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arXiv · 2508.09405

Hall algebras and shifted quantum affine algebras

Pallav Goyal·Peter Samuelson
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Abstract

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 $\mathfrak{sl}_2(\mathbb{F}_q)$.

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Pallav Goyal, Peter Samuelson. 2025-08-13. Hall algebras and shifted quantum affine algebras. https://arxiv.org/abs/2508.09405

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