Associating deformed $\phi$-coordinated modules for the quantum affine vertex algebra with orthogonal twisted $h$-Yangians

TL;DR

This paper introduces deformed $$-coordinated modules for quantum affine vertex algebras and connects them to orthogonal twisted $h$-Yangians, expanding the algebraic framework and applications.

Contribution

It defines deformed $$-coordinated modules for quantum vertex algebras and links them to orthogonal twisted $h$-Yangians, providing new algebraic structures and insights.

Findings

Orthogonal twisted $h$-Yangians can be structured as deformed $$-coordinated modules.

The framework applies to restricted modules of generalized orthogonal twisted $h$-Yangians.

New applications of deformed $$-coordinated modules in quantum algebra are demonstrated.

Abstract

We consider the Etingof-Kazhdan quantum vertex algebra $\mathcal{V}^c(\mathfrak{gl}_N)$ associated with the trigonometric $R$-matrix of type $A$. By combining Li's theory of $\phi$-coordinated modules and the ideas from our previous paper, we introduce the notion of deformed $\phi$-coordinated quantum vertex algebra module. We show that the orthogonal twisted $h$-Yangians and restricted modules for the generalized orthogonal twisted $h$-Yangians can be equipped with the structure of (truncated) deformed $\phi$-coordinated $\mathcal{V}^c(\mathfrak{gl}_N)$-module and demonstrate its applications.