References
Bernstein, I.N., Gelfand, I.M., Gelfand, S.I.: Structure of representations generated by highest weight vectors. Funct. Anal. i evo prilojence.5, 1–9 (1971)
Carter, R.W.: Simple Groups of Lie Type. New York: John Wiley and Sons 1972
Cartier, P.: Vecteure différentiables dans les représentations unitaire des groupes de Lie, Seminaire Bourbaki, 454 (1974–1975)
Dixmier, J.: Algèbres Enveloppantes. In: Cahiers scientifiques,37, Paris: Gauthier-Villars 1974
Gelfand, I.M., Kazhdan, D.A.: Representations of the groupGl(n, K) whereK is a local field. In: Lie Groups and Their Representations (I.M. Gelfand, ed.), pp. 95–118. John Wiley and Sons 1975
Jacquet, H.: Fonctions de Whittaker associées aux groupes de Chevalley. Bull. Soc. Math. France,95, 243–309 (1967)
Kostant, B.: The principal three-dimensional subgroup and the Betti numbers of a complex simple Lie group. Amer. J. Math.81, 973–1032 (1959)
Kostant, B.: Lie group representations on polynomial rings. Amer. J. Math.85, 327–404 (1963)
Kostant, B.: On the existence and irreducibility of certain series of representations. In: Lie groups and Their Representations (I.M. Gelfand, ed.) pp. 231–329. John Wiley and Sons 1975
Kostant, B., Rallis, S.: Orbits and representations associated with symmetric spaces. Amer. J. Math.93, 753–809 (1971)
Kostant, B.: On the tensor product of a finite and an infinite dimensional representation. J. Functional Analysis,20, 257–285 (1975)
Lepowsky, J.: Algebraic results on representations of semi-simple Lie groups. Trans. Amer. Math. Soc.176, 1–44 (1973)
Lepowsky, J., Wallach, N.R.: Finite and infinite dimensional representations of linear semisimple groups. Trans. Amer. Math. Soc.,184, 223–246 (1973)
Nouazé, Y., Gabriel, P.: Idéaux premier de l'algèbre enveloppante d'une algèbre de Lie nilpotent. J. of Algebra,6, 77–99 (1967)
Schiffmann, G.: Integrals d'entrelacement et fonctions de Whittaker. Bull. Soc. Math. France,99, 3–72 (1971)
Shalika, J.A.: The multiplicity one theorem forGl(n). Anal. Math.100, 171–193 (1974)
Vogan, D.: Gelland-Kirillov dimension for Harish-Chandra modules. Inventiones math.48, 75–98 (1978)
Wallach, N.R.: Cyclic vectors and irreducibility for principal series representations. I. Trans. Amer. Math. Soc.158, 107–113 (1971), Wallach, N.R.: Cyclic vectors and irreducibility for principal series representations. Il. ibid., Trans. Amer. Math. Soc.164, 389–396 (1972)
Wallach, N.R.: Harmonic Analysis on Homogeneous Spaces New York: Marcel Dekker, Inc. 1973
Warner, G.: Harmonic Analysis on Semi-simple Lie Groups. Die Grundlehren der mathematischen Wissenschaften. Band 188. Berlin: Springer-Verlag 1972
Whittaker, E.T., Watson, G.N.: A Course in Modern Analysis. London: Cambridge University Press 1963
Author information
Authors and Affiliations
Additional information
Supported in part by NSF grant MCS 7609177
Rights and permissions
About this article
Cite this article
Kostant, B. On Whittaker vectors and representation theory. Invent Math 48, 101–184 (1978). https://doi.org/10.1007/BF01390249
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01390249