LAUSR

We consider the quantum affine vertex algebra $${\mathcal{V}_{c}(\mathfrak{gl}_N)}$$Vc(glN) associated with the rational R-matrix, as defined by Etingof and Kazhdan. We introduce certain subalgebras $${\textrm{A}_c (\mathfrak{gl}_N)}$$Ac(glN) of the completed double Yangian $${\widetilde{\textrm{DY}}_{c}(\mathfrak{gl}_N)}$$DY~c(glN) at the level $${c\in\mathbb{C}}$$c∈C, associated with the reflection equation, and we employ their structure to construct examples of quasi $${\mathcal{V}_{c}(\mathfrak{gl}_N)}$$Vc(glN)-modules. Finally, we use the quasi module map, together with the explicit description of the center of $${\mathcal{V}_{c}(\mathfrak{gl}_N)}$$Vc(glN), to obtain formulae for families of central elements in the completed algebra $${\widetilde{\textrm{A}}_c (\mathfrak{gl}_N)}$$A~c(glN).