  We study spin correlations in Bose-Einstein condensates of spin 1 bosons with
scatterings dominated by a total spin equal 2 channel. We show the low energy
spin dynamics in the system can be mapped into an $o(n)$ nonlinear sigma
model(NL$\sigma$M). $n=3$ at the zero magnetic field limit and $n=2$ in the
presence of weak magnetic fields. In an ordered phase, the ground state has a
hidden $Z_2$ symmetry and is degenerate under the group $[U(1)\times
S^{n-1}]/Z_2$. We explore consequences of the hidden symmetry and propose some
measurements to probe it.
