Hall algebras and shifted quantum affine algebras
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909735662387200 |
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| author | Goyal, Pallav Samuelson, Peter |
| author_facet | Goyal, Pallav Samuelson, Peter |
| contents | In \cite{FT19}, Finkelberg and Tsymbaliuk introduced the notion of shifted quantum affine algebras and described their role in the study of quantized Coulomb branches associated to certain 3D $N = 4$ quiver gauge theories. We describe a new geometric construction of a deformation of one of these shifted quantum affine algebras as the Hall algebra of the category of representations of a certain quiver $Q_{\textrm{Rud}}$ (modulo relations). This quiver first arose in the work of Rudakov in the study of the tame blocks of the category of restricted representations of the Lie algebra $\mathfrak{sl}_2(\mathbb{F}_q)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_09405 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hall algebras and shifted quantum affine algebras Goyal, Pallav Samuelson, Peter Representation Theory Quantum Algebra In \cite{FT19}, Finkelberg and Tsymbaliuk introduced the notion of shifted quantum affine algebras and described their role in the study of quantized Coulomb branches associated to certain 3D $N = 4$ quiver gauge theories. We describe a new geometric construction of a deformation of one of these shifted quantum affine algebras as the Hall algebra of the category of representations of a certain quiver $Q_{\textrm{Rud}}$ (modulo relations). This quiver first arose in the work of Rudakov in the study of the tame blocks of the category of restricted representations of the Lie algebra $\mathfrak{sl}_2(\mathbb{F}_q)$. |
| title | Hall algebras and shifted quantum affine algebras |
| topic | Representation Theory Quantum Algebra |
| url | https://arxiv.org/abs/2508.09405 |