W-representation is a miraculous possibility to define a non-perturbative (exact) partition function as an exponential action of somehow integrated Ward identities on unity. It is well known for numerous eigenvalue matrix models, when the relevant operators are of a kind of W-operators: for the Hermitian matrix model with the Virasoro constraints, it is a $W_3$-like operator, and so on. We extend this statement to the monomial generalized Kontsevich models (GKM), where the new feature is appearance of an ordered P-exponential for the set of non-commuting operators of different gradings.

中文翻译：

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GKM 的非阿贝尔 W 表示

W表示是一种奇迹般的可能性，可以将非微扰（精确）分区函数定义为以某种方式集成的 Ward 恒等式对统一性的指数作用。众所周知，有许多特征值矩阵模型，当相关算子是一种W算子时：对于具有 Virasoro 约束的 Hermitian 矩阵模型，它是一个${宽}_3$-like 运算符等。我们将此陈述扩展到单项式广义 Kontsevich 模型（GKM），其中新特征是出现不同等级的非交换算子集合的有序 P 指数。