Correlation functions in the Itzykson-Zuber model

Then-point function for the integral over unitary matrices with Itzykson-Zuber measure is reduced to the integral over the Gelfand-Tzetlin table; the integrand (for genericn) is given by linear exponential times the rational function. Forn=2 and in some cases forn>2 later in fast is the polynomial and this allows to give an explicit and simple expression for all 2-point and a set ofn-point functions. For the most generaln-point function a simple linear differential equation is constructed.