Cluster algebras and quantum affine Kac-Moody algebras

David Hernandez

This is a joint work with B. Leclerc. In the general framework of monoidal categorification of cluster algebras, we present results related to the representation theory of quantum affine Kac-Moody algebras. In particular we establish relations in the Grothendieck ring of finite dimensional representations of quantum affine algebras predicted from exchange relations in cluster algebras.