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


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 


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  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

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