Relation between the Virasoro constraints and KP integrability (determinant formulas) for matrix models is a lasting mystery. We elaborate on the claim that the situation is improved when integrability is enhanced to super-integrability, i.e. to explicit formulas for Gaussian averages of characters. In this case, the Virasoro constraints are equivalent to simple recursive formulas, which have appropriate combinations of characters as their solutions. Moreover, one can easily separate dependence on the size of matrix, and deduce superintegrability from the Virasoro constraints. We describe one of the ways to do so for the Gaussian Hermitian matrix model. The result is a spectacularly elegant reformulation of Virasoro constraints as identities for the Schur functions evaluated at appropriate loci in the space of time-variables.

矩阵模型的Virasoro约束与KP可积性（行列式）之间的关系是一个持久的谜。我们详细阐述了以下主张：将可积性增强为超可积性，即使用高斯平均字符的显式公式时，情况会得到改善。在这种情况下，Virasoro约束等效于简单的递归公式，这些公式具有适当的字符组合作为其解决方案。而且，可以很容易地将对矩阵大小的依赖性分开，并从Virasoro约束中推断出超可积性。我们描述了针对高斯Hermitian矩阵模型的一种方法。结果是，在时间变量的空间中，在适当的位点对Schur函数的恒等式进行了评估，对Virasoro约束进行了极好的优雅的重新形式。