Shifted quantum groups, cluster algebras and geometric character formulas

Algebra, Geometry and Topology Seminar

Shifted quantum groups emerged from the study of quantized Coulomb branches (which are symplectic duals to quiver varieties). We show that the Grothendieck ring of the category O for the shifted quantum affine algebras has the structure of a cluster algebra (jt work with Geiss and Leclerc). This has several applications, such as geometric character formulas for simple classes corresponding to cluster variables.