  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.
