As was demonstrated in our previous papers [1-6] devoted to the theory of strongly correlated electron systems the new elements of such theory are the irreducible Green’s functions or Kubo cumulants. These functions contain all spin, charge and pairing quantum fluctuations. The quadruple integrals, which contained in ( 1,2,3) n Kn  are calculated and frequency Fourier representation of irreducible Green’s function established.  The two particles irreducible Green’s function is the simplest irreducible Green’s function which permit to close the system of equations for Green’s functions and to use them for discussing the physical properties of the system.