Solvability of the G_2 Integrable System

Abstract

It is shown that the 3-body trigonometric G_2 integrable system is exactly-solvable. If the configuration space is parametrized by certain symmetric functions of the coordinates then, for arbitrary values of the coupling constants, the Hamiltonian can be expressed as a quadratic polynomial in the generators of some Lie algebra of differential operators in a finite-dimensional representation. Four infinite families of eigenstates, represented by polynomials, and the corresponding eigenvalues are described explicitly.

18 pages, LaTeX, some minor typos corrected

References in corpus (4)

• Exact Solvability of the Calogero and Sutherland Models
• Hidden Algebras of the (super) Calogero and Sutherland models
• Quasi-Exactly-Solvable Many-Body Problems
• An exactly solvable three-particle problem with three-body interaction

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