Consider the Hubbard model on a square lattice H=tijCiCj+Uinini. Here ij stands of the nearest neighbors and the ni=CiCi. a) Show that C.N. Yang's -operator =i(1)iCiCi Hint: use the equations of motion method. b) Show that the charge operator (relative to half-filling) Q=21i(ni21) and the -operators (that is, and ) can be combined to form the pseudospin SU(2) algrebra [J,J]=iJ. This algebra can be combined with the spin SU(2) to give the SO(4) symmetry of the Hubbard model at half-filling (C.N. Yang and S.C. Zhang, 1990)