Three q-Painlevé equations with affine Weyl group symmetry of type E₇⁽¹⁾

2023/04/18 by Nagao, Hidehito, Yamada, Yasuhiko
#14H70 #34M55 #37K20 #39A13 #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2304.08730

Abstract

Three q-Painlevé type equations are derived through degenerations of the q-Painlevé equation with affine Weyl group symmetry of type q-E₈⁽¹⁾. The three q-Painlevé 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.

Related

• Lax formalism for q-Painleve equations with affine Weyl group symmetry of type E⁽¹⁾_n
• Affine Weyl group approach to Painlevé equations
• New Expressions for Discrete Painlevé Equations
• A higher-order generalization of an A₄⁽¹⁾-surface type q-Painlevé equation with \widetildeW((A_2N\rtimes A₁)⁽¹⁾× A₁⁽¹⁾) symmetry
• Higher-order generalizations of the A₆⁽¹⁾- and A₄⁽¹⁾-surface type q-Painlevé equations