2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/72140We 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 addedCombinatoricsQuantum Algebratext