Recently, J.-B. Bost has introduced a theory of infinite rank metrized lattices and explained their role in diophantine geometry. We will explain how to attach to elements in an affine Kac-Moody group several such lattices as well as some (new?) theta-type functions. We will also try to explain some conjectural relations of this construction to the theory of automorphic forms.

Joint work with Mathieu Dutour.