Several realizations of Fock modules for toroidal ${Ü}_{q,d}\left({𝖘𝖑}_n\right)$

In this paper, we relate the well-known Fock representations of ${Ü}_{q,d}\left({𝔰𝔩}_n\right)$ to the vertex, shuffle, and 'L-operator' representations of ${Ü}_{q,d}\left({𝔰𝔩}_n\right)$. These identifications generalize those for the quantum toroidal algebra of ${gl}_1$, which were recently established in Feigin et al. (J. Phys. A 48(24), 244001, 2015).