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Lie Group Representations I pp 30–76Cite as

On the classification of primitive ideals in the enveloping algebra of a semisimple lie algebra

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References

  1. D. Barbasch and D. Vogan, Primitive ideals and orbital integrals in complex classical groups, Math. Ann., 259 (1982), 153–199.

    Article  MathSciNet  MATH  Google Scholar 

  2. __, Primitive ideals and orbital integrals in exceptional groups, preprint, MIT-Rutgers (1981).

    Google Scholar 

  3. A. Beilinson and J. Bernstein, Localisation de g modules, Comptes Rendus, 292 (1981), 15–18.

    MathSciNet  MATH  Google Scholar 

  4. J. N. Bernstein, Modules over a ring of differential operators, Funct. Anal. Prilož., 5 (1970), 89–101.

    Article  MATH  Google Scholar 

  5. J. N. Bernstein and S. I. Gelfand, Tensor products of finite and infinite dimensional representations of semisimple Lie algebras, Compos. Math., 41 (1980), 245–285.

    MathSciNet  MATH  Google Scholar 

  6. W. Borho and J.-L. Brylinski, Differential operators on homogeneous spaces I: Irreducibility of the associated variety for annihilators of induced modules, Invent. Math., 6 (1982), 437–476.

    Article  MathSciNet  MATH  Google Scholar 

  7. __, to appear.

    Google Scholar 

  8. W. Borho and J. C. Jantzen, Über primitive Ideale in der Einhüllenden einer halbeinfacher Lie-Algebra, Invent. Math., 39 (1977), 1–53.

    Article  MathSciNet  MATH  Google Scholar 

  9. W. Borho and H. Kraft, Über die Gelfand-Kirillov Dimension, Math. Ann., 220 (1976), 1–24.

    Article  MathSciNet  MATH  Google Scholar 

  10. J.-L. Brylinski and M. Kashiwara, Kazhdan-Lusztig Conjecture and Holonomic Systems, Invent. Math., 64 (1981), 387–410.

    Article  MathSciNet  MATH  Google Scholar 

  11. N. Conze-Berline and M. Duflo, Sur les représentations induites des groupes semi-simples complexes, Compos. Math., 34 (1977), 307–336.

    MathSciNet  MATH  Google Scholar 

  12. P. Deligne, Preprint, I.H.E.S. (1982).

    Google Scholar 

  13. J. Dixmier, Algèbres enveloppantes, Cahiers Scientifiques, XXXVII, Gauthier-Villars, Paris, 1974.

    Google Scholar 

  14. M. Duflo, Sur la classification des idéaux primitifs dans l'algèbre enveloppante d'une algèbre de Lie semi-simple, Ann. of Math., 105 (1977), 107–130.

    Article  MathSciNet  MATH  Google Scholar 

  15. O. Gabber, The integrability of the characteristic variety, Amer. J. Math., 103 (1981), 445–468.

    Article  MathSciNet  MATH  Google Scholar 

  16. O. Gabber and A. Joseph, On the Bernstein-Gelfand-Gelfand resolution and the Duflo sum formula, Compos. Math., 43 (1981), 107–131.

    MathSciNet  MATH  Google Scholar 

  17. __, Towards the Kazhdan-Lusztig conjecture, Ann. Éc. Norm. Sup., 14 (1981), 261–302.

    MathSciNet  MATH  Google Scholar 

  18. J.-C. Jantzen, Moduln mit einem höchsten Gewicht, LN 750, Springer-Verlag, Berlin/Heidelberg/New York, 1980.

    Google Scholar 

  19. A. Joseph, On the annihilators of simple subquotients of the principal series, Ann. Ec. Norm. Sup., 10 (1977), 419–439.

    MathSciNet  MATH  Google Scholar 

  20. A. Joseph, Sur la classification des idéaux primitifs dans l'algèbre enveloppante de sl(n+1,C), Comptes Rendus, A 287 (1978), 302–306.

    MATH  Google Scholar 

  21. __, Towards the Jantzen conjecture, Compos. Math., 40 (1980), 35–67.

    MathSciNet  MATH  Google Scholar 

  22. __, Dixmier's problem for Verma and Principal series submodules, J. London Math. Soc., 20 (1979), 193–204.

    Article  MathSciNet  MATH  Google Scholar 

  23. __, W-module structure in the primitive spectrum of the enveloping algebra of a semisimple Lie algebra, in LN 728, Springer-Verlag, Berlin/Heidelberg/New York, 1979, pp. 116–135.

    MATH  Google Scholar 

  24. __, Goldie rank in the enveloping algebra of a semisimple Lie algebra, I, J. Algebra, 65 (1980), 269–283.

