Affinization of shifted quantum affine $\mathfrak{gl}_2$

Fuente: arXiv
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Autores principales: Feigin, B., Jimbo, M., Mukhin, E.
Formato: Preprint
Publicado: 2025
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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