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

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.

Quantum vertex algebra ; Double Yangian ; Center at the critical level

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