Fusion and specialization for type ADE shuffle algebras

Abstract: Root vectors in quantum groups (of finite type) generalize to fused currents in quantum loop groups ([5]). In the present paper, we construct fused currents as duals to specialization maps of the corresponding shuffle algebras ([7,8,9]) in types ADE. Both root vectors and fused currents depend on a convex order of the positive roots, and the choice we make in the present paper is that of the Auslander-Reiten order ([24]) corresponding to an orientation of the type ADE Dynkin diagram.