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

Abstract

We introduce the $h$-adic quantum vertex algebras associated with the rational $R$-matrix in types $B$, $C$ and $D$, thus generalizing the 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 $D$.

arXiv comment27 pages

References in corpus (7)

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• Feigin-Frenkel center in types B, C and D
• On quantum vertex algebras and their modules
• Isomorphism between the $R$-matrix and Drinfeld presentations of Yangian in types $B$, $C$ and $D$
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Cited by in corpus (6)

• On the structure of quantum vertex algebras
• Quantum affine vertex algebras associated to untwisted quantum affinization algebras
• On the quantum affine vertex algebra associated with trigonometric $R$-matrix
• $h$-adic quantum vertex algebras in types $B$, $C$, $D$ and their $\varphi$-coordinated modules
• Yangian deformations of $\mathcal{S}$-commutative quantum vertex algebras and Bethe subalgebras
• A note on constructing quasi modules for quantum vertex algebras from twisted Yangians