Three q-Painlev\'e equations with affine Weyl group symmetry of type E7(1)
Abstract
Three q-Painlev\'e type equations are derived through degenerations of the q-Painlev\'e equation with affine Weyl group symmetry of type q-E8(1). The three q-Painlev\'e type equations are associated with different realizations of the same symmetry/surface type q-E7(1)/q-A1(1). We give three representations of affine Weyl group actions of type q-E7(1), and relations among them. The three q-E7(1) equations are also derived from the three representations respectively.
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