Extremal weight modules of quantum affine algebras
arXiv:math/0204183
Abstract
Let $\ag$ 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 , having a global crystal base for an integrable weight 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 , using a result of Beck-Chari-Pressley [BCP].
24 pages; Several ref's are added