The octahedron recurrence and gl(n) crystals
Combinatorics
2007-05-23 v3 Quantum Algebra
Abstract
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.
Keywords
Cite
@article{arxiv.math/0408114,
title = {The octahedron recurrence and gl(n) crystals},
author = {Andre Henriques and Joel Kamnitzer},
journal= {arXiv preprint arXiv:math/0408114},
year = {2007}
}
Comments
25 pages, 19 figures, counterexample to Yang-Baxter equation added