Quantum Hall states and boson triplet condensate for rotating spin-1 bosons

We propose and analyze two series of clustered quantum Hall states for rotating systems of spin-1 bosons. The first series [labeled SU(4)(k)] includes the exact ground states of a model Hamiltonian at large angular momentum L, and also for N = 3k particles at L = N. The latter is a: spin-singlet boson-triplet condensate. The second series, labeled SO(5)(k), includes exact ground states' at large L for different parameter values.