Periodicities of T-systems and Y-systems, dilogarithm identities, and cluster algebras II: Types Cr, F4, and G2

Abstract

We prove the periodicities of the restricted T-systems and Y-systems associated with the quantum affine algebra of type Cr, F4, and G2 at any level. We also prove the dilogarithm identities for these Y-systems at any level. Our proof is based on the tropical Y-systems and the categorication of the cluster algebra associated with any skew-symmetric matrix by Plamondon. © 2013 Research Institute for Mathematical Sciences, Kyoto University. All rights reserved.