SU(3) and SU(4) singlet quantum Hall states at $\nu=2/3$*

We report on an exact diagonalization study of fractional quantum Hall states at a filling factor $\nu=2/3$ in a system with a four-fold degenerate $n$=0 Landau level and SU(4) symmetric Coulomb interactions. Our investigation reveals previously unidentified SU(3) and SU(4) singlet ground states which appear at flux quantum shift 2 when a spherical geometry is employed, and lie outside the established composite-fermion or multicomponent Halperin state patterns. We will present the pair correlation functions of these states, and describe similar singlets at another filling factor 2/5. Strategies to construct trial wave functions will be discussed.