Hidden Algebra of Three-Body Integrable Systems

Details Hidden Algebra of Three-Body Integrable Systems Hidden Algebra of Three-Body Integrable Systems

1998-05-08

arxiv.org/abs/solv-int/9805003v2

Modern Physics Letters A, 13(1998)1473-1483

Physics

Condensed Matter

Statistical Mechanics

11 pages, AMS-LaTeX, no figures, minor typos corrected, to appear in Mod.Phys.Lett.A

Scientific paper

10.1142/S0217732398001558

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.

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