Kirillov-Reshetikhin modules and fusion rings from conformal field theory

The Kirillov-Reshetikhin modules form a special class of finite dimensional representations of quantum groups. Their characters are known to satisfy some functional relations called T-systems and Q-systems. In an attempt to calculate the central charges of some conformal field theories using the dilogarithm function based on the Thermodynamic Bethe Ansatz, some conjectures about solutions of level restricted version of Q-systems have been proposed. In this talk, I will explain how the fusion rings of conformal field theory can be used to answer some of them and will add some new conjectures about the Kirillov-Reshetikhin modules.