Rinat Kedem 2008 J. Phys. A: Math. Theor. 41 194011 doi:10.1088/1751-8113/41/19/194011
Q-systems as cluster algebras
Rinat Kedem
Show affiliationsQ-systems first appeared in the analysis of the Bethe equations for the XXX model and generalized Heisenberg spin chains (Kirillov and Reshetikhin 1987 Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst. Steklov. 160 211–21, 301). 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 
in the language of cluster algebras (Fomin and Zelevinsky 2002 J. Am. Math. Soc. 15 497–529), 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 (Fomin and Zelevinsky 2002 Adv. Appl. Math. 28 119–44).
- PACS
- MSC
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17B67 Kac-Moody (super)algebras (structure and representation theory)
- Subjects
- Dates
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Issue 19 (16 May 2008)
Received 6 December 2007, in final form 6 February 2008
Published 29 April 2008
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Q-systems as cluster algebras
Rinat Kedem 2008 J. Phys. A: Math. Theor. 41 194011
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