Lepowsky, J. A generalization of the Bernstein-Gelfand-Gelfand resolution. (English) Zbl 0381.17006 J. Algebra 49, 496-511 (1977). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 3 ReviewsCited in 79 Documents MSC: 17B55 Homological methods in Lie (super)algebras 17B56 Cohomology of Lie (super)algebras 17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) PDFBibTeX XMLCite \textit{J. Lepowsky}, J. Algebra 49, 496--511 (1977; Zbl 0381.17006) Full Text: DOI References: [1] Bernstein, I. N.; Gelfand, I. M.; Gelfand, S. I., Functional Anal. Appl., 5, 1-8 (1971), English translation · Zbl 0246.17008 [2] Bernstein, I. N.; Gelfand, I. M.; Gelfand, S. I., Differential operators on the base affine space and a study of g-modules, (Gelfand, I. M., “Lie Groups and Their Representations,” Summer School of the Bolyai János Math. Soc. (1975), Halsted Press: Halsted Press New York), 21-64 · Zbl 0338.58019 [3] Dixmier, J., Algèbres Enveloppantes (1974), Gauthier-Villars: Gauthier-Villars Paris · Zbl 0308.17007 [4] Garland, H.; Lepowsky, J., Lie algebra homology and the Macdonald-Kac formulas, Invent. Math., 34, 37-76 (1976) · Zbl 0358.17015 [5] Harish-Chandra, On some applications of the universal enveloping algebra of a semisimple Lie algebra, Trans. Amer. Math. Soc., 70, 28-96 (1951) · Zbl 0042.12701 [6] Kostant, B., Lie algebra cohomology and the generalized Borel-Weil theorem, Ann. of Math., 74, 329-387 (1961) · Zbl 0134.03501 [7] Lepowsky, J., Conical vectors in induced modules, Trans. Amer. Math. Soc., 208, 219-272 (1975) · Zbl 0311.17002 [8] Lepowsky, J., Existence of conical vectors in induced modules, Ann. of Math., 102, 17-40 (1975) · Zbl 0314.17006 [9] Lepowsky, J., Uniqueness of embeddings of certain induced modules, (Proc. Amer. Math. Soc., 56 (1976)), 55-58 · Zbl 0335.17004 [10] Lepowsky, J., Generalized Verma modules, the Cartan-Helgason theorem, and the Harish-Chandra homomorphism, J. Algebra, 49, 470-495 (1977) · Zbl 0381.17005 [11] Verma, D.-N, Structure of Certain Induced Representations of Complex Semi-simple Lie Algebras, (Thesis (1966), Yale University) · Zbl 0157.07604 [12] Verma, D.-N, Structure of certain induced representations of complex semisimple Lie algebras, Bull. Amer. Math. Soc., 74, 628 (1968) · Zbl 0157.07604 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.