  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.
