  We present an exact analytical solution of the fundamental system of
quasi-one-dimensional spin-1 bosons with infinite delta-repulsion. The
eigenfunctions are constructed from the wave functions of non-interacting
spinless fermions, based on Girardeau's Fermi-Bose mapping, and from the wave
functions of distinguishable spins. We show that the spinor bosons behave like
a compound of non-interacting spinless fermions and non-interacting
distinguishable spins. This duality is especially reflected in the spin
densities and the energy spectrum. We find that the momentum distribution of
the eigenstates depends on the symmetry of the spin function. Furthermore, we
discuss the splitting of the ground state multiplet in the regime of large but
finite repulsion.
