Abstract
We give an algorithm to construct modular invariant sesquilinear combinations of characters of both affine Kac-Moody and Virasoro algebras. It provides an insight into why the modular invariant combinations for the A 1 (1) and the Virasoro algebra are so closely related. Apart from reproducing all known combinations for A 1 (1) and the Virasoro algebra we will find some new combinations for other affine Kac-Moody algebras. Finally, as a byproduct, we obtain an algorithm to compute characters of C n (1) representations at level 1.
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