Affine Lie Algebras and Hecke Modular Forms

The character of a highest weight representation of an affine lie algebra can be written as a finite sum of products of classical 0-functions and certain modular functions, called string functions. We find the transformation law for the string functions, which allows us to compute them explicitly in many interesting cases. Finally, we write an explicit formula for the partition function, in the simplest case A[\ and compute the string functions directly. After multiplication by the cube of the T?-function, they turn out to be Hecke modular forms!