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.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/node/5312