Joseph, A. Goldie rank in the enveloping algebra of a semisimple Lie algebra. I, II. (English) Zbl 0441.17004 J. Algebra 65, 269-283, 284-306 (1980). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 4 ReviewsCited in 53 Documents MSC: 17B35 Universal enveloping (super)algebras 17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) Keywords:complex semisimple Lie algebra; enveloping algebra; primitive ideals; Goldie ranks; Gelfand-Kirillov dimension; highest weight modules; character theory PDF BibTeX XML Cite \textit{A. Joseph}, J. Algebra 65, 269--283, 284--306 (1980; Zbl 0441.17004) Full Text: DOI OpenURL References: [1] Borho, W.; Jantzen, J.C., U¨ber primitive ideale in der einhu¨llenden einer halbeinfacher Lie-algebra, Invent. math., 39, 1-53, (1977) [2] Dixmier, J., Alge‘bres enveloppantes, () [3] Duflo, M., Repre´sentations irre´ductibles des groupes semi-simples complexes, (), 26-88 [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) [5] Duflo, M., Polynoˆmes de vogan pour SL(n,C), (), 64-75 · Zbl 0414.22018 [6] Jantzen, J.C., Moduln mit einem ho¨chsten gewicht, () [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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.