Anosov groups that are indiscrete in rank one

Abstract

Abstract We exhibit Anosov subgroups of $\mathsf{SL}_{d}(\mathbb{R})$ that do not embed discretely in any rank-$1$ simple Lie group of noncompact type, or indeed, in any finite product of such Lie groups. These subgroups are isomorphic to free products $\Gamma * \Delta $, where $\Gamma $ is a uniform lattice in $\textsf{F}_{4}^{(-20)}$ and $\Delta $ is a uniform lattice in $\textsf{Sp}(m,1)$, $m \geq 51$.