Discrete dynamical systems with W(A⁽¹⁾_m-1 × A⁽¹⁾_n-1) symmetry

2001/06/19 by Kenji Kajiwara, Kajiwara, Kenji, Masatoshi Noumi +3
Mathematics · Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #nlin.SI

paper · pdf · doi:10.48550/arxiv.nlin/0106029

10 pages

arxiv created 2001/06/19 · openalex publication_date 2001/06/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a birational realization of affine Weyl group of type A⁽¹⁾_m-1 × A⁽¹⁾_n-1. We apply this representation to construct some discrete integrable systems and discrete Painlevé equations. Our construction has a combinatorial counterpart through the ultra-discretization procedure.

Related

• Affine Weyl groups and non-Abelian discrete systems: an application to the d-Painlevé equations
• New Expressions for Discrete Painlevé Equations
• On the geometry of a 4-dimensional extension of a q-Painlevé I equation with symmetry type A₁⁽¹⁾
• On a non-commutative sixth q-Painlevé system: from discrete system to surface theory
• Determination of the symmetry group for some QRT roots