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

TL;DR

This paper explores the relationship between quantum affine algebras and quantum vertex algebras, introducing $ham$-adic deformations and establishing connections with twisted quantum affine algebras and $$-coordinated modules.

Contribution

It constructs $ham$-adic quantum vertex algebras as deformations of lattice vertex algebras and links twisted quantum affine algebras to equivariant $$-coordinated modules.

Findings

Established $ham$-adic versions of the smash product construction.

Constructed $ham$-adic quantum vertex algebras $V_L[[ham]]^{ eta}$ as deformations of $V_L$.

Connected twisted quantum affine algebras of types A, D, E with $$-coordinated modules.

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 $\eta$.