Title: A Variation of the $q$-Painlevé System with Affine Weyl Group Symmetry of Type $E_7^{(1)}$,
Abstract: Recently a certain $q$-Painlevé type system has been obtained from a
reduction of the $q$-Garnier system. In this paper it is shown that the
$q$-Painlevé type system is associated with another realization of the affine
Weyl group symmetry of type $E_7^{(1)}$ and is different from the well-known
$q$-Painlevé system of type $E_7^{(1)}$ from the point of view of evolution
directions. We also study a connection between the $q$-Painlevé type system
and the $q$-Painlevé system of type $E_7^{(1)}$. Furthermore determinant
formulas of particular solutions for the $q$-Painlevé type system are
constructed in terms of the terminating $q$-hypergeometric function.