论文标题
圆柱形状上的格拉曼尼亚的量子质量质量规则
An equivariant quantum Pieri rule for the Grassmannian on cylindric shapes
论文作者
论文摘要
格拉斯曼尼亚人的量子共同体学环由量子pieri规则确定，该规则是由舒伯特类乘以行或柱状分区索引的舒伯特类。我们在尼古夫的量子pieri规则上为格拉曼尼亚人提供了直接的概括，就圆柱形形状而言，在量子整合系统中补充了戈布诺夫和korff相关的工作。我们的格雷厄姆阳性规则中的模棱两可的术语只需编码一个圆柱偏斜图中所有可能添加框的位置。因此，与早期的量子量子Pieri规则不同，以及Li和已知的量子Littlewood-Richardson规则，我们的公式不需要在不同的Grassmannian或Twipep Flag品种中进行任何计算。
The quantum cohomology ring of the Grassmannian is determined by the quantum Pieri rule for multiplying by Schubert classes indexed by row or column-shaped partitions. We provide a direct equivariant generalization of Postnikov's quantum Pieri rule for the Grassmannian in terms of cylindric shapes, complementing related work of Gorbounov and Korff in quantum integrable systems. The equivariant terms in our Graham-positive rule simply encode the positions of all possible addable boxes within one cylindric skew diagram. As such, unlike the earlier equivariant quantum Pieri rule of Huang and Li and known equivariant quantum Littlewood-Richardson rules, our formula does not require any calculations in a different Grassmannian or two-step flag variety.
