Lowest-energy states in parity-transformation eigenspaces of SO(N) spin   chain
  We expand the symmetry of the open finite-size SO(N) symmetric spin chain to O(N). We partition its space of states into the eigenspaces of the parity transformations in the flavor space, generating the subgroup $Z_2^{\times(N-1)}$. It is proven that the lowest-energy states in these eigenspaces are nondegenerate and assemble in antisymmetric tensors or pseudotensors. At the valence-bond solid point, they constitute the $2^{N-1}$-fold degenerate ground state with fully broken parity-transformation symmetry. 
Tigran Hakobyan
cond-mat.str-el math-ph math.MP