Weight Lowering Operators and the Multiplicity-Free Isoscalar Factors for the Group R5

Expressions for the matrix elements of powers of infinitesimal operators of R₅ are obtained in a basis reduced according to $R_5{\mathrm{\supset (SU}}_2{\mathrm{\times SU}}_2)$ . Operators producing the basis functions of any weight from those of highest weight are considered. The coupling and recoupling procedures for the semistretched and the other multiplicity‐free cases are considered. By use of projection operators the expressions for the isoscalar factors of both kinds of semistretched Clebsch‐Gordan coefficients of R₅, as well as a new formula for the 9j‐coefficient of SU₂ involving only three summation parameters, are obtained. Methods of obtaining the normalized isoscalar factor coupling the basis functions of two symmetrized representations of R₅ are discussed.