Abstract The structure of the irreducible collective spaces of the group&#xD;$Sp(12,R)$, which many-particle nuclear states are classified&#xD;according to the chain $Sp(12,R) \supset U(6) \supset SO(6) \supset&#xD;SU_{pn}(3) \otimes SO(2) \supset SO(3)$ of the proton-neutron&#xD;symplectic model (PNSM), is considered in detail. This chain of the&#xD;PNSM was recently shown to correspond to a microscopic shell-model version of&#xD;the Bohr-Mottelson collective model. The construction of the&#xD;relevant shell-model representations of the $Sp(12,R)$ group along&#xD;this chain is considered for three nuclei with varying collective&#xD;properties and from different mass regions. It is shown that the&#xD;$SU_{pn}(3)$ basis states of the $Sp(12,R)$ representations&#xD;belonging to $SO(6)$ irreps with seniority&#xD;$\upsilon \geq \upsilon_{0}$, with $v_{0}$ denoting the maximal&#xD;seniority $SO(6)$ irrep contained in the $Sp(12,R)$ bandhead, are&#xD;always Pauli allowed, but organized in a different way into&#xD;different $SO(6)$ shells. This is in contrast to the case of filling&#xD;the levels of the standard three-dimensional harmonic oscillator and&#xD;using the plethysm operation. Although the $SU_{pn}(3)$ multiplets&#xD;with $\upsilon < \upsilon_{0}$ are not all Pauli forbidden, it is&#xD;safe to discard them. The results obtained in the present work are&#xD;important for the practical application of the microscopic version&#xD;of the Bohr-Mottelson collective model.