标题： 剪接偏斜形状的正向矩阵 显示英文标题

标题： Splicing skew shaped positroids

摘要： 斜形状正向簇（或斜形状正向簇簇）是旗簇中某些允许在 Grassmannian $\mathrm{Gr}(k,n)$ 中实现为明确子簇的 Richardon 簇。它们由一对嵌套在一个 $k \times (n-k)$-矩形内的 Young 图表 $\mu \subseteq \lambda$参数化。对于每个 $a = 1, \dots, n-k$，我们在斜形状正向簇 $S^{\circ}_{\lambda/\mu}$ 内定义一个明确的开集 $U_a$，并证明 $U_a$ 同构于两个较小的斜形状正向簇的乘积。 此外，$U_a$赋予了一个自然的簇结构，上述同构按 Fraser 的意义是准簇同构。 我们的方法依赖于将斜形状的positroid实现为明确的辫簇，并推广了第一作者和第三作者关于Grassmannian中的开positroid胞腔的工作。 显示英文摘要

摘要： Skew shaped positroids (or skew shaped positroid varieties) are certain Richardson varieties in the flag variety that admit a realization as explicit subvarieties of the Grassmannian $\mathrm{Gr}(k,n)$. They are parametrized by a pair of Young diagrams $\mu \subseteq \lambda$ fitting inside a $k \times (n-k)$-rectangle. For every $a = 1, \dots, n-k$, we define an explicit open set $U_a$ inside the skew shaped positroid $S^{\circ}_{\lambda/\mu}$, and show that $U_a$ is isomorphic to the product of two smaller skew shaped positroids. Moreover, $U_a$ admits a natural cluster structure and the aforementioned isomorphism is quasi-cluster in the sense of Fraser. Our methods depend on realizing the skew shaped positroid as an explicit braid variety, and generalize the work of the first and third authors for open positroid cells in the Grassmannian.