We construct simple geometric operations on faces of the Cayley sum of two polytopes. These operations can be thought of as convex geometric counterparts of divided difference operators in Schubert calculus. We show that these operations give a uniform construction of Knutson–Miller mitosis in the type A and Fujita mitosis in the type C on Kogan faces of Gelfand–Zetlin polytopes.

中文翻译：

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 简单几何有丝分裂


我们在两个多面体的 Cayley 和的面上构造简单的几何运算。这些运算可以被认为是舒伯特微积分中除以差分算子的凸几何对应物。我们表明，这些作在 Gelfand-Zetlin 多位体的 Kogan 面上给出了 A 型 Knutson-Miller 有丝分裂和 C 型藤田有丝分裂的统一构建。