  The rational quantized Knizhnik-Zamolodchikov equation (qKZ equation)
associated with the Lie algebra $sl_2$ is a system of linear difference
equations with values in a tensor product of $sl_2$ Verma modules. We solve the
equation in terms of multidimensional $q$-hypergeometric functions and define a
natural isomorphism between the space of solutions and the tensor product of
the corresponding quantum group $U_q(sl_2)$ Verma modules, where the parameter
$q$ is related to the step $p$ of the qKZ equation via $q=e^{pi i/p}$.
  We construct asymptotic solutions associated with suitable asymptotic zones
and compute the transition functions between the asymptotic solutions in terms
of the trigonometric $R$-matrices. This description of the transition functions
gives a new connection between representation theories of Yangians and quantum
loop algebras and is analogous to the Kohno-Drinfeld theorem on the monodromy
group of the differential Knizhnik-Zamolodchikov equation.
  In order to establish these results we construct a discrete Gauss-Manin
connection, in particular, a suitable discrete local system, discrete homology
and cohomology groups with coefficients in this local system, and identify an
associated difference equation with the qKZ equation.
