QUANTUM PAINLEVÉ SYSTEMS OF TYPE $A_l^{(1)}$

DOI10.1142/S0129167X0400265XzbMath1066.34087arXivmath/0402281MaRDI QIDQ4653531

Hajime Nagoya

Publication date: 7 March 2005

Published in: International Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0402281

zbMATH Keywords

Painlevé equationquantizationaffine Weyl groupdiscrete symmetry

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) General quantum mechanics and problems of quantization (81S99) Difference equations (39A99) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35)

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QUANTUM PAINLEVÉ SYSTEMS OF TYPE $A_{n-1}^{(1)}$ WITH HIGHER DEGREE LAX OPERATORS ⋮ Realizations of affine Weyl group symmetries on the quantum Painlevé equations by fractional calculus ⋮ Quantum Painlev\'e II solution and Approximated analytic solution of the Yukawa Potential ⋮ Integral formulas for quantum isomonodromic systems ⋮ Quantum Painlevé equations: from continuous to discrete and back ⋮ Symmetries of quantum Lax equations for the Painlevé equations ⋮ Quasideterminant solutions of NC Painlevé II equation with the Toda solution at \(n = 1\) as a seed solution in its Darboux transformation ⋮ POLYNOMIAL HAMILTONIANS FOR QUANTUM PAINLEVÉ EQUATIONS ⋮ Hypergeometric solutions to Schrödinger equations for the quantum Painlevé equations ⋮ A fully noncommutative analog of the Painlevé IV equation and a structure of its solutions*

Cites Work

• Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. I: General theory and \(\tau \)-function
• The Knizhnik-Zamolodchikov system as a deformation of the isomonodromy problem
• Affine Weyl groups, discrete dynamical systems and Painlevé equations
• Dressing chains and the spectral theory of the Schrödinger operator
• Nonlinear chains and Painlevé equations
• Differential equations compatible with KZ equations
• Discrete dynamical systems with \(W(A^{(1)}_{m-1} \times A^{(1)}_{n-1})\) symmetry
• Generalized Knizhnik–Zamolodchikov equations and isomonodromy quantization of the equations integrable via the Inverse Scattering Transform: Maxwell–Bloch system with pumping
• Symmetries in the fourth Painlevé equation and Okamoto polynomials
• A study on the fourthq-Painlevé equation
• Unnamed Item

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