We will recall the construction of certain families of representations of the toroidal algebras of sl_n, due to [Feigin-Jimbo-Miwa-Mukhin]. We explain how to adapt those to the setting of the affine Yangians. We will generalize the result of [Gautam-Toledano Laredo] to the toroidal setting. Using an alternative realization of Fock representations, due to [Saito], we recover a functional realization of certain commutative subalgebras in the toroidal/affine quantum algebras