Finite-dimensional irreducible representations of the SU(3/1) superalgebra

The SU(3/1) superalgebra is constructed using Schwinger’s harmonic oscillator technique. Finite-dimensional irreducible representations of the superalgebra are obtained choosing a suitable weight Ψm, which will be called the maximal weight, using the commutation relations of the superalgebra only and without any knowledge of the matrix elements of the generators of the superalgebra. Atypical representations of the superalgebra are obtained and a comparison of these representations is made with finite-dimensional irreducible representations of SU(4).