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A geometric construction of intertwining operators for reductive p-adic groups

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Abstract

In this paper we construct standard intertwining operators for reductive p-adic groups by a method of Bernstein.

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References

  1. Banks W. (1998). A corollary to Bernstein’s theorem and Whittaker functionals on the metaplectic group. Math. Res. Lett. 5(6): 781–790

    MATH  MathSciNet  Google Scholar 

  2. Bernstein J.N., Deligne P. and Kazhdan D. (1986). Trace Paley–Wiener theorem for reductive p-adic groups. J. Anal. Math. 47: 180–192

    Article  MATH  MathSciNet  Google Scholar 

  3. Bernstein J. and Zelevinsky A.V. (1976). Representations of the group GL(n, F), where F is a local non-Archimedean field (Russian). Uspehi Mat. Nauk 31(3(189)): 5–70

    MATH  Google Scholar 

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

    MATH  MathSciNet  Google Scholar 

  5. Bushnell J.C. (2001). Representations of reductive p-adic groups: localization of Hecke algebras and applications. J. Lond. Math. Soc. 63: 364–386

    Article  MATH  MathSciNet  Google Scholar 

  6. Cartier, P.: Representations of p-adic groups: a survey. Automorphic forms, representations and L-functions (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Ore., 1977), Part 1, Proc. Sympos. Pure Math., XXXIII Amer. Math. Soc., Providence, R.I, pp. 111–155 (1979)

  7. Casselman, W.: Introduction to the theory of admissible representations of p-adic reductive groups (preprint)

  8. Casselman W. (1980). The unramified principal series of p-adic groups I. The spherical function. Compositio Mathematica 40(3): 387–406

    MATH  MathSciNet  Google Scholar 

  9. Dat J.F. (2005). ν-tempered representations of p-adic groups I: l-adic case. Duke Math. J. 126: 397–469

    Article  MATH  MathSciNet  Google Scholar 

  10. Muić G. (2006). Construction of Steinberg type representations for reductive p-adic groups. Math. Z. 253(3): 635–652

    Article  MathSciNet  MATH  Google Scholar 

  11. Shahidi F. (1981). On certain L-functions. Am. J. Math. 103: 297–356

    Article  MATH  MathSciNet  Google Scholar 

  12. Shahidi F. (1988). On the Ramanujan conjecture and finitness of poles for certain L-functions. Ann. Math. 127: 547–584

    Article  MathSciNet  Google Scholar 

  13. Waldspurger J.L. (2003). La formule de Plancherel pour les groupes p-adiques, d’après Harish-Chandra. J. Inst. Math. Jussieu 2(2): 235–333

    Article  MATH  MathSciNet  Google Scholar 

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Correspondence to Goran Muić.

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Muić, G. A geometric construction of intertwining operators for reductive p-adic groups. manuscripta math. 125, 241–272 (2008). https://doi.org/10.1007/s00229-007-0146-7

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  • DOI: https://doi.org/10.1007/s00229-007-0146-7

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