Quantum vertex algebra associated to quantum toroidal 𝔤𝔩_N

In this paper, we associate the quantum toroidal algebra ℰ_N of type 𝔤𝔩_N with quantum vertex algebra through equivariant ϕ-coordinated quasi modules. More precisely, for every ℓ∈ℂ, by deforming the universal affine vertex algebra of 𝔰𝔩_∞, we construct an ħ-adic quantum -vertex algebra V_𝔰𝔩_∞,ħ(ℓ,0). Then we prove that the category of restricted ℰ_N-modules of level ℓ is canonically isomorphic to that of equivariant ϕ-coordinated quasi V_𝔰𝔩_∞,ħ(ℓ,0)-modules.