A geometric approach to tau-functions of difference Painlevé equations

DOI10.1007/s11005-008-0251-xzbMath1173.39003arXiv0804.1680OpenAlexW2138604128MaRDI QIDQ1024841

Teruhisa Tsuda

Publication date: 17 June 2009

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0804.1680

zbMATH Keywords

Weyl groupDynkin diagramsbirational transformationtau-functiondifference Painlevé equation

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Additive difference equations (39A10) Discrete version of topics in analysis (39A12) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions (37K20) Rational and birational maps (14E05) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35) Painlevé-type functions (33E17)

Related Items

Lattice equations arising from discrete Painlevé systems. I. (A2 + A1)(1) and (A1+A1′)(1) cases ⋮ Reduction of quad-equations consistent around a cuboctahedron I: Additive case

Cites Work

• Moduli spaces of \(d\)-connections and difference Painlevé equations
• Tropical Weyl group action via point configurations and \(\tau\)-functions of the \(q\)-Painlevé equations
• Tropical representation of Weyl groups associated with certain rational varieties
• Rational surfaces associated with affine root systems and geometry of the Painlevé equations
• Rational surfaces with an anti-canonical cycle
• An affine Weyl group approach to the eight-parameter discrete Painlevé equation
• Quivers and difference Painleve equations
• ₁₀E₉solution to the elliptic Painlev  equation
• Riccati solutions of discrete Painlevé equations with Weyl group symmetry of type E8(1)
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