We start with a given modular invariant M of a two-dimensional (su) over cap (n)(k) conformal field theory (CFT) and present a general method for solving the Ocneanu modular splitting equation and then determine, in a step-by-step explicit construction, ( 1) the generalized partition functions corresponding to the introduction of boundary conditions and defect lines; ( 2) the quantum symmetries of the higher ADE graph G associated with the initial modular invariant M. Note that one does not suppose here that the graph G is already known, since it appears as a by-product of the calculations. We analyse several (su) over cap (3)(k) exceptional cases at levels 5 and 9.
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