Math. Soc., (3),68 (1992), 317–379.

    MathSciNet  Google Scholar 

  4. 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.

    MathSciNet  Google Scholar 

  5. C. J. Bushnell andP. C. Kutzko,Semisimple types in GL(N), Preprint, 1995.

  6. 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.

    Google Scholar 

  7. L. Clozel, Characters of non-connected, reductivep-adic groups,Can. J. Math.,39 (1987), 149–167.

    MATH  MathSciNet  Google Scholar 

  8. 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.

    Google Scholar 

  9. 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.

    Google Scholar 

  10. A. Fröhlich, Local fields, inAlgebraic Number Theory (J. Cassels andA. Fröhlich, ed.), London, 1967, 1–41.

  11. P. Gérardin, Weil representations associated to finite fields,J. Alg.,46 (1977), 54–101.

    Article  MATH  Google Scholar 

  12. G. Glauberman, Correspondences of characters for relatively prime operator groups,Canad. J. Math.,20 (1968), 1465–1488.

    MATH  MathSciNet  Google Scholar 

  13. Harish-Chandra,Harmonic analysis on reductive p-adic groups (notes byG. Van Dijk),Lecture Notes in Math.,162, Springer, Berlin, 1970.

    MATH  Google Scholar 

  14. Harish-Chandra, A submersion principle and its applications,Proc. Ind. Acad. Sci.,90 (1981), 95–102;Collected Papers, IV, Springer, Berlin, 1984, 439–446.

    Article  MATH  MathSciNet  Google Scholar 

  15. 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.

    Google Scholar 

  16. G. Henniart andR. Herb, Automorphic induction for GL(n) (over local non-archimedean fields),Duke Math. J., to appear.

  17. R. Howe, On the character of Weil’s representation,Trans. Amer. Math. Soc.,177 (1973), 287–298.

    Article  MATH  MathSciNet  Google Scholar 

  18. H. Jacquet andJ. Shalika, On Euler products and the classification of automorphic representations II,Amer. J. Math.,103 (1981), 777–815.

    Article  MATH  MathSciNet  Google Scholar 

  19. R. Kottwitz, Base change for unit elements of Hecke algebras,Compositio Math.,60 (1986), 237–250.

    MathSciNet  Google Scholar 

  20. P. Kutzko, The Langlands conjecture for GL2 of a local field,Ann. Math.,112 (1980), 381–412.

    Article  MathSciNet  Google Scholar 

  21. P. Kutzko andA. Moy, On the local Langlands conjecture in prime dimension,Ann. Math.,121 (1985), 495–517.

    Article  MathSciNet  Google Scholar 

  22. P. C. Kutzko andJ. Pantoja, The restriction to SL2 of a supercuspidal representation of GL2,Compositio Math.,79 (1991), 139–155.

    MATH  MathSciNet  Google Scholar 

  23. R. P. Langlands,Base change for GL(2),Annals of Math. Studies,96, Princeton, 1980.

  24. 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.

    Google Scholar 

  25. J. Pantoja, Liftings of supercuspidal representations of GL2,Pacific J. Math.,116 (1985), 307–351.

    MATH  MathSciNet  Google Scholar 

  26. C. Rader andA. Silberger, Some consequences of Harish-Chandra’s submersion principle,Proc. Amer. Math. Soc.,118 (1993), 1271–1279.

    Article  MATH  MathSciNet  Google Scholar 

  27. J. Rogawski, Representations of GL(n) and division algebras over a local field,Duke Math. J.,50 (1983), 161–196.

    Article  MATH  MathSciNet  Google Scholar 

  28. H. Saito,Automorphic forms and algebraic extensions of number fields, Lectures in Math.,8, Kyoto University, 1975.

  29. 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.

    MathSciNet  Google Scholar 

  30. 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.

    Google Scholar 

  31. A. Weil, Exercices dyadiques,Invent. Math.,27 (1974), 1–22;Œuvres scientifiques, III, Berlin, 1980, 343–364.

    Article  MATH  MathSciNet  Google Scholar 

  32. 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.

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

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

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02698646

Keywords

Navigation