Abstract:
We consider an example of the joint system of dynamical differential equations and qKZ
difference equations
with parameters corresponding to equations for elliptic integrals.
We solve this system of
equations modulo
any power
$p^n$
of a
prime integer
$p$.
We show that the
$p$-adic limit of these solutions as
$n\to\infty$
determines
a sequence of line bundles, each of which is invariant with respect to the corresponding
dynamical connection,
and that the sequence of line bundles is invariant with respect to
the corresponding qKZ difference connection.
Keywords:Dynamical and qKZ equations,
$p^s$-hypergeometric solution, master polynomial, Dwork
congruence.