  We introduce a class of exactly solvable SO(n) symmetric Hamiltonians with
matrix product ground states. For an odd $n\geq 3$ case, the ground state is a
translational invariant Haldane gap spin liquid state; while for an even $n\geq
4$ case, the ground state is a spontaneously dimerized state with twofold
degeneracy. In the matrix product ground states for both cases, we identify a
hidden antiferromagnetic order, which is characterized by nonlocal string order
parameters. The ground-state phase diagram of a generalized SO(n) symmetric
bilinear-biquadratic model is discussed.
