\(\mathfrak{gl}(3)\) polynomial integrable system: different faces of the 3-body/\(\mathcal{A}_2\) elliptic Calogero model

arXiv2305.00529MaRDI QIDQ6151685

Juan Carlos Lopez Vieyra, Alexander~V. Turbiner, Miguel A. Guadarrama-Ayala

Publication date: 12 February 2024

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

Full work available at URL: https://arxiv.org/abs/2305.00529

zbMATH Keywords

integrable systems3-body systemselliptic Calogero model

Mathematics Subject Classification ID

Exactly and quasi-solvable systems arising in quantum theory (81U15) Groups and algebras in quantum theory and relations with integrable systems (81R12) Commutation relations and statistics as related to quantum mechanics (general) (81S05)

Cites Work

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• Poly-analytic functions and representation theory
• Completely integrable systems associated with classical root systems
• LIE ALGEBRAIC DISCRETIZATION OF DIFFERENTIAL EQUATIONS
• Canonical commutation relation preserving maps
• The Heun operator as a Hamiltonian
• An infinite family of solvable and integrable quantum systems on a plane
• Lame equation, sl(2) algebra and isospectral deformations
• Lie-algebras and linear operators with invariant subspaces
• Quasi-exact-solvability of the ${{A}_{2}}/{{G}_{2}}$ elliptic model: algebraic forms, $sl(3)/{{g}^{(2)}}$ hidden algebra, and polynomial eigenfunctions
• From two-dimensional (super-integrable) quantum dynamics to (super-integrable) three-body dynamics

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