Many eigenvalue matrix models possess a peculiar basis of observables that have explicitly calculable averages. This explicit calculability is a stronger feature than ordinary integrability, just like the cases of quadratic and Coulomb potentials are distinguished among other central potentials, and we call it superintegrability. As a peculiarity of matrix models, the relevant basis is formed by the Schur polynomials (characters) and their generalizations, and superintegrability looks like a property \(\langle character\rangle \,\sim character\). This is already known to happen in the most important cases of Hermitian, unitary, and complex matrix models. Here we add two more examples of principal importance, where the model depends on external fields: a special version of complex model and the cubic Kontsevich model. In the former case, straightforward is a generalization to the complex tensor model. In the latter case, the relevant characters are the celebrated Q Schur functions appearing in the description of spin Hurwitz numbers and other related contexts.

许多特征值矩阵模型具有可观察到的，具有明确可计算平均值的特殊基础。这种显式的可计算性是比普通可积性更强大的功能，就像在其他中心电势中区分二次势和库仑势的情况一样，我们称之为超可积性。作为矩阵模型的一种特殊性，相关的基础由Schur多项式（字符）及其一般化形成，并且超可积性看起来像一个属性\（\ langle character \ rangle \，\ sim character \）。在Hermitian，unit和复数矩阵模型的最重要情况下，这种情况已经众所周知。在这里，我们再添加两个主要重要性示例，其中模型取决于外部字段：复杂模型和三次Kontsevich模型的特殊版本。在前一种情况下，简单是对复数张量模型的概括。在后一种情况下，相关字符是出现在自旋Hurwitz数和其他相关上下文的描述中的著名的Q Schur函数。