  Starting from a one-particle quasi-exactly solvable system, which is
characterized by an intrinsic sl(2) algebraic structure and the
energy-reflection symmetry, we construct a daughter N-body Hamiltonian
presenting a deformation of the Calogero model. The features of this
Hamiltonian are (i) it reduces to a quadratic combination of the generators of
sl(N+1); (ii) the interaction potential contains two-body terms and interaction
with the force center at the origin; (iii) for quantized values of a certain
cohomology parameter n it is quasi-exactly solvable, the multiplicity of states
in the algebraic sector is (N+n)!/(N!n!); (iv) the energy-reflection symmetry
of the parent system is preserved.
