Abstract
A method for finding algebraic expressions of the Clebsch-Gordan (CG) coefficients of point groups is proposed and applied to the tetrahedral group. It is shown that in constructing the CG coefficients the irreducible symmetry operator (ISO) of a double group G† can be replaced by an effective ISO which is much simpler than the usual ISO. The effective ISO for the group chain T†⊃C3† is Pμ,μ̄(λ)=δμμ̄+3dμμ̄(λ)(C2z)*C2z, where d(λ)(C2z) is the matrix of C2z in the irrep λ of T†. With this effective ISO and the algebraic expression of d(λ)(C2z), the algebraic expressions are derived for the real CG coefficients of T† in the group chain T†⊃C3†. The algebraic expressions for the complex (real) CG coefficients of the group chain T†⊃D2†⊃C2† (T†⊃C2†) have also been obtained.
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