Periodicities of T-systems and Y-systems, Dilogarithm Identities, and Cluster Algebras II: Types $C_r$, $F_4$, and $G_2$
Publications of the Research Institute for Mathematical Sciences2013Vol. 49(1), pp. 43–85
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Abstract
We prove the periodicities of the restricted T-systems 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.
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