标题： 等变量子上同调的傅里叶分析 显示英文标题

标题： Fourier analysis of equivariant quantum cohomology

摘要： 等变量子上同调通过等变参数的移位算子（Seidel表示）具有差分模的结构。 Teleman的猜想表明，作用在QH_T(X)上的移位算子和等变参数应分别与GIT商X//T的诺维科夫变量和量子联络相识别。 这可以被解释为X的等变量子上同调（D-模）与X//T的量子上同调（D-模）之间的傅里叶对偶形式。 我们引入了“量子体积”的概念，该概念源自Givental在Floer基本循环上的路径积分，并提出了X的T-等变量子体积与X//T的量子体积之间的假设性傅里叶对偶关系。 我们还探讨了与Fumihiko Sanda合作开发的“约化猜想”，该猜想将X//T的I函数表示为X的等变J函数的离散傅里叶变换。 此外，我们展示了如何利用等变量子上同调的傅里叶分析来观察环面镜像对称性，并证明射影丛或爆破的量子上同调D-模的分解。 显示英文摘要

摘要： Equivariant quantum cohomology possesses the structure of a difference module by shift operators (Seidel representation) of equivariant parameters. Teleman's conjecture suggests that shift operators and equivariant parameters acting on QH_T(X) should be identified, respectively, with the Novikov variables and the quantum connection of the GIT quotient X//T. This can be interpreted as a form of Fourier duality between equivariant quantum cohomology (D-module) of X and quantum cohomology (D-module) of the GIT quotient X//T. We introduce the notion of "quantum volume," derived from Givental's path integral over the Floer fundamental cycle, and present a conjectural Fourier duality relationship between the T-equivariant quantum volume of X and the quantum volume of X//T. We also explore the "reduction conjecture," developed in collaboration with Fumihiko Sanda, which expresses the I-function of X//T as a discrete Fourier transform of the equivariant J-function of X. Furthermore, we demonstrate how to use Fourier analysis of equivariant quantum cohomology to observe toric mirror symmetry and prove a decomposition of quantum cohomology D-modules of projective bundles or blowups.