Irreducible representations of the ‘unitary symmetry’ group

Abstract A systematic study is made of the irreducible representations of the unitary unimodular group in three dimensions, an algebraic technique being used that is based on the well-known theory of the rotation group in three dimensions. Explicit representation matrices are found. The representations are characterized by the ranges of the ‘hypercharge’ and ‘isobaric spin’ that occur in them. The dimension formula is derived and the invariants are determined. Two identities are found relating the generators of the group.