2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68771A proof of Thompson's conjecture for real semi-simple Lie groups has been given by Kapovich, Millson, and Leeb. In this note, we give another proof of the conjecture by using a theorem of Alekseev, Meinrenken, and Woodward from symplectic geometry.18 pages, LaTeXSymplectic GeometryRepresentation Theorytext