  We introduce a simple representation for irreducible spherical tensor
operators of the rotation group of arbitrary integer or half integer rank and
use these tensor operators to construct matrix product states corresponding to
all the variety of valence-bond states proposed in the
Affleck-Kennedy-Lieb-Tasaki (AKLT) construction. These include the fully
dimerized states of arbitrary spins, with uniform or alternating patterns of
spins, which are ground states of Hamiltonians with nearest and next-nearest
neighbor interactions, and the partially dimerized or AKLT/VBS (Valence Bond
Solid) states, which are constructed from them by projection. The latter states
are translation-invariant ground states of Hamiltonians with nearest-neighbor
interactions.
