Divergent extended geometrically finite representations via flows

The notion of extended geometrically finite representations introduced by Weisman generalizes Anosov representations by studying the convergence dynamics on group boundary extensions. We prove that divergent, extended geometrically finite representations can be interpreted as admitting dominated splitting over certain flow spaces. In particular, we provide an example of such representation constructed by Tholozan–Wang in the study of simple Anosov representations.