Oscillator versus prefundamental representations

For the case of quantum loop algebras $\mathrm U_q(\mathcal L(\mathfrak{sl}_{l + 1}))$with$l = 1, 2$wefindthe$\ell$-weights and the corresponding $\mathrm{\ell }$-weight vectors for the representations obtained via Jimbo’s homomorphism, known also as evaluation representations. Then we find the $\mathrm{\ell }$-weights and the $\mathrm{\ell }$-weight vectors for the $q$-oscillator representations of Borel subalgebras of the same quantum loop algebras. This allows, in particular, to relate $q$-oscillator and prefundamental representations.