  A framework to calculate two-particle matrix elements for fully
antisymmetrized three-cluster configurations is presented. The theory is
developed for a scattering situation described in terms of the Algebraic Model.
This means that the nuclear many-particle state and its asymptotic behaviour
are expanded in terms of oscillator states of the intra-cluster coordinates.
The Generating Function technique is used to optimize the calculation of matrix
elements. In order to derive the dynamical equations, a multichannel version of
the Algebraic Model is presented.
