Quantum affine algebras and universalR-matrix with spectral parameter

Using the previously obtained universalR-matrix for the quantized nontwisted affine Lie algebras U_q(A₁⁽¹⁾) and U_q(A₂⁽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.