The BC(n) 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)\times 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 BC(n) Sutherland Hamiltonian previously studied by
Oblomkov.Comment: 30 pages, LateX; v2: final version with minor stylistic modification