论文标题
双线性角色相关因子在可巩固理论中
Bilinear character correlators in superintegrable theory
论文作者
论文摘要
我们继续研究矩阵模型的可整合性属性，即矩阵模型平均分解。本文重点介绍了高斯的遗产示例，其中人物的角色是由Schur功能扮演的。我们发现了一个新的有趣的糖化性推论：Schur函数中双线性的无限相关因子的分解。更确切地说，这些是Schur函数和多项式$K_δ$的产品的相关因子，它们在不变矩阵多项式的空间中构成了完整的基础。这些相关器用这些$k_δ$的一小部分将这些相关器分解得出，从以下事实中，Schur函数是广义切割的运算符的本征函数，但是全套$k_Δ$是由另一组无限的交换运算符产生的，我们表明了这一点。
We continue investigating the superintegrability property of matrix models, i.e. factorization of the matrix model averages of characters. This paper focuses on the Gaussian Hermitian example, where the role of characters is played by the Schur functions. We find a new intriguing corollary of superintegrability: factorization of an infinite set of correlators bilinear in the Schur functions. More exactly, these are correlators of products of the Schur functions and polynomials $K_Δ$ that form a complete basis in the space of invariant matrix polynomials. Factorization of these correlators with a small subset of these $K_Δ$ follow from the fact that the Schur functions are eigenfunctions of the generalized cut-an-join operators, but the full set of $K_Δ$ is generated by another infinite commutative set of operators, which we manifestly describe.
