Advertisement

Inventiones mathematicae

, Volume 184, Issue 1, pp 117–124 | Cite as

The multiplicity one conjecture for local theta correspondences

  • Jian-Shu LiEmail author
  • Binyong Sun
  • Ye Tian
Article

Abstract

Over a non-archimedean local field of characteristic zero, we prove multiplicity preservation of local theta correspondences for orthogonal-symplectic dual pairs. The same proof works for dual pairs of unitary groups.

Mathematics Subject Classification (2000)

22E35 22E46 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bernstein, I.N., Zelevinsky, A.V.: Representations of the group GL(n,F) where F is a non-archimedean local field. Russ. Math. Surv. 31(3), 1–68 (1976) CrossRefzbMATHGoogle Scholar
  2. 2.
    Howe, R.: Transcending classical invariant theory. J. Am. Math. Soc. 2(3), 535–552 (1989) CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Minguez, A.: Correspondance de Howe: paires duales de type II. Ann. Sci. Ecole Norm. Superieure (Serie 4) 41, 717–741 (2008) zbMATHMathSciNetGoogle Scholar
  4. 4.
    Moeglin, C., Vigneras, M.-F., Waldspurger, J.-L.: Correspondence de Howe sur un corp p-adique. Lecture Notes in Math., vol. 1291. Springer, Berlin (1987) Google Scholar
  5. 5.
    Prasad, D.: Trilinear forms for representations of GL(2) and local ε-factors. Compos. Math. 75(1), 1–46 (1990) zbMATHGoogle Scholar
  6. 6.
    Rallis, S.: On the Howe duality conjecture. Compos. Math. 51, 333–399 (1984) zbMATHMathSciNetGoogle Scholar
  7. 7.
    Sun, B.: Multiplicity one theorems for Fourier-Jacobi models. arXiv:0903.1417
  8. 8.
    Sun, B.: Dual pairs and contragredients of irreducible representations, arXiv:0903.1418 (to appear in Pac. J. Math.)
  9. 9.
    Sun, B., Zhu, C.-B.: A general form of Gelfand-Kazhdan criterion. arXiv:0903.1409
  10. 10.
    Waldspurger, J.-L.: Démonstration d’une conjecture de dualité de Howe dans le cas p-adique, p≠2. In: Festschrift in Honor of I.I. Piatetski-Shapiro on the Occasion of his Sixtieth Birthday, Part I, Ramat Aviv, 1989. Israel Math. Conf. Proc., vol. 2, pp. 267–324. Weizmann, Jerusalem (1990) Google Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Department of MathematicsHong Kong University of Science and TechnologyClear Water BayHong Kong
  2. 2.Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingPR China

Personalised recommendations