Periodicities of T and Y-systems, dilogarithm identities, and cluster algebras I: Type B_r

Details Periodicities of T and Y-systems, dilogarithm identities, and cluster algebras I: Type B_r Periodicities of T and Y-systems, dilogarithm identities, and cluster algebras I: Type B_r

2010-01-12

arxiv.org/abs/1001.1880v4

Mathematics

Quantum Algebra

35 pages; minor changes, references updated

Scientific paper

We prove the periodicities of the restricted T and Y-systems associated with the quantum affine algebra of type B_r at any level. We also prove the dilogarithm identities for the Y-systems of type B_r at any level. Our proof is based on the tropical Y-systems and the categorification of the cluster algebra associated with any skew-symmetric matrix by Plamondon. Using this new method, we also give an alternative and simplified proof of the periodicities of the T and Y-systems associated with pairs of simply laced Dynkin diagrams.

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