Hall algebras and shifted quantum affine algebras

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