DERIVATIONS OF THE TRIGONOMETRIC BCn SUTHERLAND MODEL BY QUANTUM HAMILTONIAN REDUCTION

The BCn Sutherland Hamiltonian with coupling constants parametrized by three arbitrary integers is derived by reductions of the Laplace operator of the group U(N). The reductions are obtained by applying the Laplace operator on spaces of certain vector valued functions equivariant under suitable symmetric subgroups of U(N) x U(N). Three different reduction schemes are considered, the simplest one being the compact real form of the reduction of the Laplacian of GL(2n, C) to the complex BCn Sutherland Hamiltonian previously studied by Oblomkov.