A Lax formulation of a generalized \(q\)-Garnier system

DOI10.1007/s11040-021-09412-3OpenAlexW3215774939MaRDI QIDQ2059034

Takao Suzuki

Publication date: 13 December 2021

Published in: Mathematical Physics, Analysis and Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2103.15336

zbMATH Keywords

affine Weyl groupdiscrete Painlevé equationGarnier system

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Rational and birational maps (14E05) Applications of Lie algebras and superalgebras to integrable systems (17B80) Difference equations, scaling ((q)-differences) (39A13) Integrable difference and lattice equations; integrability tests (39A36) Nonautonomous Hamiltonian dynamical systems (Painlevé equations, etc.) (37J65) Completely integrable discrete dynamical systems (37J70)

Related Items (3)

A \(3 \times 3\) Lax form for the \(q\)-Painlevé equation of type \(E_6\) ⋮ On additional symmetry and bilinearization of the \(q\)-Painlevé systems associated with the affine Weyl group of type \(A\) ⋮ An affine Weyl group action on the basic hypergeometric series arising from the \(q\)-Garnier system

Cites Work

• Symmetries of the Garnier system and of the associated polynomial Hamiltonian system
• \(q\)-Painlevé systems arising from \(q\)-KP hierarchy
• Discrete dynamical systems with \(W(A^{(1)}_{m-1} \times A^{(1)}_{n-1})\) symmetry
• Cluster realizations of Weyl groups and higher Teichmüller theory
• A 𝑞-analogue of the Drinfeld-Sokolov Hierarchy of Type 𝐴 and 𝑞-Painlevé System
• Affine Weyl Group Symmetry of the Garnier System
• A q-Analog of the Garnier System
• Variations of theq-Garnier system
• A certain generalization of $q$-hypergeometric functions and their related monodromy preserving deformation
• Study of <i>q</i>-Garnier System by Padé Method
• Unnamed Item

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