Geodesic
Recursive construction of irreducible tensor spaces of unitary groups and fractional parentage expansion of single-configuration wave function
Teoretičeskaâ i matematičeskaâ fizika, Tome 13 (1972) no. 1, pp. 102-107 
V. V. Vanagas; R. K. Kalinauskas. Recursive construction of irreducible tensor spaces of unitary groups and fractional parentage expansion of single-configuration wave function. Teoretičeskaâ i matematičeskaâ fizika, Tome 13 (1972) no. 1, pp. 102-107. http://geodesic.mathdoc.fr/item/TMF_1972_13_1_a7/
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It is shown that irreducible tensor spaces of the unitary group $U_r$ with special bases fixed by a definite choice of the embedded chain of unitary subgroups $U_{r_1}+\dots+U_{r_k}$ $(r_1+\dots+r_k=r)$, each of which, in its turn, is reduced on an arbitrary group $G$, can be constructed recursively by means of the Clebsch–Gordan coefficients of the group $U_r$. These coefficients are factorized and the relationship between the recursive construction of the irreducible tensor spaces and the fractional parentage decomposition of a single-configuration wave function is established.

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