PHYSICAL METHODS OF GROUP REPRESENTATION THEORY (Ⅰ)——A NEW APPROACH TO THE THEORY OF FINITE GROUP REPRESENTATIONS

Abstract

This paper advocates a new approach to the theory of finite group representa-tions by applying exclusively the method of commuting operators in quantum me-chanics. The basic problems of group representation theory such as the labeling of irreducible representations, the finding of characters, irreducible bases and matrix ele-ments and the CG coefficients et al are all simplified to the solving of the eigenfunc-tions of a certain complete set of commuting operators. This method has the advan-tage of being concise in theory and easily manageable in practice.