Several realizations of Fock modules for toroidal Üq,d(𝖘𝖑n)

Abstract

In this paper, we relate the well-known Fock representations of Üq,d(𝔰𝔩n) to the vertex, shuffle, and ‘L-operator’ representations of Üq,d(𝔰𝔩n). These identifications generalize those for the quantum toroidal algebra of 𝔤𝔩1, which were recently established in Feigin et al. (J. Phys. A 48(24), 244001, 2015).