论文标题
Kontsevich Matrix模型的整合性
Superintegrability of Kontsevich matrix model
论文作者
论文摘要
许多特征值矩阵模型都具有明确可计算的平均值的可观察到的特殊基础。这种显式的可计算性比普通的集成性更强，就像二次和库仑电位的情况一样，在其他中心电位中也有区别，我们称其为共同性。矩阵模型的特殊性，相关基础是由schur多项式（字符）及其概括形成的，并且可稳定性看起来像属性$ <trace> \，\ sim targe $。众所周知，这已经发生在遗传学，统一和复杂矩阵模型的最重要情况下。在这里，我们添加了两个主要重要性的示例，其中模型取决于外部字段：复杂模型和Cubic Kontsevich模型的特殊版本。在前一种情况下，直接是对复杂张量模型的概括。在后一种情况下，相关角色是著名的$ q $ schur函数，在旋转Hurwitz数字和其他相关上下文的描述中出现。
Many eigenvalue matrix models possess a peculiar basis of observables which 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. Aa a peculiarity of matrix models, the relevant basis is formed by the Schur polynomials (characters) and their generalizations, and superintegrability looks like a property $<character>\,\sim character$. 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 the 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.
