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We show that the WZW fusion rings at finite levels form a projective systemwith respect to the partial ordering provided by divisibility of the height,i.e. the level shifted by a constant. From this projective system we obtain WZWfusion rings in the limit of infinite level. This projective limit constitutesa mathematically well-defined prescription for the `classical limit' of WZWtheories which replaces the naive idea of `sending the level to infinity'. Theprojective limit can be endowed with a natural topology, which plays animportant role for studying its structure. The representation theory of thelimit can be worked out by considering the associated fusion algebra; this waywe obtain in particular an analogue of the Verlinde formula.Comment: Latex2e, 31 pages (A4

WZW Fusion Rings in the Limit of Infinite Level