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

TL;DR

This paper extends the theory of $h$-adic quantum vertex algebras to types $B$, $C$, and $D$, connecting them with quantum affine algebras and their modules, generalizing known constructions from type $A$.

Contribution

It introduces $h$-adic quantum vertex algebras for types $B$, $C$, and $D$, and links these structures to modules of quantum affine algebras in these types.

Findings

Construction of $h$-adic quantum vertex algebras for types $B$, $C$, $D$

Restricted modules for quantum affine algebras are $$-coordinated modules

Generalization of Etingof-Kazhdan construction to non-$A$ types

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.