Littelmann's path crystal and combinatorics of certain integrable slℓ+1 modules of level zero

2002/06/30 by Jacob Greenstein
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #math.QA

paper · pdf · doi:10.1016/s0021-8693(03)00304-1

published as J. Algebra, 269 (2003), no. 1, 347-372 · 25 pages, AMSLaTeX; to appear in the "Journal of Algebra"

arxiv created 2002/09/04 · openalex publication_date 2003/05/27 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We construct a subcrystal of the Littelmann's path crystal whose formal character coincides with that of a certain simple integrable module of level zero over the untwisted affine Lie algebra associated to sl_n. We also establish an analogue of the Littlewood-Richardson rule for the tensor product of that crystal with a highest weight crystal.

Citations

• Quantum loop modules

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