# $h$-adic quantum vertex algebras associated with rational $R$-matrix in types $B$, $C$ and $D$

## TL;DR

This paper generalizes the construction of $h$-adic quantum vertex algebras from type A to types B, C, and D, and explores their centers and related algebraic structures at the critical level.

## Contribution

It introduces $h$-adic quantum vertex algebras for types B, C, D, extending previous type A results, and constructs their centers and central elements.

## Key findings

- Constructed $h$-adic quantum vertex algebras for types B, C, D.
- Identified algebraically independent generators of the center at the critical level.
- Established commutative subalgebras of dual Yangian and central elements of double Yangian.

## Abstract

We introduce the $h$-adic quantum vertex algebras associated with the rational $R$-matrix in types $B$, $C$ and $D$, thus generalizing the Etingof--Kazhdan's construction in type $A$. Next, we construct the algebraically independent generators of the center of the $h$-adic quantum vertex algebra in type $B$ at the critical level, as well as the families of central elements in types $C$ and $D$. Finally, as an application, we obtain commutative subalgebras of the dual Yangian and the families of central elements of the appropriately completed double Yangian at the critical level, in types $B$, $C$ and $D$.