Abstract
A modification of one of the defining relations of quantized Kac-Moody algebras, introduced by Drinfeld and Jimbo, is given. This modification allows one to extend the concept of quantized Kac-Moody algebras to the case of Kac-Moody superalgebras. A q-analogue of the Cartan-Weyl basis is introduced, which has properties similar to the Cartan-Weyl basis of the Kac-Moody (super) algebras. Explicit expressions of the extremal projectors for all quantized Kac-Moody (super) algebras of finite growth are written down. A complete derivation of the Gel'fand-Tsetlin formulae for the quantized gl(n,C)is given.
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© 1990 Springer-Verlag
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Tolstoy, V.N. (1990). Extremal projectors for quantized kac-moody superalgebras and some of their applications. In: Doebner, H.D., Hennig, J.D. (eds) Quantum Groups. Lecture Notes in Physics, vol 370. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-53503-9_45
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DOI: https://doi.org/10.1007/3-540-53503-9_45
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