A note on constructing quasi modules for quantum vertex algebras from twisted Yangians

In this note, we consider the twisted Yangians $\text{Y}({\mathfrak{g}}_N)$ associated with the orthogonal and symplectic Lie algebras ${\mathfrak{g}}_N={\mathfrak{o}}_N,{\mathfrak{s}\mathfrak{p}}_N$. First, we introduce a certain subalgebra ${\text{A}}_c({\mathfrak{g}}_N)$ of the double Yangian for ${\mathfrak{g}\mathfrak{l}}_N$ at the level $c\in \mathbb{C}$, which contains the centrally extended $\text{Y}({\mathfrak{g}}_N)$ at the level $c$ as well as its vacuum module ${\mathcal{M}}_c({\mathfrak{g}}_N)$. Next, we employ its structure to construct examples of quasi modules for the quantum affine vertex algebra ${\mathcal{V}}_c({\mathfrak{g}\mathfrak{l}}_N)$ associated with the Yang $R$-matrix. Finally, we use the description of the center of ${\mathcal{V}}_c({\mathfrak{g}\mathfrak{l}}_N)$ to obtain explicit formulae for families of central elements for a certain completion of ${\text{A}}_c({\mathfrak{g}}_N)$ and invariants of ${\mathcal{M}}_c({\mathfrak{g}}_N)$.