Twisted quantum affine algebras and equivariant $φ$-coordinated modules for quantum vertex algebras

Abstract: This paper is about establishing a natural connection of quantum affine algebras with quantum vertex algebras. Among the main results, we establish $\hbar$-adic versions of the smash product construction of quantum vertex algebras and their $\phi$-coordinated quasi modules, which were obtained before in a sequel, we construct a family of $\hbar$-adic quantum vertex algebras $V_L[[\hbar]]^{\eta}$ as deformations of the lattice vertex algebras $V_L$, and establish a natural connection between twisted quantum affine algebras of type $A, D, E$ and equivariant $\phi$-coordinated quasi modules for the $\hbar$-adic quantum vertex algebras $V_L[[\hbar]]^{\eta}$ with certain specialized $\eta$.