The octahedron recurrence and gl(n) crystals

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We study the hive model of gl(n) tensor products, following Knutson, Tao, and Woodward. We define a coboundary category where the tensor product is given by hives and where the associator and commutor are defined using a modified octahedron recurrence. We then prove that this category is equivalent to the category of crystals for the Lie algebra gl(n). The proof of this equivalence uses a new connection between the octahedron recurrence and the Jeu de Taquin and Schutzenberger involution procedures on Young tableaux.
25 pages, 19 figures, counterexample to Yang-Baxter equation added

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Combinatorics, Quantum Algebra

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http://salesiana.dossiersoluciones.com/handle/123456789/72140

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0408114
 http://arxiv.org/abs/math/0408114

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arXiv