Quasi-exact-solvability of the ${{A}_{2}}/{{G}_{2}}$ elliptic model: algebraic forms, $sl(3)/{{g}^{(2)}}$ hidden algebra, and polynomial eigenfunctions

DOI10.1088/1751-8113/48/15/155201zbMath1329.81434arXiv1409.7439OpenAlexW3124376535MaRDI QIDQ5248732

Vladimir Sokolov, Alexander~V. Turbiner

Publication date: 8 May 2015

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1409.7439

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Many-body theory; quantum Hall effect (81V70) Groups and algebras in quantum theory and relations with integrable systems (81R12) Applications of Lie algebras and superalgebras to integrable systems (17B80)

Related Items (6)

Defect in gauge theory and quantum Hall states ⋮ \(\mathfrak{gl}(3)\) polynomial integrable system: different faces of the 3-body/\(\mathcal{A}_2\) elliptic Calogero model ⋮ Two-body Coulomb problem and \(g^{(2)}\) algebra (once again about the hydrogen atom) ⋮ Polynomial forms for quantum elliptic Calogero-Moser Hamiltonians ⋮ Algebraic quantum Hamiltonians on the plane ⋮ Three-body problem in 3D space: ground state, (quasi)-exact-solvability

This page was built for publication: Quasi-exact-solvability of the ${{A}_{2}}/{{G}_{2}}$ elliptic model: algebraic forms, $sl(3)/{{g}^{(2)}}$ hidden algebra, and polynomial eigenfunctions