The R-matrix formalism for quantized enveloping algebras

Let $U_\hbar\mathfrak{g}$ denote the Drinfeld-Jimbo quantum group associated to a simple Lie algebra $\mathfrak{g}$. We apply a modification of the $R$-matrix construction for quantum groups to the evaluation of the universal $R$-matrix of $U_\hbar\mathfrak{g}$ on any of its finite-dimensional repre