标题： 杜布罗文对偶性和ADE分辨率的镜像对称性 显示英文标题

标题： Dubrovin duality and mirror symmetry for ADE resolutions

摘要： 我们证明，在Dubrovin的“几乎”对偶性的概念下，类型为$\mathrm{ADE}$的仿射Weyl群扩张轨道空间上的Frobenius流形结构，在合适的权标记选择下，与相同Dynkin类型的du Val奇点的极小解析的等变量子上同调是对偶的。 我们还为$\mathrm{ADE}$解析的量子上同调提供了Lie理论构造的一致Landau-Ginzburg镜像。B模型的镜像由与$\widehat{\mathrm{ADE}}$仿射相对Toda链谱曲线相关的单变量LG超势描述。 显示英文摘要

摘要： We show that, under Dubrovin's notion of ''almost'' duality, the Frobenius manifold structure on the orbit spaces of the extended affine Weyl groups of type $\mathrm{ADE}$ is dual, for suitable choices of weight markings, to the equivariant quantum cohomology of the minimal resolution of the du Val singularity of the same Dynkin type. We also provide a uniform Lie-theoretic construction of Landau-Ginzburg mirrors for the quantum cohomology of $\mathrm{ADE}$ resolutions. The mirror B-model is described by a one-dimensional LG superpotential associated to the spectral curve of the $\widehat{\mathrm{ADE}}$ affine relativistic Toda chain.