Abstract
The characters of the integrable representations of an affine Lie algebra at fixed level have been shown to be covariant under modular transformations. These characters have subsequently been identified with those of the WZW primary fields. More precisely, a WZW primary field is associated with both a left and a right integrable highest weight, and its descendants are associated with the different states in the tensor product of the two modules. To a large extent, the holomorphic and the antiholomorphic sectors can be studied independently. However, they must ultimately be combined to form a modular-invariant partition function. The construction of modular invariant partition functions is the subject of the present chapter.
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