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Totally symmetric irreducible representations of the group SO(6) in the principal SO(3) subgroup basis On the relations between irreducible representations of the hyperoctahedral group and O(4) and SO (4) An explicit basis is constructed for the symmetric irreducible representation (irrep) of SU(9) ~ SO(9) ~ SO(5) X SU 1(2) X SU 2 (2). It is also indicated how good angular momentum states can be constructed. The techniques used are based on the well-known tensor algebra for the infinitesimal generators of simple Lie groups.

The mathematical group chain of an n g-boson system is SU(9) ::)SO(9) ::)SO(5) XSU 1 (2) XSU 2 (2) U SUa (2) XSU b (2).In this paper, the mathematical basis of this group chain is obtained by using the briefer method and then constructing the states of n g-bosons with good angular momentum.