Hidden Algebra of Three-Body 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.

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

References in corpus (2)

• Hidden Algebras of the (super) Calogero and Sutherland models
• Solvability of the G_2 Integrable System

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