Extremal weight modules of quantum affine algebras

Details Extremal weight modules of quantum affine algebras Extremal weight modules of quantum affine algebras

2002-04-14

arxiv.org/abs/math/0204183v2

Mathematics

Quantum Algebra

24 pages; Several ref's are added

Scientific paper

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 $V(\lambda)$, having a global crystal base for an integrable weight $\lambda$ 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].

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