$\ell$-weights and factorization of transfer operators

We analyze the $\ell$-weights of the evaluation and $q$-oscillator representations of the quantum loop algebras $\mathrm U_q(\mathcal L(\mathfrak{sl}_{l+1}))$ for $l=1$ and $l=2$ and prove factorization relations for the transfer operators of the associated quantum integrable systems.