zbMATH — the first resource for mathematics

On Whittaker vectors and representation theory. (English) Zbl 0405.22013

22E47 Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.)
22E46 Semisimple Lie groups and their representations
17B35 Universal enveloping (super)algebras
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
Full Text: DOI EuDML
[1] 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) · Zbl 0246.17008 · doi:10.1007/BF01075841
[2] Carter, R.W.: Simple Groups of Lie Type. New York: John Wiley and Sons 1972 · Zbl 0248.20015
[3] Cartier, P.: Vecteure différentiables dans les représentations unitaire des groupes de Lie, Seminaire Bourbaki, 454 (1974-1975)
[4] Dixmier, J.: Algèbres Enveloppantes. In: Cahiers scientifiques,37, Paris: Gauthier-Villars 1974 · Zbl 0308.17007
[5] 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
[6] Jacquet, H.: Fonctions de Whittaker associées aux groupes de Chevalley. Bull. Soc. Math. France,95, 243-309 (1967) · Zbl 0155.05901
[7] Kostant, B.: The principal three-dimensional subgroup and the Betti numbers of a complex simple Lie group. Amer. J. Math.81, 973-1032 (1959) · Zbl 0099.25603 · doi:10.2307/2372999
[8] Kostant, B.: Lie group representations on polynomial rings. Amer. J. Math.85, 327-404 (1963) · Zbl 0124.26802 · doi:10.2307/2373130
[9] 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 · Zbl 0327.22010
[10] Kostant, B., Rallis, S.: Orbits and representations associated with symmetric spaces. Amer. J. Math.93, 753-809 (1971) · Zbl 0224.22013 · doi:10.2307/2373470
[11] Kostant, B.: On the tensor product of a finite and an infinite dimensional representation. J. Functional Analysis,20, 257-285 (1975) · Zbl 0355.17010 · doi:10.1016/0022-1236(75)90035-X
[12] Lepowsky, J.: Algebraic results on representations of semi-simple Lie groups. Trans. Amer. Math. Soc.176, 1-44 (1973) · Zbl 0264.22012 · doi:10.1090/S0002-9947-1973-0346093-X
[13] Lepowsky, J., Wallach, N.R.: Finite and infinite dimensional representations of linear semisimple groups. Trans. Amer. Math. Soc.,184, 223-246 (1973) · Zbl 0279.17001
[14] Nouazé, Y., Gabriel, P.: Idéaux premier de l’algèbre enveloppante d’une algèbre de Lie nilpotent. J. of Algebra,6, 77-99 (1967) · Zbl 0159.04101 · doi:10.1016/0021-8693(67)90015-4
[15] Schiffmann, G.: Integrals d’entrelacement et fonctions de Whittaker. Bull. Soc. Math. France,99, 3-72 (1971) · Zbl 0223.22017
[16] Shalika, J.A.: The multiplicity one theorem forGl(n). Anal. Math.100, 171-193 (1974) · Zbl 0316.12010 · doi:10.2307/1971071
[17] Vogan, D.: Gelland-Kirillov dimension for Harish-Chandra modules. Inventiones math.48, 75-98 (1978) · Zbl 0389.17002 · doi:10.1007/BF01390063
[18] 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) · Zbl 0227.22016
[19] Wallach, N.R.: Harmonic Analysis on Homogeneous Spaces New York: Marcel Dekker, Inc. 1973 · Zbl 0265.22022
[20] Warner, G.: Harmonic Analysis on Semi-simple Lie Groups. Die Grundlehren der mathematischen Wissenschaften. Band 188. Berlin: Springer-Verlag 1972 · Zbl 0265.22020
[21] Whittaker, E.T., Watson, G.N.: A Course in Modern Analysis. London: Cambridge University Press 1963 · Zbl 0108.26903
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.