Periodicities of T and Y-systems, dilogarithm identities, and cluster algebras II: Types C_r, F_4, and G_2

Abstract

We prove the periodicities of the restricted T and Y-systems associated with the quantum affine algebra of type C_r, F_4, and G_2 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 categorification of the cluster algebra associated with any skew-symmetric matrix by Plamondon.

36 pages; minor changes, references updated

References in corpus (2)

• Cluster algebras via cluster categories with infinite-dimensional morphism spaces
• Periodicities of T and Y-systems, dilogarithm identities, and cluster algebras I: Type B_r

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