2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/105020We prove that an irreducible quasifinite module over the central extension of the Lie algebra of $N\times N$-matrix differential operators on the circle is either a highest or lowest weight module or else a module of the intermediate series. Furthermore, we give a complete classification of indecomposable uniformly bounded modules.LaTeX, 10 pagesRepresentation TheoryQuantum Algebra17B10; 17B65; 17B66; 17B68text