Séminaire Lotharingien de Combinatoire, 89B.9 (2023), 12 pp.
Christian Gaetz, Oliver Pechenik, Stephan Pfannerer,
Jessica Striker, and Joshua P. Swanson
An SL4-Web Basis from Hourglass Plabic Graphs
Abstract.
We introduce hourglass plabic graphs and prove that certain of these graphs index a rotation-invariant SL4-web basis, a structure that has been sought since Kuperberg's introduction of the SL3-web basis in 1996. These graphs exhibit connections to the combinatorics of standard Young tableaux, crystals, alternating sign matrices, six-vertex configurations, and plane partitions.
Received: November 15, 2022.
Accepted: February 20, 2023.
Final version: April 1, 2023.
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