Rigidity of Iwasawa nilpotent Lie groups via Tanaka’s theory

Abstract

We provide a new proof to the known result on rigidity of Iwasawa nilpotent Lie groups [5, 12]. More precisely, we use Tanaka’s prolongation theory for establishing the rigidity type of those nilpotent groups. This note aims to complement [8], 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.