2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/228080The based loop space homology of a special family of homogeneous spaces, flag manifolds of connected compact Lie groups is studied. First, the rational homology of the based loop space on a complete flag manifold is calculated together with its Pontrjagin structure. Second, it is shown that the integral homology of the based loop space on a flag manifold is torsion free. This results in a description of the integral homology. In addition, the integral Pontrjagin structure is determined.revised version, 17 pages, to appear in Osaka Journal of MathematicsAlgebraic TopologyGeometric Topology57T20, 55P62 (Primary) 55P35, 57T35 (Secondary)text