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Polynomial identities for simple Lie superalgebras

Published online by Cambridge University Press:  17 February 2009

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Abstract

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Polynomial identities for the generators of a simple basic classical Lie superalgebra are derived in arbitrary representations generated by a maximal (or minimal) weight vector. The infinitesimal characters occurring in the tensor product of two finite dimensional irreducible representations are also determined.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1987

References

[1]Bracken, A. J. and Green, H. S., J. Math. Phys. 12 (1971), 2099.CrossRefGoogle Scholar
[2]Corwin, L., Ne'eman, Y. and Sternberg, S., Rev. Modern Phys. 47 (1975), 573.CrossRefGoogle Scholar
[3]Dixmier, J., Enveloping algebras (North Holland, Amsterdam-New York-Oxford 1977).Google Scholar
[4]Farmer, R. J. and Jarvis, P. D., “Representations of Orthosympectic Superalgebras 11. Young Diagrams and Weight Space Techniques”, (Univ. of Tasmania preprint, 1983).Google Scholar
[5]Fayet, P. and Ferrara, S., Phys. Rep. C 32 (1977), 69.CrossRefGoogle Scholar
[6]Gould, M. D., J. Math. Phys. 21 (1980), 444.CrossRefGoogle Scholar
[7]Gould, M. D., J. Math. Phys. 22 (1981), 2376.CrossRefGoogle Scholar
[8]Gould, M. D. and Chandler, G. S., Int. J. Quantum Chem. 25 (1984), 553.CrossRefGoogle Scholar
[9]Gould, M. D. and Chandler, G. S., Int. J. Quantum Chem. 25 (1984), 603.CrossRefGoogle Scholar
[10]Gould, M. D., J. Phys. A 17 (1984), 1.CrossRefGoogle Scholar
[11]Gould, M. D., J. Austral. Math. Soc. Ser. B 26 (1984), 257.CrossRefGoogle Scholar
[12]Green, H. S., J. Math. Phys. 12 (1971), 2106.CrossRefGoogle Scholar
[13]Humphreys, J. E., Introduction to Lie algebras and representation theory (Springer-Verlag, New York-Heidelberg-Berlin, 1972).CrossRefGoogle Scholar
[14]Jarvis, P. D. and Green, H. S., J. Math. Phys. 20 (1979), 2115.CrossRefGoogle Scholar
[15]Jarvis, P. D. and Murray, M. K., J. Math. Phys. 24 (1983), 1705.CrossRefGoogle Scholar
[16]Kac, V. G., Adv. in Math. 26 (1977), 8.CrossRefGoogle Scholar
[17]Kac, V. G., Comm. Algebra 5 (1977), 889.CrossRefGoogle Scholar
[18]Kac, V. G., Lecture Notes in Math. 676 (Springer, Berlin, 1978), 597.Google Scholar
[19]Kostant, B., J. Funct. Anal. 20 (1975), 257.CrossRefGoogle Scholar
[20]Nahm, W. and Scheunert, M., J. Math. Phys. 17 (1976), 868.CrossRefGoogle Scholar
[21]Salam, A. and Strathdee, J., Nuclear Phys. B 76 (1974), 477.CrossRefGoogle Scholar
[22]Scherk, J., Rev. Modern Phys. 47 (1975), 123.CrossRefGoogle Scholar
[23]Scheunert, M., Nahm, W. and Rittenberg, V., J. Math. Phys. 17 (1976), 1626.CrossRefGoogle Scholar
[24]Scheunert, M., Lecture Notes in Math. 716 (Springer, Berlin, 1979).Google Scholar
[25]Wess, J. and Zumino, B., Nuclear Phys. B 70 (1974), 39.CrossRefGoogle Scholar