Conformal transformation method and symmetry aspects of the group C4v in a model of high-T c superconductors with anisotropic gap

The application of a method of conformal transformation of the momentum space is presented and discussed with regard to two-dimensional anisotropic high-T c superconductors. A new function, the kernel of the density of states is introduced. Properties of the group C4v are studied and specific sets of basis functions of C4v irreducible representations are given. The attractive interaction is expressed by means of Fourier harmonics chosen as basis functions. Particular coefficients of the expansion in the Fourier series are considered, the order parameter is classified with respect to the Fourier harmonics, and plausible pairing states are given