Restricted modules for the quantum affine algebra in type A are equivalent, with submodule correspondence, to phi-coordinated modules for the Etingof-Kazhdan quantum affine vertex algebra with phi(z2,z0)=z2 e^{z0}.
On the structure of quantum vertex algebras
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abstract
A definition of a quantum vertex algebra, which is a deformation of a vertex algebra, was proposed by Etingof and Kazhdan in 1998. In a nutshell, a quantum vertex algebra is a braided state-field correspondence which satisfies associativity and braided locality axioms. We develop a structure theory of quantum vertex algebras, parallel to that of vertex algebras. In particular, we introduce braided n-products for a braided state-field correspondence and prove for quantum vertex algebras a version of the Borcherds identity.
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On the quantum affine vertex algebra associated with trigonometric $R$-matrix
Restricted modules for the quantum affine algebra in type A are equivalent, with submodule correspondence, to phi-coordinated modules for the Etingof-Kazhdan quantum affine vertex algebra with phi(z2,z0)=z2 e^{z0}.