PERIODICITIES OF T AND Y-SYSTEMS, DILOGARITHM IDENTITIES, AND CLUSTER ALGEBRAS I: TYPE Br

By Rei Inoue, Osamu Iyama, B. Keller, A. Kuniba, Tomoki Nakanishi. 2010

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

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/60bbbf6ca44b10311bc8021001f73ba6836867fc