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

Atsuo Kuniba; Bernhard Keller; Osamu Iyama; Rei Inoue; Tomoki Nakanishi

arxiv: 1001.1881 · v4 · pith:FHJ2DEXAnew · submitted 2010-01-12 · 🧮 math.QA · math.RT

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

Rei Inoue , Osamu Iyama , Bernhard Keller , Atsuo Kuniba , Tomoki Nakanishi This is my paper

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keywords y-systemsalgebraassociatedclusterdilogarithmidentitieslevelperiodicities

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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.

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

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