On Rational Conformal Field Theories: Explicit Modular Formulae

We derive compact formulae for modular transformation matrices of Wess–Zumino–Witten (WZW) affine characters. We start in this text with the simple case of A1 algebra at positive level k=n-2, for which we can easily provide some description of isometry group and genus formula in a special case. We also point to general features of these expressions, formulating and proving theorems for rational conformal field theories (sometimes called RCFT’s) which seem new.