Correlation Functions of the Tri-Critical 3-STATE Potts Model

We build the Z₃ invariants fusion rules associated to the (D₄,A₆) conformal algebra. This algebra is known to describe the tri-critical Potts model. The 4-point correlation functions of critical fields are developed in the bootstrap approach, and on the other hand, they are written in terms of integral representation of the conformal blocks. By comparing both expressions, one can determine the structure constants of the operator algebra.