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.
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.
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@article{CRMATH_2018__356_6_581_0, author = {Fang, Xin and Fourier, Ghislain}, title = {Symmetries on plabic graphs and associated polytopes}, journal = {Comptes Rendus. Math\'ematique}, pages = {581--585}, publisher = {Elsevier}, volume = {356}, number = {6}, year = {2018}, doi = {10.1016/j.crma.2018.05.003}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2018.05.003/} }
TY - JOUR AU - Fang, Xin AU - Fourier, Ghislain TI - Symmetries on plabic graphs and associated polytopes JO - Comptes Rendus. Mathématique PY - 2018 SP - 581 EP - 585 VL - 356 IS - 6 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2018.05.003/ DO - 10.1016/j.crma.2018.05.003 LA - en ID - CRMATH_2018__356_6_581_0 ER -
%0 Journal Article %A Fang, Xin %A Fourier, Ghislain %T Symmetries on plabic graphs and associated polytopes %J Comptes Rendus. Mathématique %D 2018 %P 581-585 %V 356 %N 6 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2018.05.003/ %R 10.1016/j.crma.2018.05.003 %G en %F CRMATH_2018__356_6_581_0
Fang, Xin; Fourier, Ghislain. Symmetries on plabic graphs and associated polytopes. Comptes Rendus. Mathématique, Tome 356 (2018) no. 6, pp. 581-585. doi : 10.1016/j.crma.2018.05.003. http://archive.numdam.org/articles/10.1016/j.crma.2018.05.003/
[1] Gelfand–Tsetlin polytopes and Feigin–Fourier–Littelmann–Vinberg polytopes as marked poset polytopes, J. Comb. Theory, Ser. A, Volume 118 (2011) no. 8, pp. 2454-2462
[2] Polytopes arising from mirror plabic graphs, Oberwolfach Rep., Volume 13 (2016) no. 1, pp. 626-628
[3] PBW filtration and bases for irreducible modules in type , Transform. Groups, Volume 16 (2011) no. 1, pp. 71-89
[4] Finite-dimensional representations of the group of unimodular matrices, Dokl. Akad. Nauk SSSR (N.S.), Volume 71 (1950), pp. 825-828
[5] Newton–Okounkov bodies, semigroups of integral points, graded algebras and intersection theory, Ann. of Math. (2), Volume 176 (2012) no. 2, pp. 925-978
[6] On cluster theory and quantum dilogarithm identities, Representations of Algebras and Related Topics, EMS Ser. Congr. Rep., Eur. Math. Soc., Zürich, Switzerland, 2011, pp. 85-116
[7] Convex bodies associated to linear series, Ann. Sci. Éc. Norm. Supér. (4), Volume 42 (2009), pp. 783-835
[8] Total positivity, Grassmannians, and networks | arXiv
[9] Matching polytopes, toric geometry, and the non-negative part of the Grassmannian, J. Algebraic Comb., Volume 30 (2009) no. 2, pp. 173-191
[10] Newton–Okounkov bodies, cluster duality, and mirror symmetry for Grassmannians, 2017 (preprint) | arXiv
[11] Two poset polytopes, Discrete Comput. Geom., Volume 1 (1986) no. 1, pp. 9-23
[12] A formula for Plücker coordinates associated with a planar network, Int. Math. Res. Not. (2008) (rnn-081)
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