Periodicities of T-systems and Y-systems, Dilogarithm Identities, and Cluster Algebras II : Types ${C}_r$, ${F}_4$, and ${G}_2$
Periodicities of T-systems and Y-systems, Dilogarithm Identities, and Cluster Algebras II : Types ${C}_r$, ${F}_4$, and ${G}_2$
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DOI：
10.4171/prims/96
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发表时间：
2010-01
影响因子：
1.2
通讯作者：
Rei Inoue;O. Iyama;B. Keller;A. Kuniba;T. Nakanishi
中科院分区：
文献类型：
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作者：
Rei Inoue;O. Iyama;B. Keller;A. Kuniba;T. Nakanishi
我们证明了与任何级别的 Cr、F4 和 G2 型量子仿射代数相关的受限 T 和 Y 系统的周期性。我们还证明了这些 Y 系统在任何级别上的双对数恒等式。我们的证明基于热带 Y 系统以及 Plamondon 与任何斜对称矩阵相关的簇代数的分类。
We prove the periodicities of the restricted T and Y-systems as- sociated with the quantum affine algebra of typeCr, 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 categorification of the cluster algebra associated with any skew-symmetric matrix by Plamondon.