Invariant classification and limits of maximally superintegrable systems in 3D

DOI10.3842/SIGMA.2015.038zbMath1318.33014arXiv1501.06601OpenAlexW1670825336MaRDI QIDQ2353219

Joshua J. Capel, Sarah Post, Jonathan M. Kress

Publication date: 8 July 2015

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1501.06601

zbMATH Keywords

integrable systemscontractionssuperintegrable systemsLie algebra invariants

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Groups and algebras in quantum theory and relations with integrable systems (81R12) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45) Connections of basic hypergeometric functions with quantum groups, Chevalley groups, (p)-adic groups, Hecke algebras, and related topics (33D80)

Related Items

Bôcher contractions of conformally superintegrable Laplace equations, Construction of polynomial algebras from intermediate Casimir invariants of Lie algebras, Projectively equivalent 2-dimensional superintegrable systems with projective symmetries, Separation equations for 2D superintegrable systems on constant curvature spaces, Superintegrable systems on 3 dimensional conformally flat spaces, An algebraic geometric foundation for a classification of second-order superintegrable systems in arbitrary dimension, Contractions of degenerate quadratic algebras, abstract and geometric, Fourth order superintegrable systems separating in polar coordinates. I. Exotic potentials, Algebraic conditions for conformal superintegrability in arbitrary dimension, Toward a classification of semidegenerate 3D superintegrable systems, On Superintegrable Systems with a Cubic Integral of Motion, Bôcher and abstract contractions of 2nd order quadratic algebras, Superintegrable systems from block separation of variables and unified derivation of their quadratic algebras, Fourth-order superintegrable systems separating in polar coordinates. II. Standard potentials, N-dimensional Smorodinsky–Winternitz model and related higher rank quadratic algebra SW(N)