Work

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

Year: 2026

Type: article

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.

Source: JoNAS - Journal of Non-Associative Structures

DOI: 10.46298/jonas.18022

Authors: Lucia Bagnoli, Slaven Kožić

Institutions: University of Zagreb, Sapienza University of Rome

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid