# Linear recurrence relations in Q-systems

There exists a system of difference equations called the Q-system for each simple Lie algebra. It was first introduced by Kirillov and Reshetikhin in an attempt to understand the completeness of the Bethe ansatz in representation theoretic context. A solution of the Q-system is a finite set of compatible sequences, each attached to a node in its Dynkin diagram. A remarkable fact from representation theory is that there exists a family of finite-dimensional representations of quantum affine algebra whose characters form a solution of the Q-system. This particular solution can be used to construct solutions of the Q-system in other rings by specializing it appropriately. In this talk, I will discuss linear recurrence relations in these character solutions and applications of them.