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Highest weight modules for semisimple Lie algebras

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Representation Theory I

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 831))

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References

  1. I. N. Bernštein, I. M. Gelfand, S. I. Gelfand, The structure of representations generated by vectors of highest weight, Functional Anal. Appl. 5 (1971), 1–9.

    Article  MathSciNet  Google Scholar 

  2. _____, Differential operators on the base affine space and a study of g-modules, pp. 21–64, Lie Groups and their Representations, Halsted, New York, 1975.

    MATH  Google Scholar 

  3. _____, A category of g-modules, Functional Anal. Appl. 10 (1976), 87–92.

    Article  MathSciNet  MATH  Google Scholar 

  4. P. Delorme, Extensions dans la categorie 0 de Bernštein-Gelfand-Gelfand, Applications. (preprint).

    Google Scholar 

  5. V. V. Deodhar, Some characterizations of Bruhat ordering on a Coxeter group and determination of the relative Möbius function, Invent. Math. 39 (1977), 187–198.

    Article  MathSciNet  MATH  Google Scholar 

  6. _____, On a construction of representations and a problem of Enright (preprint).

    Google Scholar 

  7. J. Dixmier, Algèbres Enveloppantes, Gauthier-Villars, Paris, 1974; English translation, North-Holland, Amsterdam, 1977.

    Google Scholar 

  8. T. J. Enright, On the algebraic construction and classification of Harish-Chandra modules, Proc. Nat. Acad. Sci. U.S.A. 75 (1978), 1063–1065.

    Article  MathSciNet  MATH  Google Scholar 

  9. _____, On the fundamental series of a real semisimple Lie algebra: their irreducibility, resolutions and multiplicity formulae, Ann. of Math. 110 (1979), 1–82.

    Article  MathSciNet  MATH  Google Scholar 

  10. _____, The representations of complex semisimple Lie groups (preprint).

    Google Scholar 

  11. T. J. Enright, V. S. Varadarajan, On an infinitesimal characterization of the discrete series, Ann. of Math. 102 (1975), 1–15.

    Article  MathSciNet  MATH  Google Scholar 

  12. H. Garland, J. Lepowsky, Lie algebra homology and the Macdonald-Kac formulas, Invent. Math. 34 (1976), 37–76.

    Article  MathSciNet  MATH  Google Scholar 

  13. H. Hecht, W. Schmid, A proof of Blattner's conjecture, Invent. Math. 31 (1975), 129–154.

    Article  MathSciNet  MATH  Google Scholar 

  14. J. E. Humphreys, Finite and infinite dimensional modules for semisimple Lie algebras, pp. 1–64, Queen's Papers in Pure & Appl. Math. No. 48, Kingston, Ont., 1978.

    Google Scholar 

  15. J. C. Jantzen, Kontravariante Formen auf induzierten Darstellungen halbeinfacher Lie-Algebren, Math. Ann. 226 (1977), 53–65.

    Article  MathSciNet  MATH  Google Scholar 

  16. _____, Moduln mit einem höchsten Gewicht, Habilitationsschrift, U. Bonn, 1977, to appear in Lect. Notes in Math.750, Springer, 1979.

    Google Scholar 

  17. A. Joseph, Dixmier's problem for Verma and principal series submodules, J. London Math. Soc. 20(1979), 193–204.

    Article  MathSciNet  MATH  Google Scholar 

  18. D. Kazhdan, G. Lusztig, Representations of Coxeter groups and Hecke algebras, Invent. Math. 53 (1979), 165–184.

    Article  MathSciNet  MATH  Google Scholar 

  19. J. Lepowsky, A generalization of the Bernštein-Gelfand-Gelfand resolution, J. Algebra 49 (1977), 496–511.

    Article  MathSciNet  MATH  Google Scholar 

  20. A. Rocha-Caridi, Splitting criteria for g-modules induced from a parabolic and the Bernštein-Gelfand-Gelfand resolution of a finite dimensional, irreducible g-module, Trans. Amer. Math. Soc., to appear.

    Google Scholar 

  21. N. N. Šapovalov, On a bilinear form on the universal enveloping algebra of a complex semisimple Lie algebra, Funkcional. Analiz. i Priložen, 6, no. 4 (1972), 65–70 = Functional Anal. Appl. 6 (1972), 307–312.

    MathSciNet  Google Scholar 

  22. V. S. Varadarajan, Infinitesimal theory of representations of semisimple Lie groups, lectures given at NATO Advanced Study Institute, Liège, 1977.

    Google Scholar 

  23. D. A. Vogan, Irreducible characters of semisimple Lie groups II Duke Math. J. 46(1979), 805–859.

    Article  MathSciNet  MATH  Google Scholar 

  24. N. R. Wallach, On the Enright-Varadarajan modules: A construction of the discrete series, Ann. Sci. École Norm Sup. (4) 9 (1976), 81–102.

    MathSciNet  MATH  Google Scholar 

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  1. University of Massachusetts, 01003, Amherst, MA

    James E. Humphreys

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  1. James E. Humphreys
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Vlastimil Dlab Peter Gabriel

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© 1980 Springer-Verlag

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Humphreys, J.E. (1980). Highest weight modules for semisimple Lie algebras. In: Dlab, V., Gabriel, P. (eds) Representation Theory I. Lecture Notes in Mathematics, vol 831. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0089779

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  • DOI: https://doi.org/10.1007/BFb0089779

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  • Print ISBN: 978-3-540-10263-2

  • Online ISBN: 978-3-540-38385-7

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