Level one Kac-Moody characters and modular invariance

In this work are presented investigations on modular transformation properties of Kac-Moody characters and associated conformal theories. The study is limited to preliminary remarks pertaining to the group SU(N), specializing even to level one representation of its untwisted Kac-Moody or affine algebra. A specific property of (SU(N), N ≥ 3, is the existence of an automorphism of the Lie Algebra which extends to a correspondence between representations and their complexe conjugates. This has the consequence that affine restricted characters attached to conjugate ground states are undistinguishable