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Goldie rank in the enveloping algebra of a semisimple Lie algebra. I, II. (English) Zbl 0441.17004


MSC:

17B35 Universal enveloping (super)algebras
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
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[1] Borho, W.; Jantzen, J. C., U¨ber primitive Ideale in der Einhu¨llenden einer halbeinfacher Lie-Algebra, Invent. Math., 39, 1-53 (1977) · Zbl 0327.17002
[2] Dixmier, J., Alge‘bres enveloppantes, (Cahiers Scientifiques, XXXVII (1974), Gauthier-Villars: Gauthier-Villars Paris) · Zbl 0308.17007
[3] Duflo, M., Repre´sentations irre´ductibles des groupes semi-simples complexes, (Analyse Harmonique sur les Groupes de Lie. Analyse Harmonique sur les Groupes de Lie, Lecture Notes in Mathematics No. 497 (1975), Springer-Verlag: Springer-Verlag Berlin/Heidelberg/New York), 26-88 · Zbl 0315.22008
[4] Duflo, M., Sur la classification des ide´aux primitifs dans l’alge“bre enveloppante d”une alge‘bre de Lie semi-simple, Ann. of Math., 105, 107-130 (1977) · Zbl 0346.17011
[5] Duflo, M., Polynoˆmes de Vogan pour SL(n,C), (Non-commutative Harmonic Analysis Proceedings. Non-commutative Harmonic Analysis Proceedings, 1978. Non-commutative Harmonic Analysis Proceedings. Non-commutative Harmonic Analysis Proceedings, 1978, Lecture Notes in Mathematics No. 728 (1979), Springer-Verlag: Springer-Verlag Berlin/Heidelberg/New York), 64-75 · Zbl 0414.22018
[6] Jantzen, J. C., Moduln mit einem ho¨chsten Gewicht, (Lectures Notes in Mathematics No. 750 (1972), Springer-Verlag: Springer-Verlag Berlin/Heidelberg/New York) · Zbl 0426.17001
[7] Joseph, A., Gelfand-Kirillov dimension for the annihilators of simple quotients of Verma modules, J. London Math. Soc., 18, 50-60 (1978) · Zbl 0401.17007
[8] Joseph, A., Towards the Jantzen conjecture, Compositio Math., 40, 35-67 (1980) · Zbl 0424.17004
[9] Joseph, A., Towards the Jantzen conjecture, II, Compositio Math., 40, 69-78 (1980) · Zbl 0424.17005
[10] Joseph, A., Kostant’s problem, Goldie rank and the Gelfand-Kirillov conjecture, Invent. Math., 56, 191-213 (1980) · Zbl 0446.17006
[11] Joseph, A., Dixmier’s problem for Verma and principal series submodules, J. London Math. Soc., 20, 193-204 (1979) · Zbl 0421.17005
[12] Joseph, A.; Small, L. W., An additivity principle for Goldie rank, Israel J. Math., 31, 105-114 (1978) · Zbl 0395.17010
[13] Macdonald, I. G., Some irreducible representations of the Weyl groups, Bull. London Math. Soc., 4, 148-150 (1972) · Zbl 0251.20043
[14] Vogan, D., Gelfand-Kirillov dimension for Harish-Chandra modules, Invent. Math., 48, 75-98 (1978) · Zbl 0389.17002
[15] Vogan, D., A Generalized τ-invariant for the primitive spectrum of a semisimple Lie algebra, Math. Ann., 242, 209-224 (1979) · Zbl 0387.17007
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