2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78679A notion of generalized highest weight modules over the high rank Virasoro algebras is introduced, and a theorem, which was originally given as a conjecture by Kac over the Virasoro algebra, is generalized. Mainly, we prove that a simple Harish-Chandra module over a high rank Virasoro algebra is either a generalized highest weight module, or a module of the intermediate series.16 pages, LatexRepresentation TheoryMathematical Physicstext