Monodromy operators for higher rank

We find the explicit form of the basic monodromy operators for the case of the quantum group ${\mathrm{U}}_q(\mathcal{L}({\mathfrak{s}\mathfrak{l}}_3))$. Expressions for the quantum Casimir elements of the quantum groups $\mathrm U_q(\mathfrak{gl}_3)$and$\mathrm U_q(\mathfrak{sl}_3)$ are obtained as a by-product.