GROUP REPRESENTATION VERSUS QUANTUM REPRESENTATION AND A NEW APPROACH TO GROUP REPRESENTATION CALCULATIONS

We developed a group representation theory and calculation method based on quantum representation theory. All the calculations, such as Character, Irreducible bases and Matrices, Projection operators, Clebsch-Gordan series and coefficients are reduced to solve a set of eigen-equations of a complete set of commuting operators consisting of the class operators of the group. This approach had been successfully applied to all of the finite groups and compact Lie groups and various useful coefficients for physical application of group representation theory had been calculated and tabulated.