Simple gradable $\mathbb{C}[\mathtt{h}]$-torsion free ${\mathfrak{sl}}_2$-modules

Abstract

We give an explicit classification as well as an explicit construction of simple ${\mathfrak{sl}}_2$-modules that are torsion-free of finite rank with respect to the action of the Cartan subalgebra and which admit a grading by a finite cyclic group corresponding to the rank of the module.