Projective Reduction of the Discrete Painleve System of Type (A2 + A1)(1)

2009/10/31 by Kenji Kajiwara, K. Kajiwara, Nobutaka Nakazono +3 · 14 citations
Mathematics · Physics and Astronomy · #Affine transformation #Algebraic structures and combinatorial models #Factorization #Group (periodic table) #Hypergeometric distribution #Nonlinear Waves and Solitons #Projective test #Quantum Mechanics and Non-Hermitian Physics #Reduction (mathematics) #Type (biology) #Weyl group #nlin.SI

paper · pdf · doi:10.1093/imrn/rnq089

published in International Mathematics Research Notices (Oxford University Press) · 27 pages, 10 figures

openalex publication_date 2010/05/28 · arxiv created 2010/06/02 · arxiv updated 2010/06/03 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We consider the q-Painlevé III equation arising from the birational representation of the affine Weyl group of type (A2 + A1)(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 τ functions.

Citations

• Linearization and solutions of the discrete Painlevé III equation
• Casorati determinant solutions for the discrete Painleve-II equation

Cited by

• On integrals of non-autonomous dynamical systems in finite characteristic
• Full-parameter discrete Painlevé systems from non-translational Cremona isometries

Related

• Hypergeometric solutions to the symmetric q-Painlevé equations
• Three q-Painlevé equations with affine Weyl group symmetry of type E₇⁽¹⁾
• New Expressions for Discrete Painlevé Equations
• Affine Weyl group approach to Painlevé equations
• q-Painlevé systems arising from q-KP hierarchy