2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/163091Every finite dimensional real representation of a compact real semisimple Lie algebra determines a metric 2-step nilpotent Lie algebra and a corresponding simply connected metric 2-step nilpotent Lie group N. We study the differential geometry of N using representation theory of the complexified complex semisimple Lie algebra.54 pagesDifferential Geometry53C30;22E25;22E46text