Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 19 (2023), 094, 17 pages      arXiv:2211.16706      https://doi.org/10.3842/SIGMA.2023.094

A $3 \times 3$ Lax Form for the $q$-Painlevé Equation of Type $E_6$

Kanam Park
National Institute of Technology, Toba College, 1-1, Ikegami-cho, Toba-shi, Mie, Japan

Received December 01, 2022, in final form November 05, 2023; Published online November 18, 2023

Abstract
For the $q$-Painlevé equation with affine Weyl group symmetry of type $E_6^{(1)}$, a $2\times 2$ matrix Lax form and a second order scalar lax form were known. We give a new $3\times 3$ matrix Lax form and a third order scalar equation related to it. Continuous limit is also discussed.

Key words: Lax formalism; $q$-Painlevé equation.

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