Virasoro Versus Superintegrability. Gaussian Hermitian Model

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