  In the first of this two-part series, we find `fixed point factorisation'
formulas, towards an understanding of the fusion ring of WZW models.
Fixed-point factorisation refers to the simplifications in the data of a CFT
involving primary fields fixed by simple-currents. Until now, it has been
worked out only for SU(n), where it has developed into a powerful tool for
understanding the fusion rings of WZW models of CFT -- e.g. it has lead to
closed formulas for NIM-reps and D-brane charges and charge-groups. In this
paper, we generalise these formulas to the other classical algebras, laying the
groundwork for future applications to fusion rings (Part 2). We also discuss
connections with the twining characters of Fuchs-Schellekens-Schweigert.
