Crystal structure of level zero extremal weight modules

2002/05/09 by Jonathan Beck, Beck, Jonathan
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Rings, Modules, and Algebras #math.QA

paper · pdf · doi:10.48550/arxiv.math/0205095

8 pages, final version

openalex publication_date 2002/05/09 · arxiv created 2002/12/20 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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