Weight Lowering Operators and the Multiplicity-Free Isoscalar Factors for the Group R5
Sigitas Ališauskas, Adolfas Pranaitis Jucys · Journal of Mathematical Physics · 1971
Expressions for the matrix elements of powers of infinitesimal operators of R5 are obtained in a basis reduced according to R5⊃(SU2×SU2). 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.