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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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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
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