Hidden Algebra of Three-Body Integrable Systems

Alexander Turbiner

doi:10.1142/s0217732398001558

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arXiv · solv-int/9805003

Hidden Algebra of Three-Body Integrable Systems

Alexander Turbiner

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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.

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solv-int cond-mat.stat-mech hep-th math-ph math.MP math.RT math.SP nlin.SI

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Alexander Turbiner. 1998-06-03. Hidden Algebra of Three-Body Integrable Systems. https://doi.org/10.1142/s0217732398001558

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