2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66746We show that untwisted respectively twisted conjugacy classes of a compact and simply connected Lie group which satisfy a certain integrality condition correspond naturally to irreducible highest weight representations of the corresponding affine Lie algebra. Along the way, review the classification of twisted conjugacy classes of a simply connected compact Lie group $G$ and give a description of their stabilizers in terms of the Dynkin diagram of the corresponding twisted affine Lie algebra.15 pages, totally new version, mistake corrected, to appear under the title "Integral conjugacy classes of compact Lie groups" in Manuscripta MathematicaQuantum AlgebraHigh Energy Physics - Theory22E46;22E67;81R10text