In this paper, we will construct the connection between the quantum Gaudin model and the universal character hierarchy by a newly defined coupled master T-operator. The coupled master T-operator of the quantum Gaudin model satisfies the bilinear identity of the universal character hierarchy, which is an extension of the Kadomtsev–Petviashvili hierarchy. In addition, for the generalized quantum integrable spin chains with rational GL(N)-invariant R-matrices, we construct its coupled master T-operator, which represents a generating function for two-folds commuting quantum transfer matrices. The functional relations for the transfer matrices are equivalent to an infinite set of Hirota bilinear equations of the modified universal character hierarchy.

中文翻译：

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Quantum Gaudin 模型、自旋链和通用字符

在本文中，我们将通过新定义的耦合主 T 算子构建量子 Gaudin 模型和通用字符层次结构之间的连接。量子 Gaudin 模型的耦合主 T 算子满足通用字符层次结构的双线性恒等式，它是 Kadomtsev-Petviashvili 层次结构的扩展。此外，对于具有有理 GL(N) 不变 R 矩阵的广义量子可积自旋链，我们构造了其耦合主 T 算子，它表示二重交换量子转移矩阵的生成函数。传递矩阵的函数关系等效于修改后的通用字符层次结构的 Hirota 双线性方程的无限集。