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Crystal structure of level zero extremal weight modules

Jonathan Beck
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Abstract

We consider the crystal structure of the level zero extremal weight modules $V(λ)$ using the crystal base of the quantum affine algebra constructed by Beck, Chari and Pressley. This approach yields an explicit form for the U^- extremal weight vectors in each connected component of the crystal of $V(λ)$, which are given as Schur functions in the imaginary root vectors. We use this fact to demonstrate Kashiwara's conjectures regarding the crystal structure of $V(λ)$.

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Jonathan Beck. 2002-12-20. Crystal structure of level zero extremal weight modules. https://arxiv.org/abs/math/0205095

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