*h*-Adic quantum vertex algebras associated with rational *R*-matrix in types *B*, *C* and *D*

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## Abstract

We introduce the *h*-adic quantum vertex algebras associated with the rational *R*-matrix in types *B*, *C* and *D*, thus generalizing Etingof–Kazhdan’s construction in type *A*. Next, we construct the algebraically independent generators of the center of the *h*-adic quantum vertex algebra in type *B* at the critical level, as well as the families of central elements in types *C* and *D*. Finally, as an application, we obtain commutative subalgebras of the dual Yangian and the families of central elements of the appropriately completed double Yangian at the critical level, in types *B*, *C* and *D*.

## Keywords

Quantum vertex algebra Double Yangian Center at the critical level## Mathematics Subject Classification

17B37 17B69## Notes

### Acknowledgements

The first author is partially supported by the QuantiXLie Centre of Excellence, a project cofinanced by the Croatian Government and European Union through the European Regional Development Fund—the Competitiveness and Cohesion Operational Programme (Grant KK.01.1.1.01.0004). The second author is supported by Simons Foundation Grant No. 523868 and National Natural Science Foundation of China Grant No. 11531004. The part of the research was carried out during the second author’s visit to the Department of Mathematics at the Faculty of Science, University of Zagreb. He would like to thank the Department for the hospitality during his visit.

### Compliance with ethical standards

### Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

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