Itzykson-Zuber correlators from character expansion

Abstract

We demonstrate the consistency of character expansion for the Itzykson-Zuber (IZ) model in terms of Schur polynomials with the old formulas for pair correlators with the IZ measure. An essential new feature of the correlators is that they are not symmetric in eigenvalues - and thus can not be expressed through Schur polynomials only. Instead, we demonstrate that an expression is possible in terms of Schur derivatives. This opens a new way to study arbitrary IZ correlators of any order in character expansion.