Bilinear character correlators in superintegrable theory

We continue investigating the superintegrability property of matrix models, i.e. factorization model averages characters. This paper focuses on Gaussian Hermitian example, where role characters is played by Schur functions. find a new intriguing corollary superintegrability: an infinite set correlators bilinear in More exactly, these are products functions and polynomials $K_\Delta$ that form complete basis space invariant polynomials. Factorization with small subset follow from fact eigenfunctions generalized cut-an-join operators, but full generated another commutative which we manifestly describe.