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Three $q$-Painlev\'e type equations are derived through degenerations of the$q$-Painlev\'e equation with affine Weyl group symmetry of type$q$-$E_8^{(1)}$. The three $q$-Painlev\'e type equations are associated withdifferent realizations of the same symmetry/surface type$q$-$E_7^{(1)}$/$q$-$A_1^{(1)}$. We give three representations of affine Weylgroup actions of type $q$-$E_7^{(1)}$, and relations among them. The three$q$-$E_7^{(1)}$ equations are also derived from the three representationsrespectively.

Three $q$-Painlev\'e equations with affine Weyl group symmetry of type $E_7^{(1)}$