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arXiv · 2601.00371

Associating modules for the $h$-Yangian and quantum elliptic algebra in type $A$ with $h$-adic quantum vertex algebras

Lucia Bagnoli·Naihuan Jing·Slaven Kožić
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Abstract

We consider the Etingof-Kazhdan quantum vertex algebra $\mathcal{V}^c(R)$ associated with the trigonometric and elliptic $R$-matrix of type $A.$ We establish a connection between (restricted) modules for the $h$-Yangian $\textrm{Y}_h(\mathfrak{gl}_N)$ and the elliptic quantum algebra $\mathcal{A}_{h,p}(\widehat{\mathfrak{gl}}_2)$ of level zero, and deformed (twisted) $\phi$-coordinated $\mathcal{V}^c(R)$-modules. As its application, in the trigonometric case, we construct new families of central elements of $\mathcal{V}^c(R)$ at the critical level $c=-N,$ which we then use to derive commutative families in the $h$-Yangian $\textrm{Y}_h(\mathfrak{gl}_N).$

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Lucia Bagnoli, Naihuan Jing, Slaven Kožić. 2026-01-01. Associating modules for the $h$-Yangian and quantum elliptic algebra in type $A$ with $h$-adic quantum vertex algebras. https://arxiv.org/abs/2601.00371

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