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A generalization of the Bernstein-Gelfand-Gelfand resolution. (English) Zbl 0381.17006

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)
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[1] Bernstein, I.N; Gelfand, I.M; Gelfand, S.I; Bernstein, I.N; Gelfand, I.M; Gelfand, S.I, Structure of representations generated by highest weight vectors (in Russian), Funktional anal. i prilozen., 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, (), 21-64 · Zbl 0338.58019
[3] Dixmier, J, Algèbres enveloppantes, (1974), 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, (), 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, () · Zbl 0157.07604
[12] Verma, D.-N; Verma, D.-N, Structure of certain induced representations of complex semisimple Lie algebras, Bull. amer. math. soc., Bull. amer. math. soc., 74, 628-166, (1968) · Zbl 0157.07604
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