Mass spectra of [Formula Presented] supersymmetric [Formula Presented] Chern-Simons-Higgs theories

An algebraic method is used to work out the mass spectra and symmetry breaking patterns of general vacuum states in (Formula presented) supersymmetric (Formula presented) Chern-Simons-Higgs systems with the matter fields being in the adjoint representation. The approach provides us with a natural basis for fields, which will be useful for further studies in the self-dual solutions and quantum corrections. As the vacuum states satisfy the (Formula presented) algebra, it is not surprising to find that their spectra are closely related to that of an angular momentum addition in quantum mechanics. The analysis can be easily generalized to other classical Lie groups.