Abstract
The projection operators for the groupsSUn are used for constructing the noncanonical basis vectors of irreducible representations of these groups as linear combinations of the Gel'fand-Tseitlin canonical basis vectors. The structure of the basis vectors of the irreducible representation of the groupsSU4,SU3,SU6 in the case of the reductionSU4 ⊃SU2×SU2,SU3⊃R3 andSU6 ⊃SU3, respectively, is discussed. A number of formulae have been obtained for the fractional parentage coefficients for the (1d-2s)-shell nuclei.
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