Hidden Algebra of Three-Body Integrable Systems
solv-int
2016-09-08 v2 Statistical Mechanics
High Energy Physics - Theory
Mathematical Physics
math.MP
Representation Theory
Spectral Theory
Exactly Solvable and Integrable Systems
Abstract
It is shown that all 3-body quantal integrable systems that emerge in the Hamiltonian reduction method possess the same hidden algebraic structure. All of them are given by a second degree polynomial in generators of an infinite-dimensional Lie algebra of differential operators. It leads to new families of the orthogonal polynomials in two variables.
Keywords
Cite
@article{arxiv.solv-int/9805003,
title = {Hidden Algebra of Three-Body Integrable Systems},
author = {Alexander Turbiner},
journal= {arXiv preprint arXiv:solv-int/9805003},
year = {2016}
}
Comments
11 pages, AMS-LaTeX, no figures, minor typos corrected, to appear in Mod.Phys.Lett.A