论文标题
Quiver Flag品种的边缘钩规则
A rim-hook rule for quiver flag varieties
论文作者
论文摘要
格拉斯曼尼亚的量子同谋的边缘钩规则使人们可以将量子计算减少到格拉斯曼尼亚的共同体中的经典计算。我们使用ABELIAN/非阿贝尔对应关系来证明Quiver Flag品种的共同体的边缘钩子去除规则。 Quiver Flag品种是A型标志品种的概括；即使在国旗案例中，此结果也是新的。这提供了一种计算产品共同体学的有效方法，从而将计算减少到了格拉斯曼尼亚人的共同体学环中。然后，我们证明了Fano Quiver Flag品种（包括A型标志品种）的量子轮钩规则。作为推论，我们看到gu-sharpe镜子到fano Quiver Flag品种计算其量子共同体。
The rim-hook rule for quantum cohomology of the Grassmannian allows one to reduce quantum calculations to classical calculations in the cohomology of the Grassmannian. We use the Abelian/non-Abelian correspondence for cohomology to prove a rim-hook removal rule for the cohomology of quiver flag varieties. Quiver flag varieties are generalisations of type A flag varieties; this result is new even in the flag case. This gives an effective way of computing products in their cohomology, reducing computations to that in the cohomology ring of the Grassmannian. We then prove a quantum rim-hook rule for Fano quiver flag varieties (including type A flag varieties). As a corollary, we see that the Gu--Sharpe mirror to a Fano quiver flag variety computes its quantum cohomology.
