Reducible boundary conditions in coupled channels

We study Hamiltonians with point interactions in spaces of vector-valued functions. Using some information from the theory of quantum graphs we describe a class of the operators which can be reduced to the direct sum of several one-dimensional problems. It shown that such reduction is closely connected with the invariance under channel permutations. Examples are provided by some "model" interactions, in particular, the so-called delta, delta-prime, and the Kirchhoff couplings.