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References
Bernstein, I.N., Gelfand, I.M., Gelfand, S.I.: Category of g-modules. Funkcional. Anal. i. Priložen.10, Nr. 2, 1–8 (1976) [Russian]. Engl. Transl: Functional. Anal. Appl.10, 87–92 (1976)
Bernstein, I.N., Gelfand, I.M., Gelfand, S.I.: Differential operators on the base affine space and a study of g-modules, Lie groups and their representations. Proceedings of the Summer School on Group Representations (I.M. Gelfand, ed.), Bolyai János Mathematical Society (Budapest 1971), pp. 39–69. London: Hilger 1975
Bernstein, I.N., Gelfand, I.M., Gelfand, S.I.: Structure of representations generated by vectors of highest weight. Funkcional. Anal. i Priložen.5, Nr. 1, 1–9 (1970) [Russian]. Engl. Transl.: Functional. Anal. Appl.5, 1–8 (1971)
Curtis, C.W., Reiner, I.: Representation theory of finite groups and associative algebras. New York-London-Sydney: Wiley-Interscience 1966
Dixmier, J.: Enveloping Algebras. North-Holland Mathematical Library14. Amsterdam-New York-Oxford: North-Holland 1977
Enright, T.: On the fundamental series of a real semisimple Lie algebra: their irreducibility, resolutions and multiplicity formulae. Ann. of Math. (2)110, 1–82 (1979)
Enright, T., Wallach, N.R.: The fundamental series of representations of a real semisimple Lie algebra. Acta Math.140, 1–32 (1978)
Garland, H., Lepowsky, J.: Lie algebra homology and the Macdonald-Kac formulas. Invent. Math.34, 37–76 (1976)
Kac, V.G.: Infinite-dimensional Lie algebras and Dedekind's η-function. Funkcional. Anal. i Prilozen.8, Nr. 1, 77–78 (1974) [Russian]. Engl. Transl.: Functional. Anal. Appl.8, 68–70 (1974)
Kac, V.G.: Simple irreducible graded Lie algebras of finite growth. Izo. Akad. Nauk SSSR Ser. Mat.32, 1323–1367 (1968) [Russian]. Engl. Transl.: Math. USSR-Izv.2, 1271–1311 (1968)
Kac, V.G., Kazhdan, D.A.: Structure of representations with highest wieght of infinite dimensional Lie algebras. Advances in Math.34, 97–108 (1979)
Lepowsky, J.: A generalization of the Bernstein-Gelfand-Gelfand resolution J. Algebra49, 496–511 (1977)
Lepowsky, J.: Lectures on Kac-Moody Lie algebras Mimeographed Notes. Paris: Université de Paris VI 1978
Mitchell, B.: Theory of Categories. Pure and Applied Mathematics XVII. New York-San Francisco-London: Academic Press 1965
Moody, R.V.: Macdonald identities and Euclidean Lie algebras Proc. Amer. Math. Soc.48, 43–52 (1975)
Rocha-Caridi, A.: Splitting criteria for g-modules induced from a parabolic and the Bernstein-Gelfand-Gelfand resolution of a finite dimensional irreducible g-modules. Ph.D. Thesis. New Brunswick: Rutgers University 1978
Rocha-Caridi, A.: Splitting Criteria for g-modules induced from a parabolic and the Bernstein-Gelfand-Gelfand resolution of a finite dimensional irreducible g-modules. Trans. Amer. Math. Soc.262, 335–366 (1980)
Wallach, N.R.: On the Enright-Varadarajan modules, a construction of the discrete series. Ann. Sci. École Norm. Sup (4)9, 81–102 (1976)
Wallach, N.R.: Unpublished manuscript notes on the Borel-Weil theorem.
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Research partially supported by National Science Foundation Grant
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Rocha-Caridi, A., Wallach, N.R. Projective modules over graded Lie algebras. I. Math Z 180, 151–177 (1982). https://doi.org/10.1007/BF01318901
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DOI: https://doi.org/10.1007/BF01318901