Highest $\mathrm{\ell }$-Weight Representations and Functional Relations

We discuss highest $\mathrm{\ell }$-weight representations of quantum loop algebras and the corresponding functional relations between integrability objects. In particular, we compare the prefundamental and $q$-oscillator representations of the positive Borel subalgebras of the quantum group $$\mathrm{U}$q(\mathcal L(\mathfrak{sl}{l+1}))$forarbitraryvaluesof$l$. Our article has partially the nature of a short review, but it also contains new results. These are the expressions for the $L$-operators, and the exact relationship between different representations, as a byproduct resulting in certain conclusions about functional relations.