  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.
