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

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

2010-01-12

arxiv.org/abs/1001.1881v4

Mathematics

Quantum Algebra

36 pages; minor changes, references updated

Scientific paper

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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