Gabber, O.; Joseph, A. Towards the Kazhdan-Lusztig conjecture. (English) Zbl 0476.17005 Ann. Sci. Éc. Norm. Supér. (4) 14, 261-302 (1981). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 2 ReviewsCited in 43 Documents MSC: 17B35 Universal enveloping (super)algebras 17B55 Homological methods in Lie (super)algebras 17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) 22E47 Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) Keywords:Kazhdan-Lusztig conjecture; enveloping algebra; complex semisimple Lie algebra; multiplicities; composition series of Verma modules; Bernstein- Gelfand-Gelfand category; extension groups; Jantzen filtration; Kazhdan- Lusztig polynomial PDF BibTeX XML Cite \textit{O. Gabber} and \textit{A. Joseph}, Ann. Sci. Éc. Norm. Supér. (4) 14, 261--302 (1981; Zbl 0476.17005) Full Text: DOI Numdam EuDML References: [1] I. N. BERNSTEIN , I. M. GELFAND and S. I. GELFAND , Category of \? Modules (Funct. Anal. Priloz., Vol. 10, 1976 , pp. 1-8). MR 53 #10880 | Zbl 0353.18013 · Zbl 0353.18013 [2] I. N. BERNSTEIN and S. I. Gelfand , Tensor Products of Finite and Infinite Dimensional Representations of Semisimple Lie Algebras (Compos. Math., Vol. 41, 1980 , pp. 245-285). Numdam | MR 82c:17003 | Zbl 0445.17006 · Zbl 0445.17006 [3] N. BOURBAKI , Groupes et algèbres de Lie , Chap. 4-6, Éléments de mathématiques, XXXIV, Hermann, Paris, 1968 . · Zbl 0186.33001 [4] H. CARTAN and S. EILENBERG , Homological Algebra , Princeton, New Jersey, 1976 . [5] P. DELORME , Extensions dans la catégorie \vartheta de Bernstein-Gelfand-Gelfand . Applications, preprint, Paris, 1978 . [6] J. DIXMIER , Algèbres enveloppantes , cahiers scientifiques, XXXVII, Gauthier-Villars, Paris, 1974 . MR 58 #16803a | Zbl 0308.17007 · Zbl 0308.17007 [7] O. GABBER and A. JOSEPH , The Bernstein-Gelfand-Gelfand Resolution and the Duflo Sum Formula (Compos. Math., Vol. 43, 1981 , pp. 107-131). Numdam | MR 82k:17009 | Zbl 0461.17004 · Zbl 0461.17004 [8] J.-C. JANTZEN , Zur Charackterformel gewisser Darstellungen halbeinfacher Gruppen und Lie-Algebren (Math. Z., Vol. 140, 1974 , pp. 127-149). Article | MR 55 #5756 | Zbl 0288.20059 · Zbl 0288.20059 [9] J.-C. JANTZEN , Moduln mit einem höchsten Gewicht , LN 750, Springer-Verlag, Berlin-Heidelberg-New York, 1980 . Zbl 0426.17001 · Zbl 0426.17001 [10] D. A. KAZHDAN and G. LUSZTIG , Representations of Coxeter Groups and Hecke Algebras (Invent. Math., Vol. 53, 1979 , pp. 165-184). MR 81j:20066 | Zbl 0499.20035 · Zbl 0499.20035 [11] D. A. KAZHDAN and G. LUSZTIG , Schubert Varieties and Poincaré Duality , preprint, Harvard, 1979 . [12] D. VOGAN , Irreducible Characters of Semisimple Lie Groups I (Duke Math. J., Vol. 46, 1979 , pp. 61-108). Article | MR 80g:22016 | Zbl 0398.22021 · Zbl 0398.22021 [13] D. VOGAN , Irreducible Characters of Semisimple Lie Groups II. The Kazhdan-Lusztig conjectures (Duke Math. J., Vol. 46, 1979 , pp. 805-859). Article | MR 81f:22024 | Zbl 0421.22008 · Zbl 0421.22008 [14] D. VOGAN , Ordering in the Primitive Spectrum of a Semisimple Lie Algebra (Math. Ann., Vol. 248, 1980 , pp. 195-203). MR 81k:17006 | Zbl 0414.17006 · Zbl 0414.17006 [15] A. A. BEILINSON and I. N. BERNSTEIN , C. R. Acad. Sc. (to appear). [16] J.-L. BRYLINSKI and M. KASHIWARA , Démonstration de la conjecture de Kazhdan-Lusztig sur les modules de Verma [C. R. Acad. Sc. (to appear)]. Zbl 0457.22012 · Zbl 0457.22012 [17] J.-L. BRYLINSKI and M. KASHIWARA , Kazhdan-Lusztig Conjecture and Holonomic Systems [Invent. Math. (to appear)]. Zbl 0473.22009 · Zbl 0473.22009 [18] S. GELFAND and R. MACPHERSON , Verma Modules and Schubert cells , Preprint, I.H.E.S., November 1980 . · Zbl 0512.22009 [19] A. JOSEPH . Goldie Rank in the Enveloping Algebra of a Semisimple Lie Algebra , III [J. Alg. (in the press)]. Zbl 0482.17002 · Zbl 0482.17002 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.