2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63816Let $\ag$ be an affine Lie algebra, and let $\Ua$ be the quantum affine algebra introduced by Drinfeld and Jimbo. In [Kas94] Kashiwara introduced a $\Ua$-module $V(λ)$, having a global crystal base for an integrable weight $λ$ of level 0. We call it an {\it extremal weight module}. In [\S13]{Kas00} Kashiwara gave a conjecture on the structure of extremal weight modules. We prove his conjecture when $\ag$ is an untwisted affine Lie algebra of a simple Lie algebra $\g$ of type $ADE$, using a result of Beck-Chari-Pressley [BCP].24 pages; Several ref's are addedQuantum Algebra17B37text