Total orbital momentum and total spin are good quantum numbers for a complete basis which we construct as explicit linear combinations of orthonormal vectors (m1m2m3), where integersverbar;thinsp;mithinsp;verbar;thinsp; le; 4. Matrix elements of generators of the orbital momentum group are found explicitly in the basis (m1m2m3) and a onehyphen;tohyphen;one correspondence between (m1m2m3) and Gel'fandmdash;Tseitlin patterns ofSU(9) is shown. The multiplicity problem is solved systematically by simplicity conventions similar to those introduced by Racah for the cases where his classification scheme for higherfnconfigurations failed. Every angular momentum multiplet we construct belongs to one irreducible representation ofO(9) only.
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