Q-systems as cluster algebras

Details Q-systems as cluster algebras Q-systems as cluster algebras

2007-12-17

arxiv.org/abs/0712.2695v3

J.Phys.A41:194011,2008

Mathematics

Representation Theory

16 pages, 3 figures

Scientific paper

10.1088/1751-8113/41/19/194011

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.

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