Associating modules for the $h$-Yangian and quantum elliptic algebra in type $A$ with $h$-adic quantum vertex algebras
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914229922037760 |
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| author | Bagnoli, Lucia Jing, Naihuan Kožić, Slaven |
| author_facet | Bagnoli, Lucia Jing, Naihuan Kožić, Slaven |
| contents | 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) $ϕ$-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 $\textrm{Y}_h(\mathfrak{gl}_N).$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_00371 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Associating modules for the $h$-Yangian and quantum elliptic algebra in type $A$ with $h$-adic quantum vertex algebras Bagnoli, Lucia Jing, Naihuan Kožić, Slaven Quantum Algebra 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) $ϕ$-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 $\textrm{Y}_h(\mathfrak{gl}_N).$ |
| title | Associating modules for the $h$-Yangian and quantum elliptic algebra in type $A$ with $h$-adic quantum vertex algebras |
| topic | Quantum Algebra |
| url | https://arxiv.org/abs/2601.00371 |