Constructing the Supercuspidal Representation of GLn(F), F p—ADIC

Part of the Progress in Mathematics book series (PM, volume 101)


In this paper I give a description of a construction of the supercuspidal representations of GL n (F). This construction, the result of work done in late 1988 and early 1989, was first given in [6], and the description here follows the same lines.


Irreducible Representation Conjugacy Class Division Algebra Invertible Element Open Subgroup 
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  1. 1.
    F. Bruhat and J. Tits, Groupes réductifs sur un corps local I, Publ. Math. IHES 41 (1972), 5–252.MathSciNetzbMATHGoogle Scholar
  2. 2.
    C. Bushnell, Hereditary orders, Gauss sums, and supercuspidal representations of GL N, J. reine angew. Math. 375/376 (1977), 184–210.MathSciNetGoogle Scholar
  3. 3.
    H. Carayol, Représentations cuspidate du groupe linéaire, Ann. Sci. École Norm. Sup. (4) 17 (1984), 191–225.MathSciNetzbMATHGoogle Scholar
  4. 4.
    L. Corwin, Representations of division algebras over local fields. Advances in Math. 13 (1974), 249–257.MathSciNetCrossRefGoogle Scholar
  5. 5.
    L. Corwin, The unitary dual for the multiplicative group of arbitrary division algebras over local fields, J. Am. Math. Soc. 2 (1989), 565–598.MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    L. Corwin, A construction of the supercuspidal representations of GL n (F), F p-adic, Trans. Amer. Math. Soc. (to appear).Google Scholar
  7. 7.
    L. Corwin and R. Howe, Computing characters of tamely ramified p-adic division algebras, Pac. J. Math. 73 (1977), 461–477.MathSciNetzbMATHGoogle Scholar
  8. 8.
    L. Corwin, A. Moy, and P. J. Sally, Jr., Degrees and formal degrees for division algebras and GLn over a p-adic field, Pac. J. Math. 141 (1990), 21–45.MathSciNetzbMATHGoogle Scholar
  9. 9.
    P. Deligne, D. Kazhdan, and M.-F. Vigneras, Représentations des algébres centrales simples p-adiques, Représentations des groupes réductifs sur un corps local, Hermann, Paris, 1984, pp. 33-117.Google Scholar
  10. 10.
    R. Godement and H. Jacquet, Zeta functions of Simple Algebras, Lecture Notes in Math., Vol. 462, Springer-Verlag, Berlin-New York, 1975.Google Scholar
  11. 11.
    R. Howe, Representation theory for division algebras over local fields (tamely ramified case), Bull. Amer. Math. Soc. 77 (1971), 1063–1066.MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    R. Howe, Tamely ramified supercuspidal representations of GL n, Pac. J. Math. 73 (1977), 365–381.MathSciNetzbMATHGoogle Scholar
  13. 13.
    N. Iwahori and H. Matsumoto, On some Bruhat decompositions and the structure of the Heche ring of p-adic Chevalley groups, Publ. Math. IHES 25 (1965), 5–48.MathSciNetGoogle Scholar
  14. 14.
    D. Kazhdan, Representations of groups over closed local fields, J. D’Analyse Math. 47, 175–179.Google Scholar
  15. 15.
    H. Koch, Eisensteinsche Polynomfolgen und Arithmetik in Divisionsalgehren ũber lokalen Kōrpern, Math. Nachr. 104 (1981), 229–251.MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    P. Kutzko and D. Manderscheid, On intertwining operators for GL N (F), F a non-archimedean p-adic field, Duke Math. J. 57 (1988), 275–293.MathSciNetzbMATHCrossRefGoogle Scholar
  17. 17.
    A. Moy, Local constants and the tame Langlands correspondence, Amer. J. Math. 108 (1986), 863–930.MathSciNetzbMATHCrossRefGoogle Scholar
  18. 18.
    J. Rogawski, Representations of GL(n) and division algebras over a p-adic field, Duke Math. J. 50 (1983), 161–196.MathSciNetzbMATHCrossRefGoogle Scholar
  19. 19.
    A. Silberger, Introduction to Harmonic Analysis on Reductive p-adic Groups, Mathematical Notes, Vol. 23, Princeton Univ. Press, Princeton, 1979.Google Scholar
  20. 20.
    T. Springer, Characters of special groups, Semisimple Algebraic Groups and Related Finite Groups, Lecture Notes in Math., Vol. 131, Springer-Verlag, Berlin-New York, 1970, pp. 121–166.CrossRefGoogle Scholar
  21. 21.
    A. Weil, Basic Number Theory, Springer-Verlag, Berlin-New York, 1967.zbMATHGoogle Scholar
  22. 22.
    A. V. Zelevinskii, Induced representations of reductive p-adic groups, II. On irreducible representations of GL(n), Ann. Sci. École Norm. Sup. (4) 13 (1980), 165–211.Google Scholar

Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  1. 1.Department of MathematicsRutgers UniversityNew BrunswickUSA

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