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arXiv · 0712.2695

Q-systems as cluster algebras

Rinat Kedem
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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 $Q$-system in the initial variables, which follows from the representation-theoretical interpretation, to the Laurent phenomenon in cluster algebras.

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BibTeXRIS

Rinat Kedem. 2008-03-02. Q-systems as cluster algebras. https://doi.org/10.1088/1751-8113/41/19/194011

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