Tarasov, VitalyVarchenko, Alexander2024-01-232024-01-232023-02Tarasov, V., & Varchenko, A. (2023). Landau–Ginzburg mirror, quantum differential equations and qKZ difference equations for a partial flag variety. Journal of Geometry and Physics, 184, 104711. https://doi.org/10.1016/j.geomphys.2022.104711https://hdl.handle.net/1805/38120We 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.en-USAttribution 4.0 Internationaldynamical differential equationsqKZ difference equationsquantum differential equationsq- hypergeometric solutionsArticle