2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63908The category of finite dimensional (type 1) representations of a quantum affine algebra $U_q(\hat{\mathfrak g})$ is not semisimple. However, as any abelian category with finite-length objects, it admits a unique decomposition into a direct sum of indecomposable subcategorie (blocks). We define the elliptic central character of a finite dimensional (type 1) representation of $U_q(\hat{\mathfrak g})$. Then we show that the block decomposition of this category is paramentrized by these elliptic central characters.28 pagesQuantum AlgebraRepresentation Theory17B37; 20G42text