Rigidity of Iwasawa nilpotent Lie groups via Tanaka's theory

We provide a new proof to the known result on rigidity of Iwasawa nilpotent Lie groups with respect to the contact structure endowed by the root space decomposition. More precisely, we use Tanaka’s prolongation theory for establishing the rigidity type of those nilpotent groups. This note aims to complement another article from the same authors, where we use the point of view of Tanaka prolongations for studying rigidity in the general setting of nilpotent stratified Lie groups. When the group is of Iwasawa type, a special formalism occurs, which is related to the theory of semisimple Lie groups, namely the formalism of root systems. We use this language in order to classify the rigidity types.