Duke Mathematical Journal

Irreducible characters of semisimple Lie groups I

David A. Vogan, Jr.

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Article information

Source
Duke Math. J. Volume 46, Number 1 (1979), 61-108.

Dates
First available in Project Euclid: 20 February 2004

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1077313255

Mathematical Reviews number (MathSciNet)
MR523602

Zentralblatt MATH identifier
0398.22021

Digital Object Identifier
doi:10.1215/S0012-7094-79-04605-2

Subjects
Primary: 22E46: Semisimple Lie groups and their representations

Citation

Vogan, Jr., David A. Irreducible characters of semisimple Lie groups I. Duke Mathematical Journal 46 (1979), no. 1, 61--108. doi:10.1215/S0012-7094-79-04605-2. http://projecteuclid.org/euclid.dmj/1077313255.


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References

  • [1] A. Borel and N. R. Wallach, Seminar on the cohomology of discrete subgroups of semi-simple groups, to appear.
  • [2] W. Borho and J. C. Jantzen, Über primitive Ideale in der Einhüllenden einer halbeinfachen Lie-Algebra, Invent. Math. 39 (1977), no. 1, 1–53.
  • [3] J. Dixmier, Algèbres enveloppantes, vol. XXXVII, Gauthier-Villars Éditeur, Paris-Brussels-Montreal, Que., 1974.
  • [4] M. Duflo, Sur la classification des idéaux primitifs dans l'algèbre enveloppante d'une algèbre de Lie semi-simple, Ann. of Math. (2) 105 (1977), no. 1, 107–120.
  • [5] Harish-Chandra, Harmonic analysis on real reductive groups. III. The Maass-Selberg relations and the Plancherel formula, Ann. of Math. (2) 104 (1976), no. 1, 117–201.
  • [6] H. Hecht and W. Schmid, A proof of Blattner's conjecture, Invent. Math. 31 (1975), no. 2, 129–154.
  • [7] J. E. Humphreys, Introduction to Lie algebras and representation theory, Springer-Verlag, New York, 1972.
  • [8] J. C. Jantzen, Moduln mit einem höchsten Gewicht, Habilitationsschrift, Universität Bonn, 1977.
  • [9] A. W. Knapp and G. Zuckerman, Classification of irreducible tempered representations of semi-simple Lie groups, Proc. Nat. Acad. Sci. U.S.A. 73 (1976), no. 7, 2178–2180.
  • [10] B. Kostant, On the tensor product of a finite and an infinite dimensional representation, J. Functional Analysis 20 (1975), no. 4, 257–285.
  • [11] R. P. Langlands, On the classification of irreducible representations of real algebraic groups, mimeographed notes, Institute for Advanced Study, 1973.
  • [12] J. Lepowsky, Algebraic results on representations of semisimple Lie groups, Trans. Amer. Math. Soc. 176 (1973), 1–44.
  • [13] J. Lepowsky and G. W. McCollum, On the determination of irreducible modules by restriction to a subalgebra, Trans. Amer. Math. Soc. 176 (1973), 45–57.
  • [14] W. Schmid, Some properties of square-integrable representations of semisimple Lie groups, Ann. of Math. (2) 102 (1975), no. 3, 535–564.
  • [15] W. Schmid, Two character identities for semisimple Lie groups, Non-commutative Harmonic Analysis (Actes Colloq., Marseille-Luminy, 1976), Lecture Notes in Mathematics, vol. 587, Springer-Verlag, Berlin, 1977, pp. 196–225.
  • [16] B. Speh and D. Vogan, Reducibility of generalized principal series representations, to appear.
  • [17] D. Vogan, The algebraic structure of the representations of semi-simple Lie groups, to appear in Ann. of Math.
  • [18] G. Warner, Harmonic analysis on semi-simple Lie groups. I, Springer-Verlag, New York, 1972.
  • [19] G. Zuckerman, Tensor products of finite and infinite dimensional representations of semisimple Lie groups, Ann. Math. (2) 106 (1977), no. 2, 295–308.

See also

  • See also: David A. Vogan, Jr.. Irreducible characters of semisimple Lie groups II. The Kazhdan-Lusztig conjectures. Duke Math. J. Vol. 46, No. 4 (1979), pp. 805–859.
  • See also: David A. Vogan, Jr.. Irreducible characters of semisimple Lie groups III. Proof of the Kazhdan-Lusztig conjectures in the integral case. Invent. Math. Vol. 71 (1983), pp. 381–417.
  • See also: David A. Vogan, Jr.. Irreducible characters of semisimple Lie groups IV. Character-multiplicity duality. Duke Math. J. Vol. 49, No. 4 (1982), pp. 943–1073.