2007/12/31 by Rinat Kedem · 1 citation
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Cluster (spacecraft) #Cluster algebra #Homotopy and Cohomology in Algebraic Topology #Laurent series #Lie algebra #Relation (database) #Simple (philosophy) #math.QA #math.RT
paper · pdf · doi:10.1088/1751-8113/41/19/194011
published as J.Phys.A41:194011,2008 · 16 pages, 3 figures
arxiv created 2008/03/02 · openalex publication_date 2008/04/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 Q-system in the initial variables, which follows from the representation-theoretical interpretation, to the Laurent phenomenon in cluster algebras.