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, Volume 115, Issue 4, pp 401–415 | Cite as

Duality and the normalization of standard intertwining operators

  • Dubravka Ban
  • Chris Jantzen


Normalized standard intertwining operators associated to an induced representation and its dual (dual in the sense of Aubert) arise in work on a conjecture of Arthur about R-groups. The purpose of this paper is to address the question of relating the normalizing factors used.


Number Theory Algebraic Geometry Topological Group 
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  1. 1.
    Arthur, J.: Unipotent automorphic representations: conjectures. Astérisque, 171–172, 13–71 (1989)Google Scholar
  2. 2.
    Arthur, J.: Intertwining operators and residues 1.weighted characters. J. Func. Anal. 84, 19–84 (1989)CrossRefzbMATHGoogle Scholar
  3. 3.
    Aubert, A.-M.: Dualité dans le groupe de Grothendieck de la catégorie des représentations lisses de longueur finie d’un groupe réductif p-adique. Trans. Am. Math. Soc. 347, 2179–2189 (1995) and Erratum, ibid. 348, 4687–4690 (1996)zbMATHGoogle Scholar
  4. 4.
    Ban, D.: Jacquet modules of parabolically induced representations and Weyl groups. Can. J. Math. 53, 675–695 (2001)zbMATHGoogle Scholar
  5. 5.
    Ban, D.: The Aubert involution and R-groups. Ann. Sci. Éc. Norm. Sup. 35, 673–693 (2002)CrossRefzbMATHGoogle Scholar
  6. 6.
    Ban, D.: Linear independence of intertwining operators. To appear in J. AlgebraGoogle Scholar
  7. 7.
    Bernstein, I.N., Zelevinsky, A.V.: Induced representations of reductive p-adic groups, I. Ann. Sci. Éc. Norm. Sup. 10, 441–472 (1977)zbMATHGoogle Scholar
  8. 8.
    Borel, A., Wallach, N.: Continuous Cohomology, Discrete Subgroups, and Representations of Reductive Groups. Princeton University Press, Princeton, 1980Google Scholar
  9. 9.
    Casselman, W.: Introduction to the theory of admissible representations of p-adic reductive groups. PreprintGoogle Scholar
  10. 10.
    Goldberg, D., Shahidi, F.: Automorphic L-functions, intertwining operators and the irreducible tempered representations of p-adic groups. PreprintGoogle Scholar
  11. 11.
    Harish-Chandra: Harmonic analysis on reductive p-adic groups. Proceedings of Symposia in Pure Mathematics 26, 167–192 (1974)Google Scholar
  12. 12.
    Iwahori, N., Matsumoto, H.: On some Bruhat decomposition and the structure of the Hecke rings of p-adic Chevalley groups. Publ. Math. IHES 25, 5–48 (1965)zbMATHGoogle Scholar
  13. 13.
    Jantzen, C.: On the Iwahori-Matsumoto involution and applications. Ann. Sci. Éc. Norm. Sup. 28, 527–547 (1995)zbMATHGoogle Scholar
  14. 14.
    Knapp, A.W., Stein, E.M.: Intertwining operators for semisimple groups. Ann. Math. 93, 489–578 (1971)zbMATHGoogle Scholar
  15. 15.
    Langlands, R.: On the Functional Equations Satisfied by Eisenstein Series. Lecture Notes in Math. 544, 1976Google Scholar
  16. 16.
    Schneider, P., Stuhler, U.: Representation theory and sheaves on the Bruhat-Tits building. Publ. Math. IHES 85, 97–191 (1997)zbMATHGoogle Scholar
  17. 17.
    Shahidi, F.: On certain L-functions. Am. J. Math. 103, 297–355 (1981)zbMATHGoogle Scholar
  18. 18.
    Shahidi, F.: A proof of Langlands’ conjecture on Plancherel measures; Complementary series for p-adic groups. Ann. Math. 132, 273–330 (1990)zbMATHGoogle Scholar
  19. 19.
    Silberger, A.: The Langlands quotient theorem for p-adic groups. Math. Ann. 236, 95–104 (1978)zbMATHGoogle Scholar
  20. 20.
    Silberger, A.: Introduction to harmonic analysis on reductive p-adic groups. Math. Notes 23, Princeton University Press, Princeton, NJ, 1979Google Scholar
  21. 21.
    Tadić, M.: Notes on representations of non-archimedean SL(n). Pac. J. Math. 152, 375–396 (1992)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Dubravka Ban
    • 1
  • Chris Jantzen
    • 2
  1. 1.Department of MathematicsSouthern Illinois UniversityCarbondaleUSA
  2. 2.Department of MathematicsEast Carolina UniversityGreenvilleUSA

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