On boson representation of angular momentum. II

The states of a system of $N$ harmonic oscillators with fixed total number of quanta are decomposed with respect to bases of irreducible representations of $SU(2)$. The previously introduced basis [1] is a basis with the highest dimensionality in this decomposition. For the case of three harmonic oscillators, the operators and a discrete basis of a representation of the noncompact group $SU(1,1)$ are constructed. Bargmann's representation is considered for these states.