T系统和Y系统的周期性
Periodicities of T-systems and Y-systems
摘要：
无限制T-系是杨代数或量子仿射代数的有限维模范畴的Grothendieck环中的一族关系，它与复单李代数相关联。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，在类型A和C下，用行列式方法，在类型A，D和B（第二层）下，用直接法。
英文摘要：
The unrestricted T-system is a family of relations in the Grothendieck ring of the category of the finite-dimensional modules of the Yangian or the 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).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
