Periodicities of T-systems and Y-systems
Periodicities of T-systems and Y-systems
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DOI：
10.1215/00277630-2009-003
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发表时间：
2008-12
影响因子：
0.8
通讯作者：
Rei Inoue;O. Iyama;A. Kuniba;T. Nakanishi;J. Suzuki
中科院分区：
文献类型：
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作者：
Rei Inoue;O. Iyama;A. Kuniba;T. Nakanishi;J. Suzuki
无限制T-系是与复单李代数相关联的Yangian或量子仿射代数的有限维模范畴的Grothendieck环中的一族关系。非限制T-系统允许一个约化，称为限制T-系统。本文给出了限制T-系统的周期性猜想，它是已知的限制Y-系统的周期性猜想的对应，并得到了部分证明。然后，我们用不同的方法部分地证明了这个猜想：在简单的情况下，用簇代数和簇范畴方法，在A和C型情况下，用行列式方法，在A、D和B型情况下，用直接方法（第二层）。
The unrestricted T-system is a family of relations in the Grothendieck ring of the category of the finite-dimensional modules of Yangian or quantum affine algebra associated with a complex simple Lie algebra. The unrestricted T-system admits a reduction called the restricted T-system. In this paper we formulate the periodicity conjecture for the restricted T-systems, which is the counterpart of the known and partially proved periodicity conjecture for the restricted Y-systems. Then, we partially prove the conjecture by various methods: the cluster algebra and cluster category method for the simply laced case, the determinant method for types A and C, and the direct method for types A, D, and B (level 2).