    Article  MathSciNet  MATH  Google Scholar 

  25. __, Goldie rank in the enveloping algebra of a semisimple Lie algebra, II, J. Algebra, 65 (1980), 284–306.

    Article  MathSciNet  MATH  Google Scholar 

  26. __, Goldie rank in the enveloping algebra of a semisimple Lie algebra, III, J. Algebra, 73 (1981), 295–326.

    Article  MathSciNet  MATH  Google Scholar 

  27. __, Kostant's problem and Goldie rank, in LN 880, Springer-Verlag, Berlin/Heidelberg/New York, 1981, pp. 249–266.

    MATH  Google Scholar 

  28. __, The Enright functor in the Bernstein-Gelfand-Gelfand 0 category, Invent. Math., 67 (1982), 423–445.

    Article  MathSciNet  MATH  Google Scholar 

  29. __, Completion functors in the 0 category, to appear in "Non-commutative Harmonic Analysis Proceedings," Marseille-Luminy, 1982.

    Google Scholar 

  30. __, On the associated variety of a highest weight module, J. Algebra, to appear.

    Google Scholar 

  31. A. Joseph and T. Stafford, to appear.

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  33. G. Lusztig and N. Spaltenstein, Induced unipotent classes, J. Lond. Math. Soc., 19 (1979), 41–52.

    Article  MathSciNet  MATH  Google Scholar 

  34. N. N. Shapovalov, On a bilinear form on the universal enveloping algebra of a complex semisimple Lie algebra, Funct. Anal. Prilož. 6 (1972), 307–311.

    Article  MathSciNet  MATH  Google Scholar 

  35. N. Spaltenstein, Classes unipotentes et scus-groupes de Borel, LN 946, Springer-Verlag, Berlin/Heidelberg/New York, 1982.

    MATH  Google Scholar 

  36. T. A. Springer, A construction of representations of Weyl groups, Invent. Math., 44 (1978), 279–293.

    Article  MathSciNet  MATH  Google Scholar 

  37. R. Steinberg, Conjugacy classes in algebraic groups, LN 366, Springer-Verlag, Berlin/Heidelberg/New York, 1974.

    MATH  Google Scholar 

  38. D. A. Vogan, Gelfand-Kirillov dimension for Harish-Chandra modules, Invent. Math., 48 (1978), 75–98.

    Article  MathSciNet  MATH  Google Scholar 

  39. __, Ordering of the primitive spectrum of a semi-simple Lie algebra, Math. Ann., 248 (1980), 195–203.

    Article  MathSciNet  MATH  Google Scholar 

  40. D. A. Vogan, Irreducible characters of semisimple Lie groups II, The Kazhdan-Lusztig conjectures, Duke Math. J., 46 (1979), 805–859.

    Article  MathSciNet  MATH  Google Scholar 

  41. D. A. Kazhdan and G. Lusztig, A topological approach to Springer's representations, Adv. Math., 38 (1980), 222–228.

    Article  MathSciNet  MATH  Google Scholar 

  42. T. Levasseur, Dimension injective des quotients primitif minimaux de l'algèbre enveloppante d'une algèbre de Lie semi-simple, Comptes Rendus, 292 (1981), 385–387.

    MathSciNet  MATH  Google Scholar 

  43. R. Hotta, On Joseph's construction of Weyl group representations, preprint, Tokyo 1982.

    Google Scholar 

  44. K. A. Brown, Ore sets in enveloping algebrass, Preprint, Glasgow (1982).

    Google Scholar 

  45. A. Joseph, The associated variety of a primitive ideal, Preprint (1983).

    Google Scholar 

  46. T. Levasseur, Preprint (1983).

    Google Scholar 

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Authors and Affiliations

  1. Department of Theoretical Mathematics, The Weizmann Institute of Science, 76100, Rehovot, Israel

    A. Joseph

  2. Laboratoire de mathématiques fondamentales (Equipe de recherche associée au CNRS), Université de Pierre et Marie Curie, France

    A. Joseph

Authors
  1. A. Joseph
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Rebecca Herb Ronald Lipsman Jonathan Rosenberg

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© 1983 Springer-Verlag

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Joseph, A. (1983). On the classification of primitive ideals in the enveloping algebra of a semisimple lie algebra. In: Herb, R., Lipsman, R., Rosenberg, J. (eds) Lie Group Representations I. Lecture Notes in Mathematics, vol 1024. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0071431

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  • DOI: https://doi.org/10.1007/BFb0071431

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  • Print ISBN: 978-3-540-12725-3

  • Online ISBN: 978-3-540-38709-1

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