The Representations of U(4)⊃U(2)⊗U(2)

The state vectors associated with an irreducible representation of U(4) restricted to the subgroup $\text{U(2)⊗U(2)}$ are explicitly constructed for the general 4‐rowed Young diagram, employing Littlewood's rules and a theorem of Cartan. Expressions are given for the degeneracy of a $\text{U(2)⊗U(2)}$ state in U(4), and the set of $\text{U(2)⊗U(2)}$ states obtained are shown to be independent and complete. Operators which break this degeneracy are constructed, and the behavior of the state vector under the conjugation operations is also discussed. The results are useful for the nuclear quasispin and Wigner supermultiplet models.