Q-systems as cluster algebras
Representation Theory
2008-11-26 v3 Quantum Algebra
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.
Cite
@article{arxiv.0712.2695,
title = {Q-systems as cluster algebras},
author = {Rinat Kedem},
journal= {arXiv preprint arXiv:0712.2695},
year = {2008}
}
Comments
16 pages, 3 figures