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Letters in Mathematical Physics

, Volume 31, Issue 2, pp 101–110 | Cite as

Quantum affine algebras and universalR-matrix with spectral parameter

  • Yao-Zhong Zhang
  • M. D. Gould
Article

Abstract

Using the previously obtained universalR-matrix for the quantized nontwisted affine Lie algebras U q (A 1 (1) ) and U q (A 2 (1) ), we determine the explicitly spectral dependent universalR-matrix for the corresponding quantum Lie algebras U q (A1) and U q (A2). As applications, we reproduce the well known results in the fundamental representations and we also derive an extremely explicit formula of the spectral-dependentR-matrix for the adjoint representation of U q (A2), the simplest nontrivial case when the tensor product decomposition of the representation with itself has nontrivial multiplicity.

Mathematics Subject Classifications (1991)

81R10 17B37 16W30 

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Copyright information

© Kluwer Academic Publishers 1994

Authors and Affiliations

  • Yao-Zhong Zhang
    • 1
  • M. D. Gould
    • 1
  1. 1.Department of MathematicsUniversity of QueenslandBrisbaneAustralia

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