论文标题
Landau-Ginzburg镜子，量子微分方程和部分标志品种的QKZ差异方程
Landau-Ginzburg mirror, quantum differential equations and qKZ difference equations for a partial flag variety
论文作者
论文摘要
我们考虑了部分标志品种的量子微分方程系统，并以多维超测量功能的形式构建解决方案的基础，即，我们为该部分标志的品种构造了Landau-Ginzburg镜像。在我们的构造中，解决方案由$ k $ - 理论的元素代数的元素标记。 为了建立这些事实，我们考虑了部分标志品种的量像量微分方程，并引入了兼容的差异方程系统，我们称之为QKZ方程。我们以多维超测量函数的形式构建了量等量子微分方程和QKZ差异方程的关节系统的解决方案的基础。然后，关于非等价量子微分方程的事实是从关于量子量微分方程的事实获得的。 分析这些结构，我们获得了量子标志品种量子微分方程基本级别解的公式。
We consider the system of quantum differential equations for a partial flag variety and construct a basis of solutions in the form of multidimensional hypergeometric functions, that is, we construct a Landau-Ginzburg mirror for that partial flag variety. In our construction, the solutions are labeled by elements of the $K$-theory algebra of the partial flag variety. To establish these facts we consider the equivariant quantum differential equations for a partial flag variety and introduce a compatible system of difference equations, which we call the qKZ equations. We construct a basis of solutions of the joint system of the equivariant quantum differential equations and qKZ difference equations in the form of multidimensional hypergeometric functions. Then the facts about the non-equivariant quantum differential equations are obtained from the facts about the equivariant quantum differential equations by a suitable limit. Analyzing these constructions we obtain a formula for the fundamental Levelt solution of the quantum differential equations for a partial flag variety.
