Highest weight state description of the isotropic spin-1 chain

We introduce an overcomplete highest weight state basis as a calculational tool for the description of the isotropic spin-1 chain with bilinear exchange coupling J(1) and biquadratic coupling J(2). The ground state can be expressed exactly at the three special points in the phase diagram where the Hamiltonian corresponds to a sum of nearest neighbor total spin projection operators (J(1)=0>J(2), J(1)=-J(2)< 0, and J(1)=-J(2)/3>0). In particular, at the phase transition point J(1)=-J(2)< 0, it is possible to exactly compute the ground states, excited states, expectation values, and correlation functions by using the new total spin basis.