Israel Journal of Mathematics

, Volume 151, Issue 1, pp 323–355 | Cite as

Certain conjectures relating unipotent orbits to automorphic representations

  • David Ginzburg


In this paper I formulate certain conjectures relating the structure of unipotent orbits to automorphic representations. We consider a few examples and prove some of these conjectures.


Fourier Coefficient Parabolic Subgroup Eisenstein Series Symplectic Group Automorphic Representation 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [B-F-G] D. Bump, S. Friedberg and D. Ginzburg,Small representations for odd orthogonal groups, International Mathematical Research Notices25 (2003), 1363–1393.MathSciNetCrossRefGoogle Scholar
  2. [C] R. Carter,Finite Groups of Lie Type, Wiley, New York, 1985.zbMATHGoogle Scholar
  3. [C-M] D. Collingwood and W. Mcgovern,Nilpotent Orbits in Semisimple Lie Algebras, Van Nostrand Reinhold, New York, 1991.zbMATHGoogle Scholar
  4. [G] D. Ginzburg,A construction of CAP representations for classical groups, International Mathematical Research Notices20 (2003), 1123–1140.MathSciNetCrossRefGoogle Scholar
  5. [G-G] D. Ginzburg and N. Gurevich,On the first occurrence of cuspidal representations on symplectic group, Journal of the Institute of Mathematics of Jussieu, to appear.Google Scholar
  6. [G-J-R] D. Ginzburg, D. Jiang and S. Rallis,On the nonvanishing of the central value of the Rankin-Selberg L-functions, Journal of the American Mathematical Society17 (2004), 679–722.MathSciNetCrossRefGoogle Scholar
  7. [G-R-S1] D. Ginzburg, S. Rallis and D. Soudry,On explicit lifts of cusp forms from GL m to classical groups, Annals of Mathematics150 (1999), 807–866.MathSciNetCrossRefGoogle Scholar
  8. [G-R-S2] D. Ginzburg, S. Rallis and D. Soudry,On Fourier coefficients of automorphic forms of symplectic groups, Manuscripta Mathematica111 (2003), 1–16.MathSciNetCrossRefGoogle Scholar
  9. [G-R-S3] D. Ginzburg, S. Rallis and D. Soudry,Construction of CAP representations for symplectic groups using the descent method, to be published in a Volume in honor of S. Rallis.Google Scholar
  10. [G-R-S4] D. Ginzburg, S. Rallis and D. Soudry, On a correspondence between cuspidal representations of GL2n and\(\widetilde{Sp}_{2n} \), Journal of the American Mathematical Society12 (1999), 849–907.MathSciNetCrossRefGoogle Scholar
  11. [G-S] D. Ginzburg and E. Sayag,Construction of certain small representations for SO 2m, unpublished manuscript.Google Scholar
  12. [I] T. Ikeda,On the lifting of Elliptic cusp forms to Siegel cusp forms of degree 2n, Annals of Mathematics154 (2001), 641–681.MathSciNetCrossRefGoogle Scholar
  13. [J] H. Jacquet,On the residual spectrum of GL(n), inLie Group Representations, II (College Park, Md., 1982/1983), Lecture Notes in Mathematics1041, Springer, Berlin, 1984, pp. 185–208.CrossRefGoogle Scholar
  14. [K] N. Kawanka,Shintani lifting and Gelfand-Graev representations, Proceedings of Symposia in Pure Mathematics47 (1987), 147–163.MathSciNetCrossRefGoogle Scholar
  15. [M] C. Moegiln,Front d'onde des représentations des groupes classiques p-adiques, American Journal of Mathematics118 (1996), 1313–1346.MathSciNetCrossRefGoogle Scholar
  16. [M-W] C. Moeglin and J. Waldspurger,Modéles de Whittaker dégénérés pour des groupes p-adiques, Mathematische Zeitschrift196 (1987), 427–452.MathSciNetCrossRefGoogle Scholar
  17. [N] M. Nevis,Admissible nilpotent coadjoint orbits of p-adic reductive lie groups, Reprentation Theory3 (1999), 105–126.MathSciNetCrossRefGoogle Scholar
  18. [Sa] G. Savin,An analogue of the Weil representation for G 2, Journal für die reine und angewandte Mathematik434 (1993), 115–126.MathSciNetzbMATHGoogle Scholar
  19. [S] N. Spaltenstein,Classes Unipotentes et Sous-Groupes de Borel, Lecture Notes in Mathematics946, Springer, Berlin, 1982.zbMATHGoogle Scholar
  20. [W] M. Weissman,The Fourier-Jacobi map and small representations, Reprentation Theory7 (2003), 275–299.MathSciNetCrossRefGoogle Scholar

Copyright information

© The Hebrew University Magnes Press 2006

Authors and Affiliations

  • David Ginzburg
    • 1
  1. 1.School of Mathematical Sciences, Sackler Faculty of Exact SciencesTel Aviv University, Ramat AvivTel AvivIsrael

Personalised recommendations