Comptes Rendus
Symmetries on plabic graphs and associated polytopes
Comptes Rendus. Mathématique, Volume 356 (2018) no. 6, pp. 581-585.

For Grassmann varieties, we explain how the duality between the Gelfand–Tsetlin polytopes and the Feigin–Fourier–Littelmann–Vinberg polytopes arises from different positive structures.

Nous expliquons, pour les variétés grasmanniennes, comment la dualité entre les polytopes de Gelfand–Tsetlin et les polytopes de Feigin–Fourier–Littelman–Vinberg émerge dans différentes structures positives.

Published online:
DOI: 10.1016/j.crma.2018.05.003
Xin Fang 1; Ghislain Fourier 2

1 University of Cologne, Mathematical Institute, Weyertal 86–90, 50931 Cologne, Germany
2 Leibniz Universität Hannover, Institute for Algebra, Number Theory and Discrete Mathematics, Welfengarten 1, 30167 Hannover, Germany
     author = {Xin Fang and Ghislain Fourier},
     title = {Symmetries on plabic graphs and associated polytopes},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {581--585},
     publisher = {Elsevier},
     volume = {356},
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     year = {2018},
     doi = {10.1016/j.crma.2018.05.003},
     language = {en},
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%A Ghislain Fourier
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Xin Fang; Ghislain Fourier. Symmetries on plabic graphs and associated polytopes. Comptes Rendus. Mathématique, Volume 356 (2018) no. 6, pp. 581-585. doi : 10.1016/j.crma.2018.05.003.

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[8] A. Postnikov Total positivity, Grassmannians, and networks | arXiv

[9] A. Postnikov; D. Speyer; L. Williams Matching polytopes, toric geometry, and the non-negative part of the Grassmannian, J. Algebraic Comb., Volume 30 (2009) no. 2, pp. 173-191

[10] K. Rietsch; L. Williams Newton–Okounkov bodies, cluster duality, and mirror symmetry for Grassmannians, 2017 (preprint) | arXiv

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