A Littlewood–Richardson rule for two-step flag varieties
A Littlewood–Richardson rule for two-step flag varieties
复制标题
两步旗品种的利特伍德-理查森规则
DOI：
--
复制
发表时间：
2009
期刊：
影响因子：
--
通讯作者：
Izzet Coskun
中科院分区：
文献类型：
--
作者：
Izzet Coskun
本文研究了格拉斯曼子变种和两步标志变种的单参数专门化的几何性质。由此，我们得到了用舒伯特基表示两阶旗变体上同调的结构常数的一个正的几何规则。一个推论是计算格拉斯曼子的小量子上同调的结构常数的一个正的几何规则。我们还得到了一个正的几何规则，用于计算由两个Schubert变异体在部分标志变异体中的交投影产生的Grassmannians子变异体的类。这些规则在几何、表示理论和对称函数理论中有许多应用。
This paper studies the geometry of one-parameter specializations of subvarieties of Grassmannians and two-step flag varieties. As a consequence, we obtain a positive, geometric rule for expressing the structure constants of the cohomology of two-step flag varieties in terms of their Schubert basis. A corollary is a positive, geometric rule for computing the structure constants of the small quantum cohomology of Grassmannians. We also obtain a positive, geometric rule for computing the classes of subvarieties of Grassmannians that arise as the projection of the intersection of two Schubert varieties in a partial flag variety. These rules have numerous applications to geometry, representation theory and the theory of symmetric functions.