Curiosities at c = 1

We consider conformal field theories on a torus with central charge c = 1, and in particular models based upon modding out string propagation on the SU(2) group manifold by its finite subgroups. We find that the partition functions for these models coincide with the continuum limit partition functions of a recently introduced class of RSOS models, defined in terms of the extended Dynkin diagrams of simply-laced Lie algebras, thus giving an alternative interpretation for the primary fields in these latter theories. Three of the models have no massless moduli and thus do not lie on the same line of critical points with the rest. The particular correspondence between simply-laced Lie algebras and finite subgroups of SU(2) that emerges coincides with that which has already appeared in other mathematical contexts.