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The BC(n) Sutherland Hamiltonian with coupling constants parametrized bythree arbitrary integers is derived by reductions of the Laplace operator ofthe group U(N). The reductions are obtained by applying the Laplace operator onspaces of certain vector valued functions equivariant under suitable symmetricsubgroups 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 Laplacianof GL(2n,C) to the complex BC(n) Sutherland Hamiltonian previously studied byOblomkov.

Derivations of the trigonometric BC(n) Sutherland model by quantum Hamiltonian reduction