Extremal weight modules of quantum affine algebras

By H. Nakajima. 2002

63 citations recorded by the source corpus.

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].

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/05d7f30d65fe91496a81090ede72fb3698b322ee

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Citations in the corpus

Level Zero Fundamental Representations over Quantized Affine Algebras and Demazure Modules (2003, result): “The following theorem is trivial for non-zero level case, and proved in [21, 2] by Nakajima and Beck-Nakajima for the zero level case.”
Weyl modules, Demazure modules, KR-modules, crystals, fusion products and limit constructions (2005, result): “The results of Beck and Nakajima [2,36,37] imply that these quotients (and hence their specializations) have the correct dimension.”
BGG reciprocity for current algebras (2011, background): “It can also be deduced from the quantum case through the work of [4], [22] and [25].”