Skip to main content
SpringerLink
Log in

Local theta correspondence and minimalK-types of positive depth

  • Published:
Israel Journal of Mathematics Aims and scope Submit manuscript

Abstract

In this paper we prove that two irreducible admissible representations of positive depth paired by the theta correspondence over ap-adic field have unrefined minimalK-types paired by the orbit correspondence. An application of our main result is that a positive depth character of a unitary group occurs as late as possible in the theta correspondence.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J. Adams,Coadjoint orbits and reductive dual pairs, Advances in Mathematics63 (1987), 138–151.

    Article  MATH  MathSciNet  Google Scholar 

  2. R. Howe and A. Moy,Minimal K-types for GL n over a p-adic field, inOrbites unipotentes et représentations II, groupes p-adiques et réels, Astérisque171–172 (1989), 257–273.

    MathSciNet  Google Scholar 

  3. R. Howe,θ-series and invariant theory, inAutomorphic Forms, Representations and L-functions, Proceedings of Symposia in Pure Mathematics33 (1979), 275–285.

    MathSciNet  Google Scholar 

  4. D. Kazhdan, B. Kostant and S. Sternberg,Hamiltonian group actions and dynamical system of Calogero type, Communications on Pure and Applied Mathematics31 (1978), 481–507.

    Article  MATH  MathSciNet  Google Scholar 

  5. M. Harris, S. Kudla and W. Sweet,Theta dichotomy for unitary groups, Journal of the American Mathematical Society9 (1996), 941–1004.

    Article  MATH  MathSciNet  Google Scholar 

  6. A. Moy and G. Prasad,Unrefined minimal K-types for p-adic groups, Inventiones Mathematicae116 (1994), 393–408.

    Article  MATH  MathSciNet  Google Scholar 

  7. A. Moy and G. Prasad,Jacquet functors and unrefined minimal K-types, Commentarii Mathematici Helvetici71 (1996), 98–121.

    Article  MATH  MathSciNet  Google Scholar 

  8. C. Mœglin, M.-F. Vigneras and J.-L. Waldspurger,Correspondances de Howe sur un corps p-adiques, Lecture Notes in Mathematics1291, Springer-Verlag, Berlin-Heidelberg-New York, 1987.

    Google Scholar 

  9. S.-Y. Pan,Splittings of metaplectic covers of some reductive dual pairs, Pacific Journal of Mathematics199 (2001), 163–226.

    Article  MATH  MathSciNet  Google Scholar 

  10. S.-Y. Pan,Depth preservation in local theta correspondence, Duke Mathematical Journal113 (2002), 531–592.

    Article  MATH  MathSciNet  Google Scholar 

  11. S.-Y. Pan,Local theta correspondence of representations of depth zero and theta dichotomy, Journal of the Mathematical Society of Japan54 (2002), 793–845.

    Article  MATH  MathSciNet  Google Scholar 

  12. J.-L. Waldspurger,Demonstration d’une conjecture de duality de Howe dans le case p-adiques, p ≠ 2, Festschrift in honor of I. Piatetski-Shapiro, Israel Mathematical Conference Proceedings2 (1990), 267–324.

    MathSciNet  Google Scholar 

  13. J.-K. Yu,Decent mapping in Bruhat-Tits theory, preprint, 1998.

  14. J.-K. Yu,Unrefined minimal K-types for p-adic classical groups, preprint, 1998.

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, National Cheng Kung University, 701, Tainan City, Taiwan

    Shu-Yen Pan

Authors
  1. Shu-Yen Pan
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pan, SY. Local theta correspondence and minimalK-types of positive depth. Isr. J. Math. 138, 317–352 (2003). https://doi.org/10.1007/BF02783431

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02783431

Keywords

Search

Navigation