Abstract We show that real semi-simple Lie groups of higher rank contain (infinitely generated) discrete subgroups with full limit sets in the corresponding Furstenberg boundaries. Additionally, we provide criteria under which discrete subgroups of G = SL (3, R) must have a full limit set in the Furstenberg boundary of G. In the appendix, we show the existence of Zariski-dense discrete subgroups of SL (n, R), where n 3, such that the Jordan projection of some loxodromic element lies on the boundary of the limit cone of.
Dey et al. (2025) studied this question.