Precise study of some number fields and Galois actions occurring in conformal field theory

We present a detailed study of some number fields and Galois groups occurring in two dimensional models built from Wess-Zumino-Novikov-Witten (WZNW) and Z/NZ theories. The observed structures may be relevant for the classification of rational conformal theories (RCFT) and for the understanding of links and three manifold invariants. More precisely we look at M, the number field generated by the modular matrix elements Sij and at L, the subfield generated by the quotients Sij/Sρj at the field generated by Moore and Seiberg data. (orig.)