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Characters of irreducible representations of the Lie algebra of vector fields on the circle. (English) Zbl 0498.17010


MSC:

17B55 Homological methods in Lie (super)algebras
17B65 Infinite-dimensional Lie (super)algebras
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)

References:

[1] Garland, H., Lepowsky, J.: Lie algebra homology and the Macdonald-Kac formulas. Invent. Math.34, 37-76 (1976) · Zbl 0358.17015 · doi:10.1007/BF01418970
[2] Gelfand, I.M.: The cohomology of infinite dimensional Lie algebras; some questions of integral geometry. Actes, Congrès intern. math., 1970, Tome 1, p. 95-111
[3] Goncharova L.V.: The cohomologies of Lie algebras of formal vector fields on the line. Functs. Anal. Prilozhen.7, No. 2, 6-14 (1973); No. 3, 33-44 (1973) · Zbl 0284.17006
[4] Jantzen, J.E.: Moduln mit einem höchsten Gewicht. Lecture Notes in Mathematics, vol. 750. Berlin-New-York-Heidelberg: Springer 1979 · Zbl 0426.17001
[5] Kac, V.G.: Highest weight representations of infinite-dimensional lie algebras. Proceedings of the International Congress of Mathematicians, Helsinki, 1978 · Zbl 0425.17009
[6] Kac, V.G.: Some problems on infinite dimensional Lie algebras and their representations (for AMS meeting at Amherst, 1981). Preprint
[7] Rocha-Caridi, A.: Resolutions of irreducible highest weight modules over infinite dimensional graded Lie algebras, Proceedings of the 1981 Conference on Lie algebras and related topics. Lecture Notes in Mathematics, Vol. 933 Berlin-Heidelberg-New York: Springer 1982 · Zbl 0495.17009
[8] Rocha-Caridi, A., Wallach, N.R.: Projective modules over graded Lie algebras I. Math. Z180, 151-177 (1982) · doi:10.1007/BF01318901
[9] Rocha-Caridi, A., Wallach, N.R.: Highest weight modules over graded lie algebras: Resolutions. Filtrations and character formulas. To appear in the transactions of the A.M.S. · Zbl 0512.17007
[10] Shapovalov, N.N.: On a bilinear form on the universal enveloping algebra of a complex semi-simple Lie algebra. Functional Anal. Appl.6, 307-312 (1972) · Zbl 0283.17001 · doi:10.1007/BF01077650
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