Reduced projection operators and algebraic expressions for the symmetry-adapted functions of the icosahedral group

The algebraic expressions for the reduced projection operators rho((lambda){\bar µ})(µ) = summation operator(i=1)(4) u(i) \hat{beta(i)} for the irreducible representation (irrep) lambda of the icosahedral group I are found by using the double-induced technique and eigenfunction method, where \hat{beta(i)} are the double-coset generators of I with respect to the cyclic subgroup C(5). Simple algebraic expressions are derived for the symmetry-adapted functions (SAF's) by applying the reduced projection operators rho((lambda){\bar µ})(µ) to Y(l {\bar m}). The SAF's are functions of the angular momentum l, the quantum numbers lambda, µ of the group chain I superset C(5) and the multiplicity label \bar m. In this way, the SAF problem of the group I is solved once for all instead of for one angular momentum l each time.