Record link: 
http://hdl.handle.net/20.500.12708/192483
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Title: 
An SL₄-web basis from hourglass plabic graphs
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Citation: 
Gaetz, C., Pechenik, O., Pfannerer-Mittas, S. H., Jessica, S., & Swanson, J. P. (2023). An SL₄-web basis from hourglass plabic graphs. In Proceedings of the 35th International Conference on “Formal Power Series and Algebraic Combinatorics.” 35th International Conference on Formal Power Series & Algebraic Combinatorics (FPSAC 2023), Davis, California, United States of America (the). http://hdl.handle.net/20.500.12708/192483
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Publication Type: 
Inproceedings - Full-Paper Contribution
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Language: 
English
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Authors: 
Gaetz, Christian 
Pechenik, Oliver 
Pfannerer-Mittas, Stephan Heinz 
Jessica, Striker 
Swanson, Joshua P. 
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Organisational Unit: 
E104 - Institut für Diskrete Mathematik und Geometrie 
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Published in: 
Proceedings of the 35th International Conference on "Formal Power Series and Algebraic Combinatorics" 
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Volume: 
89B
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Date (published): 
2023
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Event name: 
35th International Conference on Formal Power Series & Algebraic Combinatorics (FPSAC 2023) 
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Event date: 
17-Jul-2023 - 21-Jul-2023
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Event place: 
Davis, California, United States of America (the)
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Number of Pages: 
12
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Keywords: 
web; promotion; plabic graph; alternating sign matrix; six-vertex model
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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.
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Project title: 
Das Phänomen des zyklischen Siebens: P29275-N35 (FWF - Österr. Wissenschaftsfonds) 
Rotationsinvariante diagrammatische Basen für Invariantenräume: 25658 (Österr. Akademie der Wissenschaften) 
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Link (external): 
https://www.mat.univie.ac.at/~slc/
https://www.emis.de/journals/SLC/wpapers/FPSAC2023/9.html
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Research Areas: 
Fundamental Mathematics Research: 100%
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Science Branch: 
1010 - Mathematik: 100%
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