Bilinear character correlators in superintegrable theory

Abstract

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