A Kac-Weyl Character Identity

An explicit quantization of Chern-Simons theory leads to an identity between sums of the Kac-Weyl characters. One can use this identity to prove inequalities that constrain the fusion coefficients in Rational Conformal Field Theories (RCFT) that descend from current algebras. It also leads to a statement regarding the conjugacy symmetry of the sums of squares of fusion coefficients for current algebras admitting complex representations.