$h$-adic quantum vertex algebras in types $B$, $C$, $D$ and their $\phi$-coordinated modules

Abstract

We introduce the $h$-adic quantum vertex algebras associated with the trigonometric $R$-matrices in types $B$, $C$ and $D$, thus generalizing the well-known Etingof-Kazhdan construction in type $A$. We show that restricted modules for quantum affine algebras in types $B$, $C$ and $D$ are naturally equipped with the structure of $\phi$-coordinated module for the aforementioned $h$-adic quantum vertex algebras.