2004/08/09 by André Henriques, Andre Henriques, Joel Kamnitzer +2 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Quantum Algebra (math.QA) #math.CO #math.QA
paper · pdf · doi:10.48550/arxiv.math/0408114
25 pages, 19 figures, counterexample to Yang-Baxter equation added
openalex publication_date 2004/08/09 · arxiv created 2005/06/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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.