Cyclic Sieving and Cluster Duality of Grassmannian

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2020
• Main Authors: Shen, Linhui, Weng, Daping
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2020
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/210781
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Cyclic Sieving and Cluster Duality of Grassmannian. Linhui Shen and Daping Weng. SIGMA 16 (2020), 067, 41 pages

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...