Extremal projector and universal R-matrix for quantized contragredient Lie (super)algebras

  • S. M. Khoroshkin
  • V. N. Tolstoy
Part of the Mathematical Physics Studies book series (MPST, volume 13)


Two basic elements of the representation theory of quantized finite-dimensional contragredient Lie (super)algebras g (U q(g)) are presented. These are the universal R-matrix to be an interwining operator, and the extremal projector which gives a powerful method for decomposition of representations. Properties of Cartan-Weyl basis for U q(g) are discussed. Some Taylor extension of U q(g) and U q(g) ⊗ U q(g) are introduced in terms of this basis. The extremal projector p and the universal R-matrix R are described as unique elements of these extensions. Explicit formulae for p and R are given.


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Copyright information

© Springer Science+Business Media Dordrecht 1992

Authors and Affiliations

  • S. M. Khoroshkin
    • 1
  • V. N. Tolstoy
    • 2
  1. 1.Institute of New TechnologiesMoscowRussia
  2. 2.Institute of Nuclear PhysicsMoscow State UniversityMoscowRussia

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