Inventiones mathematicae

, Volume 89, Issue 1, pp 219–224 | Cite as

Whittaker vectors and associated varieties

  • Hisayosi Matumoto


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [GW] Goodman, R., Wallach, N.R.: Whittaker vectors and conical vectors. J. Funct. Anal.39, 1990–279 (1980)Google Scholar
  2. [H1] Hashizume, M.: Whittaker models for real semisimple Lie groups. Jap. J. Math.5, 349–401 (1979)Google Scholar
  3. [H2] Hashizume, M.: Whittaker models for representations with highest weights. Lectures on harmonic analysis on Lie groups and related topics (Strasbourg, 1979), 45–50, Lect. Math.14, Kinokuniya Book Store, Tokyo, 1982Google Scholar
  4. [Ja] Jacquet, H.: Fonction de Whittaker associées aux groupes de Chevalley. Bull. Soc. Math. Fr.95, 243–309 (1967)Google Scholar
  5. [Jo] Joseph, A.: Application de la théorie des anneaux aux algébres enveloppantes. Lecture Notes, Paris 1981Google Scholar
  6. [Ka1] Kawanaka, N.: Fourier transforms of nilpotently supported invariant functions on a simple Lie algebra over a finite field. Invent. Math.69, 411–435 (1982)Google Scholar
  7. [Ka2] Kawanaka, N.: Generalized Gelfand-Graev representations and Ennola duality. Adv. Stud. Pure Math.6, 1985, Algebraic Groups and Related Topics, pp. 175–206Google Scholar
  8. [Ka3] Kawanaka, N.: Generalized Gelfand-Graev Representations of exceptional simple algebraic groups over a finite field I. Invent, Math.84, 575–616 (1986)Google Scholar
  9. [Ka4] Kawanaka, N.: Shintani Lifting and Gelfand-Graev Representations. (Preprint to appear in the proceedings of 1986, AMS Summer Institute)Google Scholar
  10. [Ko1] Kostant, B.: The principal three-dimensional subgroup and the Betti numbers of a complex simple Lie group. Am. J. Math.81, 973–1032 (1959)Google Scholar
  11. [Ko2] Kostant, B.: On Whittaker vectors and representation theory. Invent. Math.48, 101–184 (1978)Google Scholar
  12. [L] Lynch, T.E.: Generalized Whittaker vectors and representations theory. Thesis, M.I.T., 1979Google Scholar
  13. [M] Matumoto, H.: Boundary value problems for Whittaker functions on real split semisimple Lie groups. Duke Math. J.53, 635–676 (1986)Google Scholar
  14. [Sch] Schiffmann, G.: Intégrales d'entrelancement et fonction de Whittaker. Bull. Soc. Math. Fr.99, 3–72 (1971)Google Scholar
  15. [Shd] Shahidi, F.: Whittaker models for real groups. Duke Math. J.47, 99–125 (1980)Google Scholar
  16. [Slk] Shalika, J.: The multiplicity one theorem forGL(n). Ann. Math.100, 171–193 (1974)Google Scholar
  17. [SS] Springer, T.A., Steinberg, R.: Conjugacy classes, in “Seminar on Algebraic Groups and Related Finite Groups,” Lect. Notes Math. 131, Part E. Berlin Heidelberg New York: Springer 1970Google Scholar
  18. [V] Vogan Jr., D.A.: The orbit method and primitive ideals for semisimple Lie algebras. (To appear in Canadian Mathematical Society Conference Proceedings Vol. 5 (1986))Google Scholar
  19. [Y] Yamashita, H.: On Whittaker vectors for generalized Gelfand-Graev representations of semisimple Lie groups. J. Math. Kyoto Univ.26, 263–298 (1986)Google Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • Hisayosi Matumoto
    • 1
  1. 1.Department of MathematicsMasachusetts Institute of TechnologyCambridgeUSA

Personalised recommendations