论文标题
编织品种的簇结构
Cluster structures on braid varieties
论文作者
论文摘要
对于任何简单的谎言组，我们都显示了群集$ \ MATHCAL {A} $ - 结构和群集Poisson结构的存在。该结构是通过编织微积分和Lusztig坐标的热带化实现的。提供了几种明确的种子，并且Quiver和cluster变量很容易计算。我们证明，这些上层群集代数等于它们的群集代数，显示局部的无环，并明确确定其DT变换为编织品种的扭曲自动形态。主要结果还解决了B. leclerc对开放式理查森品种的坐标环上存在的群集代数结构的猜想。
We show the existence of cluster $\mathcal{A}$-structures and cluster Poisson structures on any braid variety, for any simple Lie group. The construction is achieved via weave calculus and a tropicalization of Lusztig's coordinates. Several explicit seeds are provided and the quiver and cluster variables are readily computable. We prove that these upper cluster algebras equal their cluster algebras, show local acyclicity, and explicitly determine their DT-transformations as the twist automorphisms of braid varieties. The main result also resolves the conjecture of B. Leclerc on the existence of cluster algebra structures on the coordinate rings of open Richardson varieties.
