Crystal structure of level zero extremal weight modules

Details Crystal structure of level zero extremal weight modules Crystal structure of level zero extremal weight modules

2002-05-09

arxiv.org/abs/math/0205095v2

Mathematics

Quantum Algebra

8 pages, final version

Scientific paper

We consider the crystal structure of the level zero extremal weight modules $V(\lambda)$ 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 $V(\lambda)$, 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 $V(\lambda)$.

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