Associating deformed $\ddot{I}•$-coordinated modules for the quantum affine vertex algebra with orthogonal twisted $h$-Yangians

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 $\ddot{I}•$-coordinated modules and the ideas from our previous paper, we introduce the notion of deformed $\ddot{I}•$-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 $\ddot{I}•$-coordinated ${\mathcal{V}}^c({\mathfrak{gl}}_N)$-module and demonstrate its applications.

19 pages