  We analyze quantum correlation properties of a spinor-1 (f=1) Bose Einstein
condensate using the Gell-Mann realization of SU(3) symmetry. We show that
previously discussed phenomena of condensate fragmentation and spin-mixing can
be explained in terms of the hypercharge symmetry. The ground state of a
spinor-1 condensate is found to be fragmented for ferromagnetic interactions.
The notion of two bosonic mode squeezing is generalized to the two spin (U-V)
squeezing within the SU(3) formalism. Spin squeezing in the isospin subspace
(T) is found and numerically investigated. We also provide new results for the
stationary states of spinor-1 condensates.
