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Israel Journal of Mathematics

, Volume 34, Issue 1–2, pp 21–37 | Cite as

Uniqueness and existence of Whittaker models for the metaplictic group

  • Stephen Gelbart
  • Roger Howe
  • Ilya Piatetski-Shapiro
Article

Abstract

We introduce the notion of Whittaker models for representations of a metaplectic covering group of GL (2) and establish the uniqueness and existence of such models. Our results generalize corresponding results of Jacquet-Langlands, but the methods are new.

Keywords

Modular Form Automorphic Form Double Coset Ordinary Representation Bruhat Decomposition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    S Gelbart,Weil’s Representation and the Spectrum of the Metaplectic Group, Lecture Notes in Mathematics530, Springer-Verlag, Berlin, 1976.MATHGoogle Scholar
  2. 2.
    S. Gelbart and I. Piatetski-Shapiro,Automorphic L-functions of half-integral weight, Proc. Nat. Acad. Sci. U.S.A.75 (1978), 1620–1623.MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    S. Gelbart and I. Piatetski-Shapiro,On Shimura’s correspondence for modular forms of half-integral weight, to appear in Proc. Internat. Colloq. on Automorphic Forms, Representation Theory, and Arithmetic, Bombay, January 1979.Google Scholar
  4. 4.
    S. Gelbart and I. Piatetski-Shapiro,Distinguished representations and modular forms of half-integral weight, submitted to Invent. Math.Google Scholar
  5. 5.
    R. Godement,Notes on Jacquet-Langlands Theory, Institute for Advanced Study, Princeton, 1970.Google Scholar
  6. 6.
    H. Jacquet and R. P. Landlands,Automorphic Forms on GL(2), Lecture Notes in Mathematics114, Springer-Verlag, Berlin, 1970.MATHGoogle Scholar
  7. 7.
    T. Kubota,Automorphic Functions and the Reciprocity Law in a Number Field, Kyoto University, 1969.Google Scholar
  8. 8.
    S. Lang, SL2(R), Addison-Wesley, 1975.Google Scholar

Copyright information

© The Weizmann Science Press of Israel 1979

Authors and Affiliations

  • Stephen Gelbart
    • 1
    • 2
    • 3
  • Roger Howe
    • 1
    • 2
    • 3
  • Ilya Piatetski-Shapiro
    • 1
    • 2
    • 3
  1. 1.Department of MathematicsCornell UniversityIthacaUSA
  2. 2.Department of MathematicsYale UniversityNew HavenUSA
  3. 3.Tel Aviv UniversityTel AvivIsrael

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