Modular invariants for the affine algebra C(,2)('(1))

This thesis concerns the classification of the modular invariant matrices associated to the affine algebra $C12$ at level k. We provide a foundation for this classification and give a conjecture for the full solution based on the analogous proof for the affine algebra A₂. Furthermore, we describe all of the modular invariants M that are permutation matrices and prove that there is a 1–1 correspondence between the modular invariants of C_r,k and those of C _k,r. Together with a similar duality of the othogonal algebras so(n)k, this implies that the C_{2, k} classification is actually four classifications in one, and is therefore of particular interest among the affine algebras.