Cluster automorphism group of braid varieties

2025/05/20 by Kim, Soyeon · 1 citation
#Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2505.14889

Abstract

The cluster automorphism group of a cluster variety was defined by Gekhtman--Shapiro--Vainshtein, and later studied by Lam--Speyer. Braid varieties are interesting affine algebraic varieties indexed by positive braid words. It was proved recently that braid varieties are cluster varieties. In this paper, we propose a description of the cluster automorphism group and its action on braid varieties, and compute several examples.

Citations

• Legendrian loops and cluster modular groups
• Cluster deep loci and mirror symmetry
• Braid variety cluster structures, II: general type
• Braid variety cluster structures, I: 3D plabic graphs
• Plabic links, quivers, and skein relations
• Cluster structures on braid varieties
• Positroids, knots, and q,t-Catalan numbers
• Algebraic Weaves and Braid Varieties
• Positroid varieties and cluster algebras
• Cluster algebra structures on Poisson nilpotent algebras
• Quasi-homomorphisms of cluster algebras
• Cluster algebras: an introduction
• Moduli spaces of local systems and higher Teichmuller theory
• Grassmannians and Cluster Algebras
• Cluster algebras and Poisson geometry
• Cluster algebras I: Foundations

Cited by

• Bruhat intervals that are large hypercubes

Related

• Braid variety cluster structures, II: general type
• Cluster structures on braid varieties
• Comparing cluster algebras on braid varieties
• Braid group symmetries of Grassmannian cluster algebras
• Splicing braid varieties