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arXiv · 2604.12842

Evaluation-type deformed modules over the quantum affine vertex algebras of type $A$

Lucia Bagnoli·Slaven Kožić
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Abstract

Let $\mathcal{V}^c(\mathfrak{gl}_N)$ be Etingof-Kazhdan's quantum affine vertex algebra associated with the trigonometric $R$-matrix. We establish a connection between suitably generalized deformed $ϕ$-coordinated $\mathcal{V}^c(\mathfrak{gl}_N)$-modules and the representations of quantized enveloping algebra $U_h(\mathfrak{gl}_N)$ and reflection equation algebra $\mathcal{O}_h(Mat_N)$. As an application, we demonstrate how the elements of the center of $\mathcal{V}^c(\mathfrak{gl}_N)$ at the critical level $c=-N$ give rise to the $q$-analogues of quantum immanants for $U_h(\mathfrak{gl}_N)$, which were recently found by Jing, Liu and Molev. Finally, we derive the analogues of these results for the quantum affine vertex algebra associated with the normalized Yang $R$-matrix.

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Lucia Bagnoli, Slaven Kožić. 2026-09-20. Evaluation-type deformed modules over the quantum affine vertex algebras of type $A$. https://arxiv.org/abs/2604.12842

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