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arXiv · 1904.03771

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

Marijana Butorac·Naihuan Jing·Slaven Kožić
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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 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 $D$.

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Marijana Butorac, Naihuan Jing, Slaven Kožić. 2019-04-07. $h$-adic quantum vertex algebras associated with rational $R$-matrix in types $B$, $C$ and $D$. https://doi.org/10.1007/s11005-019-01199-3

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