Israel Journal of Mathematics

, Volume 178, Issue 1, pp 269–324 | Cite as

Distinction by the quasi-split unitary group

Article

Abstract

In earlier work, we proved that any quadratic base change automorphic cuspidal representation of GL(n) is distinguished by a unitary group. Here we prove that we can take the unitary group to be quasi-split

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [Art01]
    J. Arthur and L. Clozel, Simple Algebras, Base Change, and the Advanced Theory of the Trace Formula, Annals of Mathematics Studies, Vol. 120, Princeton University Press, Princeton, NJ, 1989.Google Scholar
  2. [Bar03]
    E. M. Baruch, A proof of Kirillov’s conjecture, Annales of Mathematics (2) 158 (2003), 207–252.MATHCrossRefMathSciNetGoogle Scholar
  3. [Ber84]
    J. N. Bernstein, P-invariant distributions on GL(itN) and the classification of unitary representations of GL(N) (non-Archimedean case), in Lie Group Representations, II (College Park, Md., 1982/1983), Lecture Notes in Mathematics, Vol. 1041, Springer, Berlin, 1984, pp. 50–102.CrossRefGoogle Scholar
  4. [GK75]
    I. M. Gel’fand and D. A. Kajdan, Representations of the group GL(n,K) where K is a local field, in Lie Groups and their Representations (Proc. Summer School, Bolyai János Math. Soc., Budapest, 1971), Halsted, New York, 1975, pp. 95–118.Google Scholar
  5. [Jac00]
    H. Jacquet, Factorization of period integrals, Journal of Number Theory 87 (2001), 109–143.MATHCrossRefMathSciNetGoogle Scholar
  6. [Jac01]
    H. Jacquet, Transfert lisse d’intégrales de Kloosterman, Comptes Rendus Mathématique, Académie des Sciences, Paris 335 (2002), 229–232.Google Scholar
  7. [Jac02]
    H. Jacquet, Facteurs de transfert pour les intégrales de Kloosterman., Comptes Rendus Mathématique, Académie des Sciences (2), Paris 336 (2003), 121–124.MATHMathSciNetGoogle Scholar
  8. [Jac03]
    H. Jacquet, Smooth transfer of Kloosterman integrals, Duke Mathematical Journal 120 (2003), 121–152.MATHCrossRefMathSciNetGoogle Scholar
  9. [Jac04]
    H. Jacquet, Kloosterman identities over a quadratic extension., Annals of Mathematics (2) 160 (2004), 755–779.MATHCrossRefMathSciNetGoogle Scholar
  10. [Jac05]
    H. Jacquet, Kloosterman identities over a quadratic extension. II, Annales Scientifiques de l’École Normale Supérieure (4) 38 (2005), 609–669.MATHCrossRefMathSciNetGoogle Scholar
  11. [Jacar]
    H. Jacquet, Archimedean Rankin-Selberg integrals, in Automorphic Forms and Lfunctions II. Local aspects, Contemporary Mathematics, Vol. 489, American Mathematical Society, Providence, RI, 2009, pp. 57–172.Google Scholar
  12. [JPSS83]
    H. Jacquet, I. I. Piatetskii-Shapiro and J. A. Shalika, Rankin-Selberg convolutions, American Journal of Mathematics 105 (1983), 367–464.MATHCrossRefMathSciNetGoogle Scholar
  13. [JS81]
    H. Jacquet and J. A. Shalika, On Euler products and the classification of automorphic representations. I, American Journal of Mathematics 103 (1981), 499–558.MATHCrossRefMathSciNetGoogle Scholar
  14. [JS85]
    H. Jacquet and J. Shalika, A lemma on highly ramified ε-factors, Mathematische Annalen 271 (1985), 319–332.MATHCrossRefMathSciNetGoogle Scholar
  15. [Lap06]
    E. M. Lapid, On the fine spectral expansion of Jacquet’s relative trace formula, Journal of the Institute of Mathematics of Jussieu 5 (2006), 263–308.MATHCrossRefMathSciNetGoogle Scholar
  16. [Pou72]
    N. S. Poulsen, On C -vectors and intertwining bilinear forms for representations of Lie groups, Journal of Functional Analysis 9 (1972), 87–120.MATHCrossRefMathSciNetGoogle Scholar
  17. [Sha74]
    J. A. Shalika, The multiplicity one theorem for GLn, Annals of Mathematics (2) 100 (1974), 171–193.CrossRefMathSciNetGoogle Scholar
  18. [Ume98]
    T. Umeda, Newton’s formula for gln, Proceedings of the American Mathematical Society 126 (1998), 3169–3175.MATHCrossRefMathSciNetGoogle Scholar
  19. [Vog78]
    D. A. Vogan, Jr., Gel’fand-Kirillov dimension for Harish-Chandra modules, Inventiones Mathematicae 48 (1978), 75–98.MATHCrossRefMathSciNetGoogle Scholar
  20. [Vog86]
    D. A. Vogan, Jr., The unitary dual of GL(n) over an Archimedean field, Inventiones Mathematicae 83 (1986), 449–505.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Hebrew University Magnes Press 2010

Authors and Affiliations

  1. 1.Department of Mathematics, Mathematics Building, 615Columbia UniversityNew YorkUSA

Personalised recommendations