Projective reduction of the discrete Painlevé system of type $(A_2+A_1{)}^{(1)}$

Abstract

We consider the q-Painlevé III equation arising from the birational representation of the affine Weyl group of type $(A_2+A_1{)}^{(1)}$. We study the reduction of the q-Painlevé III equation to the q-Painlevé II equation from the viewpoint of affine Weyl group symmetry. In particular, the mechanism of apparent inconsistency between the hypergeometric solutions to both equations is clarified by using factorization of difference operators and the $\tau$ functions.

27 pages, 10 figures

References in corpus (3)

• A study on the fourth q-Painlevé equation
• On a q-difference Painlevé III equation: I. Derivation, symmetry and Riccati type solutions
• On a q-difference Painlevé III equation: II. Rational solutions

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• Lattice equations arising from discrete Painlevé systems (I): $(A_2+A_1{)}^{(1)}$ and $(A_1+A_1^{\prime }{)}^{(1)}$ cases
• Elliptic Painlevé equations from next-nearest-neighbor translations on the $E_8^{(1)}$ lattice
• Full-parameter discrete Painlevé systems from non-translational Cremona isometries
• Discrete Painlevé transcendent solutions to the multiplicative type discrete KdV equations
• Discrete equations from Bäcklund transformations of the fifth Painlevé equation