  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.
