Cyclic Sieving and Cluster Duality of Grassmannian

We introduce a decorated configuration space Confˣₙ(𝑎) with a potential function 𝒲. We prove the cluster duality conjecture of Fock-Goncharov for Grassmannians, that is, the tropicalization of (Confˣₙ(𝑎), 𝒲) canonically parametrizes a linear basis of the homogeneous coordinate ring of the Grassmanni...

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Бібліографічні деталі
Опубліковано в: :Symmetry, Integrability and Geometry: Methods and Applications
Дата:2020
Автори: Shen, Linhui, Weng, Daping
Формат: Стаття
Мова:Англійська
Опубліковано: Інститут математики НАН України 2020
Онлайн доступ:https://nasplib.isofts.kiev.ua/handle/123456789/210781
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:Cyclic Sieving and Cluster Duality of Grassmannian. Linhui Shen and Daping Weng. SIGMA 16 (2020), 067, 41 pages

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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Резюме:We introduce a decorated configuration space Confˣₙ(𝑎) with a potential function 𝒲. We prove the cluster duality conjecture of Fock-Goncharov for Grassmannians, that is, the tropicalization of (Confˣₙ(𝑎), 𝒲) canonically parametrizes a linear basis of the homogeneous coordinate ring of the Grassmannian Grₐ(n) with respect to the Plücker embedding. We prove that (Confˣₙ(𝑎), 𝒲) is equivalent to the mirror Landau-Ginzburg model of the Grassmannian considered by Eguchi-Hori-Xiong, Marsh-Rietsch, and Rietsch-Williams. As an application, we show a cyclic sieving phenomenon involving plane partitions under a sequence of piecewise-linear toggles.
ISSN:1815-0659