Affinization of shifted quantum affine $\mathfrak{gl}_2$
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915620339056640 |
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| author | Feigin, B. Jimbo, M. Mukhin, E. |
| author_facet | Feigin, B. Jimbo, M. Mukhin, E. |
| contents | We give a realization $\mathcal{A}_0$ of quantum toroidal algebra associated to $\mathfrak{gl}_2$ which can be viewed as an affinization of the Drinfeld new realization of quantum affine $\mathfrak{gl}_2$. We use this realization to define an affinization $\mathcal{A}_N$, $N\in{\mathbb Z}$, of shifted quantum affine $\mathfrak{gl}_2$. We construct a large family of representations of dominantly shifted algebra $\mathcal A_N$, $N>0$. The examples of representations with even positive $N$ appear in the study of extensions of deformed $W$-algebras of type $\mathfrak{gl}(N+2|1)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_12178 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Affinization of shifted quantum affine $\mathfrak{gl}_2$ Feigin, B. Jimbo, M. Mukhin, E. Quantum Algebra Mathematical Physics We give a realization $\mathcal{A}_0$ of quantum toroidal algebra associated to $\mathfrak{gl}_2$ which can be viewed as an affinization of the Drinfeld new realization of quantum affine $\mathfrak{gl}_2$. We use this realization to define an affinization $\mathcal{A}_N$, $N\in{\mathbb Z}$, of shifted quantum affine $\mathfrak{gl}_2$. We construct a large family of representations of dominantly shifted algebra $\mathcal A_N$, $N>0$. The examples of representations with even positive $N$ appear in the study of extensions of deformed $W$-algebras of type $\mathfrak{gl}(N+2|1)$. |
| title | Affinization of shifted quantum affine $\mathfrak{gl}_2$ |
| topic | Quantum Algebra Mathematical Physics |
| url | https://arxiv.org/abs/2511.12178 |