2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/166848We study the structure of the category of integrable level zero representations with finite dimensional weight spaces of affine Lie algebras. We show that this category possesses a weaker version of the finite length property, namely that an indecomposable object has finitely many simple constituents which are non-trivial as modules over the corresponding loop algebra. Moreover, any object in this category is a direct sum of indecomposables only finitely many of which are non-trivial. We obtain a parametrization of blocks in this category.17 pages; referee's suggestions incorporated; main result extends to non-simply laced caseRepresentation Theory17B37text