Translation-invariant shell model

The classification of states in Kretschmar's translatton-invariant shell model [1] is augmoated by the tntroduction of a quantum number characterizing the irreducible representation of the orthogonal group $\mathfrak D_{A-1}$. This reduces the multiplicity wfih which irreducible representation of the group of permutations $\mathfrak S_A$ occurs on the redaction of the unitary group $\mathfrak U_{A-1}$. Some relations are also obtained which are useful for improving the model.