The integral over a group of the Harish-Chandra measure has been known for a long time. On the other side, the moments of this measure (or correlation functions) are not known in general and a general formalism to compute them is lacking. I will present a formalism that allows us to compute correlation functions of the Harish-Chandra measure for any of the classical simple groups in terms of integrals over nihilpotent algebras (triangular matrices). This formulas are, in a sense, a generalization of the Duistermaat-Heckman theorem, in other words, a localization formula.