论文标题
Leclerc在A型A型群集结构上的猜想
Leclerc's conjecture on a cluster structure for type A Richardson varieties
论文作者
论文摘要
Leclerc使用群集类别在Richardson品种上构建了一个猜想的集群结构。我们表明，在A型中，他的猜想群集结构实际上是一个集群结构。我们通过将Leclerc的构造与A型A型Richardson品种的另一个集群结构进行比较来做到这一点。 Ingermanson的构造使用了接线图和Deodhar分层的组合。尽管两个集群结构的定义非常不同，但我们表明，砂晶组的重合和簇与Galashin-Lam最近定义的Richardson品种的Twist Map相关。
Leclerc constructed a conjectural cluster structure on Richardson varieties in simply laced types using cluster categories. We show that in type A, his conjectural cluster structure is in fact a cluster structure. We do this by comparing Leclerc's construction with another cluster structure on type A Richardson varieties due to Ingermanson. Ingermanson's construction uses the combinatorics of wiring diagrams and the Deodhar stratification. Though the two cluster structures are defined very differently, we show that the quivers coincide and clusters are related by the twist map for Richardson varieties, recently defined by Galashin--Lam.
