Exact Solution of the Sutherland Model with arbitrary symmetry

An elementary theory is presented for solving the Sutherland model with arbitrary internal symmetry such as SU($\nu$) or a supersymmetry SU($\nu, \mu$). The ground state wave function and all the energy levels are derived. One starts with solving a variant of the model with distinguishable particles, and then (anti)symmetrizes the solution. The theory is also applied to various lattice versions of the model. It is proved that the Gutzwiller-type wave function is not only an eigenstate of the supersymmetric \it t-J \rm model, but is indeed the ground state.