From tensor products to the modular matrix S and back

In this paper it is described how the modular matrix S of a WZW theory can be determined by using a small number of tensor product decompositions of the underlying finite-dimensional Lie algebra bar g as an input. Having obtained the matrix S, one may then search for non-diagonal modular invariant partition functions. But one can also deduce the full fusion rule algebra and from this, by considering theories with large enough level, complicated tensor products of bar g whose direct Lie algebraic evaluation would need more computer time