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From modular invariants to graphs: the modular splitting method
We start with a given modular invariant M of a two dimensional su(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 to the initial modular
invariant M. Notice that one does not suppose here that the graph G is already
known, since it appears as a by-product of the calculations. We analyze several
su(3)_k exceptional cases at levels 5 and 9.Comment: 28 pages, 7 figures. Version 2: updated references. Typos corrected.
su(2) example has been removed to shorten the paper. Dual annular matrices
for the rejected exceptional su(3) diagram are determine