Duke Mathematical Journal

Irreducible characters of semisimple Lie groups II. The Kazhdan-Lusztig conjectures

David A. Vogan, Jr.

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Article information

Source
Duke Math. J. Volume 46, Number 4 (1979), 805-859.

Dates
First available in Project Euclid: 20 February 2004

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1077313724

Mathematical Reviews number (MathSciNet)
MR552528

Zentralblatt MATH identifier
0421.22008

Digital Object Identifier
doi:10.1215/S0012-7094-79-04642-8

Subjects
Primary: 22E46: Semisimple Lie groups and their representations
Secondary: 20G05: Representation theory 22E47: Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) [See also 17B10]

Citation

Vogan, Jr., David A. Irreducible characters of semisimple Lie groups II. The Kazhdan-Lusztig conjectures. Duke Mathematical Journal 46 (1979), no. 4, 805--859. doi:10.1215/S0012-7094-79-04642-8. http://projecteuclid.org/euclid.dmj/1077313724.


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References

  • [1] A. Borel and N. R. Wallach, Seminar on the cohomology of discrete subgroups of semisimple groups, to appear.
  • [2] W. Casselman and M. S. Osborne, The $\germ n$-cohomology of representations with an infinitesimal character, Compositio Math. 31 (1975), no. 2, 219–227.
  • [3] J. Dixmier, Algèbres enveloppantes, Gauthier-Villars Éditeur, Paris-Brussels-Montreal, Que., 1974.
  • [4] T. Enright, The representations of complex semisimple Lie groups, preprint, 1978.
  • [5] H. Hecht, On characters and asymptotics of representations of a real reductive Lie group, preprint, 1977.
  • [6] H. Hecht and W. Schmid, A proof of Osborne's conjecture, to appear.
  • [7] J. C. Jantzen, Moduln mit einem höchsten Gewicht, Habilitationsschrift, Unuversität Bonn, 1977.
  • [8] A. Joseph, Dixmier's problem for Verma and principal series submodules, preprint, 1978.
  • [9] D. Kazhdan and G. Lusztig, Representations of Coxeter groups and Hecke algebras, preprint, 1978.
  • [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] W. Schmid, On the characters of the discrete series. The Hermitian symmetric case, Invent. Math. 30 (1975), no. 1, 47–144.
  • [13] B. Speh and D. Vogan, Reducibility of generalized principal series representations, preprint, 1978.
  • [14] D. Vogan, The algebraic structure of the representation of semisimple Lie groups. I, Ann. of Math. (2) 109 (1979), no. 1, 1–60.
  • [15] D. Vogan, Irreducible characters of semisimple Lie groups. I, Duke Math. J. 46 (1979), no. 1, 61–108.
  • [16]1 G. Warner, Harmonic analysis on semi-simple Lie groups. I, Springer-Verlag, New York, 1972.
  • [16]2 G. Warner, Harmonic analysis on semi-simple Lie groups. II, Springer-Verlag, New York, 1972.
  • [17] 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 I. Duke Math. J. Vol. 46, No. 1 (1979), pp. 61–108.
  • 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.