ARTIN Workshop

Résumé

Quantum affine algebras are quantum groups with a rich representation theory which has been extensively studied from various points of view. In particular, the Grothendieck rings of certain categories of finite dimensional representations have remarkable $t$-deformations, initially defined using the geometry of quiver varieties. More recently, the theory of cluster algebras gave a new combinatorial approach to the study of representations of quantum affine algebras. In this talk, we will see how one can use $t$-deformations of cluster algebras, called quantum cluster algebras, to recovers and extends results obtained geometrically.