论文标题
国旗品种的量子钩和镜子对称性
Quantum hooks and mirror symmetry for flag varieties
论文作者
论文摘要
给定标志品种$ fl（n; r_1，\ dots，r_ρ）$，从$ r_1 $变量的对称多项式环到国旗品种的量子共同体。在本文中，我们表明，对于大量的分区$λ$，戒指同态下的$s_λ$的图像是舒伯特类别的类别，它是通过将$λ$划分为量子挂钩（或$ q $ -hook）和一个较小分区的元组来描述的。我们使用此结果表明标志品种的plücker坐标镜描述了量子同谋关系。这给了人们对这种超电势结构的新见解，以及国旗品种的超电势之间的关系和格拉斯曼尼亚人（Marsh-rietsch引入了超级电势的地方）之间的关系。
Given a flag variety $Fl(n;r_1, \dots , r_ρ)$, there is natural ring morphism from the symmetric polynomial ring in $r_1$ variables to the quantum cohomology of the flag variety. In this paper, we show that for a large class of partitions $λ$, the image of $s_λ$ under the ring homomorphism is a Schubert class which is described by partitioning $λ$ into a quantum hook (or $q$-hook) and a tuple of smaller partitions. We use this result to show that the Plücker coordinate mirror of the flag variety describes quantum cohomology relations. This gives new insight into the structure of this superpotential, and the relation between superpotentials of flag varieties and those of Grassmannians (where the superpotential was introduced by Marsh--Rietsch).
