The octahedron recurrence and gln crystals

By A. Henriques, Joel Kamnitzer. 2004

47 citations recorded by the source corpus.

Abstract We study the hive model of g l 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 g l 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.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Spectroscopy

View Paper: https://www.semanticscholar.org/paper/0c7722331d29bade424ce25c86c41fb4bbced0ce

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In Discrete Mathematics and Combinatorics

1. Neil O'Connell
2. P. Bougerol
3. Philippe Biane
4. Jim Pitman
5. Ivan Corwin
6. Alexei Borodin
7. Piotr Śniady
8. P. Ferrari

In Geometry and Topology

1. P. Bougerol
2. Neil O'Connell
3. Philippe Biane

In Spectroscopy

1. P. Bougerol
2. Neil O'Connell
3. Philippe Biane

Citations in the corpus

• Continuous crystal and Duistermaat-Heckman measure for Coxeter groups (2008, methodology): “[16] A. Henriques and J. Kamnitzer, Crystals and coboundary categories.”