Twisted quantum affine algebras and equivariant $\varphi$-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 $\hslash$-adic versions of the smash product construction of quantum vertex algebras and their $\varphi$-coordinated quasi modules, which were obtained before in a sequel, we construct a family of $\hslash$-adic quantum vertex algebras $V_L[[\hslash ]{]}^{\eta }$ 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 $\varphi$-coordinated quasi modules for the $\hslash$-adic quantum vertex algebras $V_L[[\hslash ]{]}^{\eta }$ with certain specialized $\eta$.