A Kac–Weyl character identity

The Racah–Speiser algorithm and its generalizations lead to an identity involving sums of Kac–Weyl characters, and here we recover this identity through an explicit quantization of Chern–Simons theory. One can use this identity to prove inequalities that constrain the fusion coefficients Nμνl in the case of rational conformal field theories 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.