Q-systems as cluster algebras
arXiv:0712.2695 · doi:10.1088/1751-8113/41/19/194011
Abstract
Q-systems first appeared in the analysis of the Bethe equations for the XXX-model and generalized Heisenberg spin chains. Such systems are known to exist for any simple Lie algebra and many other Kac-Moody algebras. We formulate the Q-system associated with any simple, simply-laced Lie algebras g in the language of cluster algebras, and discuss the relation of the polynomiality property of the solutions of the -system in the initial variables, which follows from the representation-theoretical interpretation, to the Laurent phenomenon in cluster algebras.
16 pages, 3 figures