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Structure of representations with highest weight of infinite-dimensional Lie algebras.(English)Zbl 0427.17011


MSC:

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

Cite

References:

[1]Jantzen, J. C., Moduln mit einem höchsten gewicht (1977), preprint ·Zbl 0426.17001
[2]Bernstein, I. N.; Gelfand, I. M.; Gelfand, S. I., Structure of representations generated by vectors of highest weight, Functional Anal. Appl., 5, 1-8 (1971) ·Zbl 0246.17008
[3]Šapovalov, N. N., On bilinear form on the universal enveloping algebra of a complex semisimple Lie algebra, Functional Anal. Appl., 6, 307-312 (1972) ·Zbl 0283.17001
[4]Kac, V. G., Simple irreducible graded Lie algebras of finite growth, Math. USSR-Izv., 2, 1271-1311 (1968) ·Zbl 0222.17007
[5]Moody, R. V., A new class of Lie algebras, J. Algebra, 10, 211-230 (1968) ·Zbl 0191.03005
[6]Kac, V. G., Infinite-dimensional Lie algebras and Dedekind’s η-function, Functional Anal. Appl., 8, 68-70 (1974) ·Zbl 0299.17005
[7]Kac, V. G., Infinite-dimensional algebras, Dedekind η-function, classical Möbius function and the very strange formula, Advances in Math., 30, 85-136 (1978) ·Zbl 0391.17010
[8]Jantzen, J. C., Kontravariante Formen auf induzierten Darstellungen halfeinfacher Lie Algebren, Math. Ann., 226, 53-65 (1977) ·Zbl 0372.17003
[9]Kac, V. G., Contravariant form for Lie algebras and superalgebras, (Lecture Notes in Physics, 94 (1979), Springer-Verlag: Springer-Verlag Berlin/New York), 441-445 ·Zbl 0574.17002
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.
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