2025/07/24 by Wen Zhang, Rui Tang, Zhang, Wen Ting +3
Mathematics · #Advanced Algebra and Geometry #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.2507.18432
openalex publication_date 2025/07/24 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28
Gaetz, Pechenik, Pfannerer, Striker, and Swanson introduced the concept of hourglass plabic graphs and provided a method for computing web diagrams and invariants corresponding to 4× n Young tableaux, while Elkin, Musiker, and Wright applied Lam's method to explicitly compute the webs compatible with cluster variables in Gr(3,n) and their twists, namely, the preimages of the immanant map introduced by Fraser, Lam, and Le. In this paper, we use these two methods to compute both the web diagrams and the dual webs corresponding to quadratic and cubic cluster variables in the Grassmannian cluster algebra C[Gr(4,8)].