Skip to main content
Log in

Duality and the normalization of standard intertwining operators

  • Published:
manuscripta mathematica Aims and scope Submit manuscript

Abstract.

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.

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.

Institutional subscriptions

Similar content being viewed by others

References

  1. Arthur, J.: Unipotent automorphic representations: conjectures. Astérisque, 171–172, 13–71 (1989)

  2. Arthur, J.: Intertwining operators and residues 1.weighted characters. J. Func. Anal. 84, 19–84 (1989)

    Article  MATH  Google Scholar 

  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)

    MATH  Google Scholar 

  4. Ban, D.: Jacquet modules of parabolically induced representations and Weyl groups. Can. J. Math. 53, 675–695 (2001)

    MATH  Google Scholar 

  5. Ban, D.: The Aubert involution and R-groups. Ann. Sci. Éc. Norm. Sup. 35, 673–693 (2002)

    Article  MATH  Google Scholar 

  6. Ban, D.: Linear independence of intertwining operators. To appear in J. Algebra

  7. Bernstein, I.N., Zelevinsky, A.V.: Induced representations of reductive p-adic groups, I. Ann. Sci. Éc. Norm. Sup. 10, 441–472 (1977)

    MATH  Google Scholar 

  8. Borel, A., Wallach, N.: Continuous Cohomology, Discrete Subgroups, and Representations of Reductive Groups. Princeton University Press, Princeton, 1980

  9. Casselman, W.: Introduction to the theory of admissible representations of p-adic reductive groups. Preprint

  10. Goldberg, D., Shahidi, F.: Automorphic L-functions, intertwining operators and the irreducible tempered representations of p-adic groups. Preprint

  11. Harish-Chandra: Harmonic analysis on reductive p-adic groups. Proceedings of Symposia in Pure Mathematics 26, 167–192 (1974)

    Google Scholar 

  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)

    MATH  Google Scholar 

  13. Jantzen, C.: On the Iwahori-Matsumoto involution and applications. Ann. Sci. Éc. Norm. Sup. 28, 527–547 (1995)

    MATH  Google Scholar 

  14. Knapp, A.W., Stein, E.M.: Intertwining operators for semisimple groups. Ann. Math. 93, 489–578 (1971)

    MATH  Google Scholar 

  15. Langlands, R.: On the Functional Equations Satisfied by Eisenstein Series. Lecture Notes in Math. 544, 1976

  16. Schneider, P., Stuhler, U.: Representation theory and sheaves on the Bruhat-Tits building. Publ. Math. IHES 85, 97–191 (1997)

    MATH  Google Scholar 

  17. Shahidi, F.: On certain L-functions. Am. J. Math. 103, 297–355 (1981)

    MATH  Google Scholar 

  18. Shahidi, F.: A proof of Langlands’ conjecture on Plancherel measures; Complementary series for p-adic groups. Ann. Math. 132, 273–330 (1990)

    MATH  Google Scholar 

  19. Silberger, A.: The Langlands quotient theorem for p-adic groups. Math. Ann. 236, 95–104 (1978)

    MATH  Google Scholar 

  20. Silberger, A.: Introduction to harmonic analysis on reductive p-adic groups. Math. Notes 23, Princeton University Press, Princeton, NJ, 1979

  21. Tadić, M.: Notes on representations of non-archimedean SL(n). Pac. J. Math. 152, 375–396 (1992)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ban, D., Jantzen, C. Duality and the normalization of standard intertwining operators. manuscripta math. 115, 401–415 (2004). https://doi.org/10.1007/s00229-004-0504-7

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00229-004-0504-7

Keywords

Navigation