Cyclic sieving and cluster duality of Grassmannian

DOI10.3842/SIGMA.2020.067zbMath1471.13048arXiv1803.06901MaRDI QIDQ784867

Daping Weng, Linhui Shen

Publication date: 3 August 2020

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1803.06901

zbMATH Keywords

mirror symmetryGrassmanniancluster algebracyclic sieving phenomenoncluster duality

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Grassmannians, Schubert varieties, flag manifolds (14M15) Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) (14N35) Applications of deformations of analytic structures to the sciences (32G81) Cluster algebras (13F60) Mirror symmetry (algebro-geometric aspects) (14J33) Tropical geometry (14T99)

Related Items

Minuscule analogues of the plane partition periodicity conjecture of Cameron and Fon-Der-Flaass, Microlocal theory of Legendrian links and cluster algebras, The valuation pairing on an upper cluster algebra, Cyclic sieving, skew Macdonald polynomials and Schur positivity, Quantum affine algebras and Grassmannians, Cyclic sieving for plane partitions and symmetry, Restriction of global bases and Rhoades's theorem, Cluster Structures on Double Bott–Samelson Cells, Donaldson-Thomas transformation of Grassmannian, Parity-Unimodality and a Cyclic Sieving Phenomenon for Necklaces, A survey on maximal green sequences, Newton-Okounkov bodies, cluster duality, and mirror symmetry for Grassmannians, Infinitely many Lagrangian fillings, Minuscule Doppelgängers, The Coincidental down-Degree Expectations Property, and Rowmotion

Cites Work

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• 2-frieze patterns and the cluster structure of the space of polygons
• Completeness of determinantal Hamiltonian flows on the matrix affine Poisson space
• Geometry of canonical bases and mirror symmetry
• Cyclic sieving, promotion, and representation theory
• Donaldson-Thomas transformations of moduli spaces of G-local systems
• Paths to understanding birational rowmotion on products of two chains
• Cluster algebras. III: Upper bounds and double Bruhat cells.
• The cyclic sieving phenomenon
• The periodicity conjecture for pairs of Dynkin diagrams
• Combinatorial, piecewise-linear, and birational homomesy for products of two chains
• Cyclic sieving for plane partitions and symmetry
• Newton-Okounkov bodies, cluster duality, and mirror symmetry for Grassmannians
• The \(B\)-model connection and mirror symmetry for Grassmannians
• Cyclic sieving, rotation, and geometric representation theory
• Stasheff polytopes and the coordinate ring of the cluster \(\mathcal X\)-variety of type \(A_n\)
• Twists of Plücker coordinates as dimer partition functions
• Gravitational Quantum Cohomology
• Cluster algebras I: Foundations
• Dynamical algebraic combinatorics and the homomesy phenomenon
• The cyclic sieving phenomenon: a survey
• Canonical bases for cluster algebras
• Birational geometry of cluster algebras
• GRASSMANNIANS AND CLUSTER ALGEBRAS
• Cluster ensembles, quantization and the dilogarithm
• Donaldson-Thomas transformation of double bruhat cells in semisimple Lie groups
• On tropical dualities in cluster algebras