Duke Mathematical Journal

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

David A. Vogan, Jr.
Source: Duke Math. J. Volume 46, Number 4 (1979), 805-859.
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Primary Subjects: 22E46
Secondary Subjects: 20G05, 22E47
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Links and Identifiers

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

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.
Mathematical Reviews (MathSciNet): MR53:566
Zentralblatt MATH: 0343.17006
[3] J. Dixmier, Algèbres enveloppantes, Gauthier-Villars Éditeur, Paris-Brussels-Montreal, Que., 1974.
Mathematical Reviews (MathSciNet): MR58:16803a
Zentralblatt MATH: 0308.17007
[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.
Mathematical Reviews (MathSciNet): MR537955
Zentralblatt MATH: 0378.22012
Digital Object Identifier: doi:10.1007/BF01420410
[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.
Mathematical Reviews (MathSciNet): MR560412
Zentralblatt MATH: 0499.20035
Digital Object Identifier: doi:10.1007/BF01390031
[10] B. Kostant, On the tensor product of a finite and an infinite dimensional representation, J. Functional Analysis 20 (1975), no. 4, 257–285.
Mathematical Reviews (MathSciNet): MR54:2888
Zentralblatt MATH: 0355.17010
Digital Object Identifier: doi:10.1016/0022-1236(75)90035-X
[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.
Mathematical Reviews (MathSciNet): MR53:714
Zentralblatt MATH: 0324.22007
Digital Object Identifier: doi:10.1007/BF01389847
[13] B. Speh and D. Vogan, Reducibility of generalized principal series representations, preprint, 1978.
Mathematical Reviews (MathSciNet): MR590291
Zentralblatt MATH: 0457.22011
Digital Object Identifier: doi:10.1007/BF02414191
[14] D. Vogan, The algebraic structure of the representation of semisimple Lie groups. I, Ann. of Math. (2) 109 (1979), no. 1, 1–60.
Mathematical Reviews (MathSciNet): MR81j:22020
Zentralblatt MATH: 0424.22010
Digital Object Identifier: doi:10.2307/1971266
[15] D. Vogan, Irreducible characters of semisimple Lie groups. I, Duke Math. J. 46 (1979), no. 1, 61–108.
Mathematical Reviews (MathSciNet): MR80g:22016
Zentralblatt MATH: 0398.22021
Digital Object Identifier: doi:10.1215/S0012-7094-79-04605-2
Project Euclid: euclid.dmj/1077313255
[16]1 G. Warner, Harmonic analysis on semi-simple Lie groups. I, Springer-Verlag, New York, 1972.
Mathematical Reviews (MathSciNet): MR58:16979
Zentralblatt MATH: 0265.22020
[16]2 G. Warner, Harmonic analysis on semi-simple Lie groups. II, Springer-Verlag, New York, 1972.
Mathematical Reviews (MathSciNet): MR58:16980
Zentralblatt MATH: 0265.22021
[17] G. Zuckerman, Tensor products of finite and infinite dimensional representations of semisimple Lie groups, Ann. Math. (2) 106 (1977), no. 2, 295–308.
Mathematical Reviews (MathSciNet): MR56:15841
Zentralblatt MATH: 0384.22004
Digital Object Identifier: doi:10.2307/1971097

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