The octahedron recurrence and gl(n) crystals

Details The octahedron recurrence and gl(n) crystals The octahedron recurrence and gl(n) crystals

2004-08-09

arxiv.org/abs/math/0408114v3

Mathematics

Combinatorics

25 pages, 19 figures, counterexample to Yang-Baxter equation added

Scientific paper

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.

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