Deformed quantum vertex algebra modules associated with braidings

TL;DR

This paper introduces deformed quantum vertex algebra modules linked to braiding maps, constructs specific families over quantum vertex algebras, and explores their applications to Yangians and reflection algebras.

Contribution

It presents a novel framework for deformed modules associated with braidings and constructs explicit examples over quantum vertex algebras of classical types.

Findings

Constructed two families of braiding maps for quantum vertex algebras.

Analyzed properties of the deformed modules.

Applied the modules to Yangians and reflection algebras.

Abstract

We introduce the notion of deformed quantum vertex algebra module associated with a braiding map. We construct two families of braiding maps over the Etingof-Kazhdan quantum vertex algebras associated with the rational $R$-matrices of classical types. We investigate their properties and demonstrate the applications of the corresponding deformed modules to the (generalized) Yangians and reflection algebras.