We characterize Y/T-system-type difference equations arising from cluster algebras by triples of matrices, which we call T-data, that have a certain symplectic property. We show that all mutation loops are essentially obtained from T-data, which generalizes the general solution for period 1 quivers given by Fordy and Marsh. We also show that any T-datum associated with a periodic Y/T-system has the simultaneous positivity. As an application, we propose a version of Nahm’s conjecture from a viewpoint of cluster algebras. We conjecture that given a periodic T/Y-system of a certain type, we have a family of hypergeometric q-series that are also modular functions.

我们用三元组矩阵（称为T数据）来表征由簇代数引起的Y / T系统类型的差分方程，这些矩阵具有一定的辛性质。我们表明，所有突变环基本上都是从T数据获得的，该数据概括了由Fordy和Marsh给出的1期颤动的一般解。我们还表明，与周期性Y / T系统关联的任何T数据都具有同时正性。作为应用程序，我们从聚类代数的角度提出了Nahm猜想的一种形式。我们推测，给定某种类型的周期性T / Y系统，我们有一系列超几何q系列，它们也是模块化函数。