QUANTUM AFFINE ALGEBRAS AND UNIVERSAL R-MATRIX WITH SPECTRAL PARAMETER

Using the previously obtained universal R-matrix for the quantized non twisted affine Lie algebras U(q)(A1(1)) and U(q)(A2(1)), we determine the explicitly spectral dependent universal R-matrix for the correspon ding quantum Lie algebras U(q)(A1) and U(q)(A2). As applications, we r eproduce the well known results in the fundamental representations and we also derive an extremely explicit formula of the spectral-dependen t R-matrix for the adjoint representation of U(q)(A2), the simplest no ntrivial case when the tensor product decomposition of the representat ion with itself has nontrivial multiplicity.