Article ID Journal Published Year Pages File Type
4668125 Advances in Mathematics 2006 39 Pages PDF
Abstract

We study the hive model of gln 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 gln. The proof of this equivalence uses a new connection between the octahedron recurrence and the Jeu de Taquin and Schützenberger involution procedures on Young tableaux.

Related Topics
Physical Sciences and Engineering Mathematics Mathematics (General)