A 3 × 3 Lax Form for the 𝑞-Painlevé Equation of Type 𝐸₆

Abstract

For the 𝑞-Painlevé equation with affine Weyl group symmetry of type 𝐸⁽¹⁾₆, a 2 × 2 matrix Lax form and a second-order scalar lax form were known. We give a new 3 × 3 matrix Lax form and a third order scalar equation related to it. Continuous limit is also discussed.